An Experiment and Estimation of Market-Incentive Effects on Altruism

Changing Preferences: An Experiment and Estimation of Market-Incentive E¤ects on Altruism Abstract This paper studies how altruistic preferences are changed by markets and incentives. We conduct a laboratory experiment in a within-subject design. Subjects are asked to choose health care qualities for hypothetical patients in monopoly, duopoly, and quadropoly. Prices, costs, and patient bene…ts are experimental incentive parameters. In monopoly, subjects choose quality to tradeo¤ between pro…ts and altruistic patient bene…ts. In duopoly and quadropoly, we model subjects playing a simultaneous-move game. Each subject is uncertain about an opponent’s altruism, and competes for patients by choosing qualities. BayesNash equilibria describe subjects’quality decisions as functions of altruism. Using a nonparametric method, we estimate the population altruism distributions from Bayes-Nash equilibrium qualities in di¤erent markets and incentive con…gurations. Markets tend to reduce altruism, although duopoly and quadropoly equilibrium qualities are much higher than those in monopoly. Although markets crowd out altruism, the disciplinary powers of market competition are stronger. Counterfactuals con rm markets change preferences. 1 Introduction Recent economic research has questioned the monolithic power of incentives and markets. Economists now legitimately question if more competition or high-powered incentives must result in more outputs or worker e¤orts. A multifaceted approach has been advanced. Economic agents’preferences may include more than utility from …nancial reward and disutility from cost or e¤ort. In fact, economic agents may be fair minded, altruistic, and socially responsible, but may also be spiteful. Clearly, social and individual preferences determine behaviors and market outcomes. The usual research methodology says that given multi-dimensional preferences, economists can write analytical and empirical models to study incentives and markets. A deeper question, of course, is what determines social preferences. There, economists often concede that anthropologists, sociologists, psychologists, and neuroscientists may have identi…ed plausible factors such as climate, cultural-historical events, physiology, and genetics to explain preferences. But when these factors remain exogenous, the usual methodology remains valid. In this paper, we assess whether social preferences can be changed by markets and incentives, the key social institutions that economists study. Our focus is on altruism, market competition, and incentives. This paper presents experimental evidences that altruistic preferences can be diminished by competition and altered by incentives. In other words, economic models that analyze market-incentive e¤ects on altruism must confront the possibility that markets and incentives themselves may change altruism. Our research proceeds in three steps. First, we use a structural model to decompose behavioral changes into preference e¤ects and market-incentive e¤ects. This is the key conceptual step. Behavioral outcomes are interactions between preferences and market-incentive institutions.1 Must altruistic preferences remain immutable when markets and incentives change? Our structural model allows altruistic preferences to be in‡uenced by markets and incentives. Behavioral changes are then results of markets and incentives changing preferences as well as equilibria. 1 A few recent papers have made claims that markets do erode morality or social responsibility, but our view is simply that the decomposition is the key. The recent papers fall short of this; more details are in the literature review subsection. 1 Second, we use a laboratory experiment in which incentives and market competition are exogenously varied for subjects. Identifying preference and market-incentive e¤ects by real data is too daunting a task. A controlled environment o¤ers a better chance. Our experimental framing is health care provision, and subjects are primed to be altruistic. They choose health care qualities which a¤ect their own payo¤s and which bene…t hypothetical patients. We also have taken care to isolate subjects, so such confounding factors as fairness, collusion, and spitefulness could be minimized. Each subject experiences di¤erent markets and incentive con…gurations. Our within-subject design is appropriate because we claim that preferences change, not just that preferences are heterogenous (which could be identi…ed by a between-subject design). Third, we adapt the nonparametric econometric method by Guerre, Perrigne and Vuong (2000) to estimate preference distributions. We estimate subjects’altruism distributions separately as subjects experience di¤erent markets and di¤erent incentive con…gurations. This is a straightforward way to see if altruism distributions are di¤erent. The nonparametric method does not restrict us to any prespeci…ed distribution classes. We show that subjects become less altruistic when they have to compete against others in a duopoly or in a quadropoly, compared to when they are monopolists. The ‡ip side is that when subjects become monopolists, they become more altruistic. Our contribution can be likened to the classic Lucas critique in policy evaluations. Given preferences, equilibrium outcomes result from market-incentive institutions. This common view is inadequate: preferences are not given. The structure of an economic model consists of equilibrium decisions based on economic agents’preferences. When preferences vary systematically with changes in the market-incentive environment, rather than remaining exogenous, a change in the marketincentive environment will systematically alter the structure of the economic model. For the theoretical model, we specify that a subject’s preferences are given by a weighted average of patients’ bene…ts from health care quality, and pro…ts. By choosing a higher quality, the subject reduces pro…t, but raises patient bene…ts. A more altruistic subject puts a higher weight on patients’bene…ts. The tradeo¤ between bene…ts and pro…ts depend on three experimental parameters: a subject’s price (revenue) per patient, quality cost, and patient bene…t. 2 A subject makes decisions in three markets: monopoly, duopoly, and quadropoly. Under monopoly a subject chooses the quality for the entire patient population. Under duopoly and quadropoly, subjects move simultaneously and each subject’s market share depends on the entire pro…le of subjects’ quality choices, according to a logistic demand function. A total of 361 subjects participated in experimental sessions in October 2017 and April 2018 at the University of Cologne. Within each of the three markets, we systematically vary the incentives using a 2 2 2 factorial design. Price, cost, and patient bene…t assume binary values for a total of eight incentive con…gurations. In total, each subject played 24 games. Each basic game is one of incomplete information: a player’s altruism is his own private information, but each is uncertain about another player’s altruism. We assume that the uncertainty on altruism is described by a distribution. It is this distribution that we would estimate, for each market and for each incentive con…guration. The estimation is by means of symmetric Bayes-Nash equilibria. Nonparametric estimation yield very di¤erent altruism distributions for the 24 games. The striking pattern is that for each incentive con…guration, estimated altruism distributions exhibit lower means in duopoly relative to monopoly, and yet even lower means in quadropoly. Subjects have become less altruistic and value pro…ts more when the market becomes more competitive. What is more striking, however, is that the observed equilibrium qualities are much higher in duopoly and quadropoly than monopoly. Although subjects have become less altruistic, the competition disciplinary force is stronger. These results o¤er a deeper interpretation from the usual, reduced-form approach. If only behavioral results are considered, then markets and incentives are shown to raise qualities, so one would conclude that there is no crowding out. We reject the simplistic conclusion. In fact, quality changes result from two e¤ects: preference changes, and market-incentive changes. The e¤ects go in opposite directions. Markets reduce altruism, but markets also discipline subjects. In our experiment, the market-incentive e¤ect is stronger than preference-change e¤ect. Together they produce the observed behavioral results. Our structural approach permits counter factual calculations. It also allows straightforward robustness checks. It has not escaped our notice that the ultimate questions are: why competition, according to our evidence, has diminished altruism, and why somehow the competitive disciplinary e¤ect turns out to be stronger? 3 These questions, perhaps, strike a counterpoint to the usual exogenous assumptions for analysis of economic models. Recent advances in neuroscience have adopted a reductionist principle that all behaviors can be traced to electrochemical activities in the brain. We are neither in any position to render an opinion nor did we manage to use brain scans to assess if competition triggered speci…c neural activities. However, we can speculate. When subjects play monopoly, they only have to consider a tradeo¤ between pro…ts and patient bene…ts. When subjects play duopoly, they are presented with an additional concern: the competitor’s quality choice. The tradeo¤ between pro…ts and patient bene…ts now depends on what the rival subject would choose. Complexity has increased, and perhaps the higher cognitive demand has diluted the concern for patient bene…ts. The plan of the paper is as follows. The next subsection is a literature review. The model is set up in Section 2. The experimental design and sessions are described in Section 3. In Section 4, we present quality choice descriptive statistics, the nonparametric estimator, and then estimation results on altruism. We end the section with some counterfactual quality estimations. Section 5 presents the reduced-form analysis. The last section draws some conclusion. Appendix A contains experiment materials. Appendix B contains robustness checks. We consider an alternate utility function, and a between-subject subsample. 1.1 Literature review Our paper is related to three strands in the literature. First, we relate to the growing body of work on the impact of markets on moral and prosocial behaviors. Evidence from laboratory experiments in such framing and contexts as altruistic motives, free-riding, and social responsibility indicates that competition reduces moral behavior. Falk and Szech (2013) show that repeated interactions in bilateral and multilateral free-o¤er markets reduce morals compared to individual decisions. Subjects are more willing to accept a negative externality imposed on a third-party (a mouse getting killed) in markets. Using a consumer and …rms in a laboratory experiment, Bartling, Weber, and Yao (2014) analyze socially responsible behavior in posted-price markets. They …nd evidence for socially responsible behaviors in market, but such behaviors are stronger in nonmarket contexts. (In a follow-up study, Bartling, Valero, and Weber (2017) report similar patterns for 4 di¤erent externalities.) Kirchler et al. (2015) analyze how trading anonymity, involvement with the traded good, and punishment in‡uence moral behavior in a double auction with negative externalities imposed on third parties (voiding measles vaccine donations). Building on Kirchler et al. (2015), Sutter et al. (2016) report that moral behaviors are consistent with lower trading volume in markets with negative externalities, but externalities do not a¤ect market prices. The above studies di¤er from ours in several ways. First, and most important, they study behavioral changes in individual and market settings. Besides behavioral changes, we investigate preference changes. Second, we use a structural model to identify changes in preferences and changes in behaviors; by contract earlier studies have used reduced-form models. Bartling, Weber, and Yao (2014) go beyond a reduced form, and model consumers’preferences by a linear utility model. Whereas they show that the average buyer cares for a third-party’s earnings, preferences are assumed to remain unchanged in di¤erent treatments. The above studies use a between-subject design. Instead, we use a within-subject design to identify preferences change. Also, we examine a (regulated) market in which economic agents on the supply-side compete for market share by bene…ting third parties. We do not let subjects do harm to third parties.2 Neither do we let subjects receive feedbacks about their decisions, so learning, reputation, and social norms are well controlled; for further discussion, see Bartling, Weber and Yao (2014) and Breyer and Weimann (2015). Furthermore, we change competition and incentives one at a time, so the confounding e¤ects of multiple changes between manipulations can be avoided. Our study relates to the literature on prosocial behavior, incentives, and crowding-out. Ultimatumdictator game experiments on public good, trust, and gift-exchange analyze behavioral changes due to incentives; see Bowles and Polania-Reyes (2012) for a summary. Economic incentives are often found to reduce pro-social behaviors. Experimental evidence tends to con…rm crowding out; see, for example, Falk and Kosfeld (2006), Gneezy and Rustichini (2000a, b), and Mellström and Johannesson (2008). Our paper points to the inadequacy of identifying only crowding out in terms of outcomes. Incentive schemes are disciplinary, 2 A prominent example in which social preferences are an important concern for supply side’s behavior is markets for public services (e.g., Besley and Ghatak, 2005) and credence goods (e.g., Dulleck and Kerschbamer, 2006; Dulleck, Kerschbamer, and Sutter, 2011), and health care (e.g., Arrow, 1963). 5 even when they may erode social motives. The missing link is that market-incentive mechanisms and social motives pull in di¤erent directions, and it is an empirical matter which is stronger. Finally, our nonparametric estimation relates to the literature on structurally estimating preferences. This literature has been on measuring inequity aversion and reciprocity (e.g., Charness and Rabin, 2002; Bellemare, Kröger, and van Soest, 2008), and altruism (e.g., Andreoni, 1989; Andreoni and Miller, 2002; Fisman, Kariv, and Markovits, 2007); see DellaVigna (2018) for a summary. Using data from …eld experiments, a few papers structurally infer social preferences to identify di¤erences between charitable giving and worker e¤ort; see DellaVigna, List, and Malmendier (2012) and DellaVigna et al. (2016). We, however, use a nonparametric estimator developed by Guerre, Perrigne and Vuong (2000) that has originated from estimating Bayes-Nash equilibria in …rst-price auctions. We have used the monotonicity of qualities in altruism for identi…cation; this is similar to identi…cation by the monotonicity of auction bids in valuations in Guerre, Perrigne and Vuong (2000). 2 A model of altruism and competition The experiment frames subjects to provide medical services at some quality to a set of patients. We study three market games: monopoly, duopoly, and quadropoly. The monopoly game is a single-person decision problem, and the simultaneous-move duopoly and quadropoly games are strategic problems. 2.1 Demand In each market, there are 100 …ctitious patients. Under monopoly, each subject simply makes the quality decision, q between 0 and 10, for all the 100 patients. In duopoly and quadropoly, subjects choose qualities simultaneously. Then the subjects’ quality pro…le determines each subject’s market share according to a logistic demand system. For duopoly, let q1 and q2 be qualities chosen by subject 1 and subject 2. The numbers of patients for subjects 1 and 2 are, respectively, 100 exp(bq1 ) exp(bq1 ) + exp(bq2 ) and 6 100 exp(bq2 ) , exp(bq1 ) + exp(bq2 ) (1) where b > 0 is a patient-bene…t parameter. For quadropoly, let q1 , q2 , q3 , and q4 denote the four subjects’ quality choices. Subject i who chooses quality qi will have 100 exp(bqi ) exp(bq1 ) + exp(bq2 ) + exp(bq3 ) + exp(bq4 ) (2) patients. The logistic demand guarantees that each subject gets some patients under any quality pro…le, and is commonly used for discrete-choice situations when consumers’utilities may be subject to Type I Extreme Value disturbances. 2.2 Quality choices and preferences A subject receives a …xed payment p > 0 for each patient that he treats. For the theoretical model, a subject’s quality choice is a continuous variable between 0 and 10 (although in the experiment we set the possible qualities to be integers between 0 and 10, a total of 11 choices). The subject bears the per-patient quality cost at cq 2 when he provides medical service at quality q, where c > 0 is a cost parameter. Medical service at quality q gives a bene…t bq to a patient. We call the environment de…ned by the three parameters, payment p, cost c, and patient bene…t b, an incentive con…guration. Our health care framing primes an experiment subject for an altruistic motive when qualities are chosen. We assume that a subject’s preferences are represented by bq + U (p cq 2 ), for some parameter and an increasing and concave function U , so preferences are linear combinations of the patient bene…t bq, and the utility of his own pro…t U (p cq 2 ). We maintain the assumption that a subject earns altruistic utility from his own patients. (We will discuss global altruism, in which a subject values all patient bene…ts, in the next Subsection.) Framing and priming a¤ect subjects di¤erently, so we assume that the preference weight on patient bene…t, , is a random variable on an interval [ ; ] 2.3 R with some distribution. Monopoly, duopoly and quadropoly In monopoly, each subject simply chooses a quality for his 100 patients. If a subject’s altruism parameter is and he chooses quality q, the subject’s per-patient payo¤ is bq + U (p (whose cq 2 ). A pro…t-maximizing subject is set at 0) chooses q = 0, whereas a subject who only cares about patient bene…t chooses the maximum quality, which is 10. Otherwise, a subject’s “interior” optimal quality is given by the …rst-order 7 condition: U 0 (p b cq 2 ) 2cq = 0: (3) In monopoly, altruism is the only reason behind a subject choosing a strictly positive quality. In fact, the …rst-order condition (3) de…nes a monotone relationship between = 2cq 0 U (p b and the optimal quality: cq 2 ): (4) A more altruistic subject is willing to forgo more pro…t for a higher quality for patients. Given a utility function U , equation (4) allows us to infer the value of from subjects’quality choices. The experiment subjects also play the duopoly and quadropoly games. We will lay out all the details in duopoly, but will be rather succinct in quadropoly. In duopoly, two subjects are randomly paired. They simultaneously choose qualities, say q1 and q2 , which result in market shares in (1). The subjects’payo¤s are [ where 1 bq1 1 + U (p and 2 cq12 )] 100 exp(bq1 ) exp(bq1 ) + exp(bq2 ) and [ 2 bq2 + U (p cq22 )] 100 exp(bq2 ) ; exp(bq1 ) + exp(bq2 ) are the subjects’altruism parameters. We model duopoly as a Bayesian game. We assume that each subject’altruism parameter, , is drawn independently from a random variable with distribution F and density f on support [ ; ]. Each subject observes his own altruism parameter, but not an opponent’s altruism parameter. The uncertainty on the altruism parameter is the basis for the Bayesian perspective, and stems from framing having di¤erent e¤ects on di¤erent subjects. A subject’s strategy in the duopoly game is a function that maps the altruism parameter say, q : [ ; ] ! [0; 10]. If subject 1 has altruism parameter 1 to a quality, and chooses q1 when the rival subject 2 follows a strategy q 0 : [ ; ] ! [0; 10], subject 1’s expected utility is EU(q1 ; q 0 ) = Z = [ [ 1 bq1 1 bq1 + U (p + U (p cq12 )] Z cq12 )] 100 exp(bq1 ) exp(bq1 ) + exp(bq 0 (x)) dF (x) 100 exp(bq1 ) dF (x): exp(bq1 ) + exp(bq 0 (x)) (5) We assume that a subject does not earn any utility from patient bene…ts provided by a rival subject. The expression in (5) only concerns those patients the subject serves. An alternate form of “global” altruism, 8 which includes patient bene…ts the rival subject provides is outside our current consideration. A …rst reason is tractability; Bayes-Nash equilibria will be more complicated, and the estimation of the equilibria would become di¢ cult. Second, global altruism will inevitably involve some concern about free riding, and some notion about social norm of quality provision, which we have chosen to suppress. The suppression of concern other than private altruism will be discussed in the experiment design. The market share is de…ned by S(q1 ; q 0 ) exp(bq1 ) ; exp(bq1 ) + exp(bq 0 ) so we can rewrite the expected utility in (5) as EU(q1 ; q 0 ) = [ 1 bq1 + U (p cq12 )] Z 100S(q1 ; q 0 (x))dF (x): The market share term is the di¤erence between monopoly and duopoly. A subject choosing a higher quality earns a higher market share: dS(q1 ; q 0 ) = bS(q1 ; q 0 )[1 dq1 S(q1 ; q 0 )] > 0 In duopoly, even a purely pro…t-maximizing subject ( = 0) has an incentive to o¤er quality because a higher quality gains market share which generates pro…ts. For each value of 1 q( 2 [ ; ], we let 0 1 ; q ) = argmax[ Z cq12 )] 1 bq1 + U (p q1 100S(q1 ; q 0 (x))dF (x) (6) be subject 1’s best response against the rival’s strategy q 0 ( ) : [ ; ] ! [0; 10]. A subject’s optimal quality choice is still a tradeo¤ between pro…t and patient bene…t. However, a subject’s payo¤ depends on what he believes about his rival subject’s qualities, which are chosen according to the strategy q 0 . A symmetric Bayes-Nash equilibrium strategy speci…es a subject’s quality choice for each value of the altruism parameter that maximizes the subject’s expected utility, given that the rival subject uses the same strategy. De…nition 1 (Duopoly Bayes-Nash Equilibrium) The strategy q Bayes-Nash equilibrium, if, at each 2 [ ; ], q ( ) = argmax [ bq + U (p 2 cq )] q 9 Z : [ ; ] ! [0; 10] is a symmetric 100S(q; q (x))dF (x): (7) The usual characterization of an equilibrium is by means of the …rst-order condition for the maximization of (5) or the best response in (6). Given a rival’s strategy q 0 , for the maximization of expected utility in (5), we obtain the …rst-order derivative with respect to q1 : @ EU(q1 ; q 0 ) =[ @q1 +[ 2cq1 U 0 (p 1b 1 bq1 + U (p Z cq12 )] Z cq12 )] 100S(q1 ; q 0 (x))dF (x) 100bS(q1 ; q 0 (x))[1 S(q1 ; q 0 (x))]dF (x): (8) We assume that the expected utility in (5) is quasi-concave for the incentive con…gurations under consideration. Hence, by setting the …rst-order derivative to zero, we obtain the implicit function that de…nes the best response at . To characterize the symmetric Bayes-Nash equilibrium q : [ ; ] ! [0; 10], we note that at the equilibrium, each subject has the same …rst-order condition. The equilibrium q therefore is de…ned by setting (5) to 0 at each 2 [ ; ] and setting q 0 to q : [ b 0 2 2cq ( )U (p +[ bq ( ) + U (p cq ( ) )] cq ( )2 )] Z Z 100S(q ( ); q (x))dF (x) 100bS(q ( ); q (x))[1 (9) S(q ( ); q (x))]dF (x) = 0: Being the solution of an integral equation, a symmetric Bayes-Nash equilibrium is di¢ cult to compute, even for simple functional forms of the utility U and distribution F . Fortunately, we do not have to rely on this computation. In fact, what makes our model operational is the following. Lemma 1 Equilibrium strategy q : [ ; ] ! [0; 10] is monotone increasing in . Proof of Lemma 1: Using the …rst-order derivative of EU with respect to q1 in (8), we further di¤erentiate this with respect to @ 2 EU(q1 ; q 0 ) =b @ 1 @q1 Z 1 to obtain 0 100S(q1 ; q (x))dF (x) + bq1 By assumption EU is quasi-concave in q1 , so as 1 Z 100bS(q1 ; q 0 (x))[1 S(q1 ; q 0 (x))]dF (x) > 0: increases, the optimal quality increases. This is true for any given strategy q 0 , so remains valid at the equilibrium q . Because is a random variable, the equilibrium strategy q ( ) is also a random variable. An equilibrium 10 outcome of duopoly is the pair of qualities speci…ed by the equilibrium strategy, (q ( independent realizations of , namely 1 for the …rst subject, and 2 1 ); q ( 2 )), for two for the second subject. Remark 1 (Duopoly Equilibrium Quality Distribution) The Bayes-Nash equilibrium q induces a joint distribution of the two subjects’equilibrium qualities on [0; 10] [0; 10]. By symmetry and independence, the marginal density is the one induced by the equilibrium strategy q . Denoting this marginal distribution by G : [0; 10] ! [0; 1], we conclude that for qe 2 [0; 10], G (e q ) = F (e ), where q (e ) = qe. The actual play of the duopoly are realizations of G . By the monotonicity of the equilibrium q , the distribution F of and the equilibrium quality distribution G are isomorphic. Whereas we have no data on F , we do have data on qualities from equilibrium play. This is the key to the estimation of the altruism distribution F under duopoly, and Subsection 4.2 will present the estimation of G by the empirical quality distribution. Next, we discuss the quadropoly. There are now four subjects, and the demands are in (2). Otherwise, there is not much conceptual di¤erence between duopoly and quadropoly. The de…nition of a symmetric Bayes-Nash equilibrium has exactly the same form. If subject i chooses quality qi , his market share now is exp(bqi ) S(qi ; q i ) = X4 ; exp(bqj ) j=1 where we use q i to denote the quality vector (q1 ; q2 ; q3 ; q4 ) with the ith element omitted. Given strategies qj , j = 1; 2; 3; 4, j 6= i, if subject i chooses quality qi his expected utility is i bqi where the notation q i ( + U (p i) cqi2 ) Z Z Z is a short hand for (qj ( 100S(qi ; q i ( i )) 4 Y dK( j ); j=1; j6=i j ); j = 1; 2; 3; 4; j 6= i), and K is the distribution of in quadropoly. De…nition 2 (Quadropoly Bayes-Nash Equilibrium) The strategy q ( ) is a symmetric Bayes-Nash equilibrium, if for each 2 [ ; ], q ( ) = argmax q bq + U (p 2 cq ) Z Z Z 11 100S(q; q i ( i )) 4 Y j=1; j6=i dK( j ): (10) We can use the …rst-order condition to characterize the equilibrium strategy q . It is straightforward to verify the same monotonicity property. Lemma 2 Equilibrium strategy q : [ ; ] ! [0; 10] is monotone increasing in . Remark 2 (Quadropoly Equilibrium Quality Distribution) The Bayes-Nash equilibrium q induces a joint distribution of the four subjects’equilibrium qualities on [0; 10]4 . By symmetry and independence, the marginal density is the one induced by the equilibrium strategy q . We denote this marginal distribution by L : [0; 10] ! [0; 1]. Notice that we have used the notation F to denote the altruism prior distribution in duopoly, but we have used a di¤erent notation K for that in quadropoly. Although we have the same set of subjects (in our within-subject) design, we do allow altruism distributions to vary according to markets and incentive con…gurations. We now turn to the experiment. 3 The experiment 3.1 Design The experimental design implements the theoretical model just described. Role playing as physicians, subjects decide on the quality of health care for a set of hypothetical patients.3 Each subject chooses a medicalservice quality q from a …nite set f0; 1; 2; : : : ; 10g.4 Three parameters determine payo¤s. These are the capitation payment to the physician p, the quality cost parameter c, and the patient bene…t parameter, b. The subject bears the quality cost, so if he chooses a quality q, his pro…t becomes p cq 2 , whereas the patient bene…t is bq, exactly the same as in the theoretical model. We use a 2 2 2 factorial design to vary each of the p, c, and b parameters systematically. The capitation payment p may be low or high, set at 10 and 15, respectively. The cost parameter c can be either 0:075 3 Hypothetical patient pro…les, characterizing patients through di¤erent bene…ts from medical treatment decisions, have been employed in several behavioral experiments in health with medical and non-medcial students (e.g., HennigSchmidt, Selten, Wiesen, 2011; Kesternich, Schumacher, Winter, 2015; and Brosig-Koch et al., 2017) and practicing physicians (e.g., Brosig-Koch et al., 2016, 2019). 4 This is the only di¤erence from the continuous quality choice assumption in the theoretical model. 12 or 0:1, whereas the bene…t parameter b can be either 0:5 or 1. All monetary amounts were in terms of the experimental currency, Taler, which was later converted to Euro at the rate of 100:1. A full set of parameters can be found in Table 10 in Appendix A. We call a game with a pro…le of price-cost-bene…t parameters an incentive con…guration. The 2 2 2 variations set up a total of 8 incentive con…gurations. There are 3 markets: monopoly, duopoly, and quadropoly. Each subject plays 24 games in the entire experiment: 8 incentive con…gurations by 3 markets. The experiment uses a within-subject design. Subjects experience di¤erent markets and incentive con…gurations, and we aim to investigate how subjects’ quality choices and preferences change according to their experiences. In the actual implementation, subjects played all 8 incentive-con…guration games in one market, and then moved onto the next market. Subjects were not informed of the market up until they were to play the 8 incentive-con…guration games in that market.5 There are 6 di¤erent ways to order the three markets, displayed in Table 1. For example, in “3 (D-Q-M)” a subject plays the duopoly game …rst, followed by quadropoly, and …nally monopoly. We roughly assigned about 1=6 of the subject population to each of the 6 orders. The last column in Table 1 lists the number of subjects who participated in each order. (In experimental conditions 3 (D-Q-M) and 5 (Q-D-M), three subjects needed to be dropped from the sample because they were unable to complete the task in Monopoly due to computer technical problems. We preserved the data of other subjects who played against them in duopoly and quadropoly.) We randomize the order in which the 8 incentive con…gurations are presented to subjects. In each market, each subject plays the 8 games in the following order: 1st, (p = 10, c = 0:1, b = 1); 2nd, (p = 10, c = 0:075, b = 1); 3rd, (p = 15, c = 0:1, b = 0:5); 4th, (p = 15, c = 0:1, b = 1); 5th, (p = 10, c = 0:1, b = 0:5); 6th, (p = 10, c = 0:075, b = 0:5); 7th (p = 15, c = 0:075, b = 1) and 8th, (p = 15, c = 0:075, b = 0:5). A subject never learns others’ decisions for any of the 8 incentive-con…guration games in a market. 5 It was impractical to get subjects to play the 24 games in a random order. Too much back-and-forth between markets and incentive con…gurations could be confusing to subjects. Random rematching for 16 times for each subject also would be too time consuming. 13 Table 1: Market orders in the experiment Number Condition Order of markets of subjects 1 (M-D-Q) Monopoly-Duopoly-Quadropoly 64 2 (M-Q-D) Monopoly-Quadropoly-Duopoly 60 3 (D-Q-M) Duopoly-Quadropoly-Monopoly 63 4 (Q-M-D) Quadropoly-Monopoly-Duopoly 60 5 (Q-D-M) Quadropoly-Duopoly-Monopoly 58 6 (D-M-Q) Duopoly-Monopoly-Quadropoly 56 Total 361 However, at the end of one market session, each subject is given a summary information of actual demands, pro…ts, and patient bene…ts, all aggregated over the 8 games. In duopoly and quadropoly, subjects are randomly paired or grouped. When subjects are done with one market, say duopoly, the match will be dissolved. Then subjects will be randomly matched for the next market, say quadropoly. Subjects do play a normal form game against others randomly drawn from a population. Our design rules out repeated plays, learning, and reputation. We have thought about the design tradeo¤. On the one hand, we would like to keep altruism as the main frame, and would like to avoid issues about norms and collusions. On the other hand, we would have to face the possibility that subjects having to learn to play a Bayes-Nash equilibrium. In the end, we have come down with a design that would rely on subjects playing a Bayes-Nash equilibrium with preferences governed by altruism. This explains our suppressing information of subjects’play and outcomes. Our approach also gives supports about the rejection of global altruism. Subjects do not have information about patient bene…ts other than those patients he has chosen bene…ts for. We have maintained the altruism frame throughout. It is inappropriate to introduce a control that eliminates the patient bene…ts, or to make the bene…ts independent of subjects’quality choices. We do want to …nd out if subjects’preferences change according to markets and incentive con…gurations. Randomly assigning subjects to play di¤erent market and incentive-con…guration games would identify differences, not changes. However, we can use a subsample for a between-subject design. We construct this subsample by taking data from a subject’s experiences in the market he or she …rst participates. Given that we have 361 subjects, a between-subject design would put only about 120 subjects in one market, and each subject would then play only 8 games. The between-subject subsample serves as a comparison with the main 14 within-subject design. The analysis is in Appendix B. Broadly, the results are consistent with the complete sample for the within-subject design. Although there are no real patients, the health bene…ts accrued in the laboratory are converted into monetary transfers to a charity dedicated to providing surgeries for ophthalmic patients. The patient bene…t is thus made salient. A subject’s consideration of patients’ bene…t from costly quality choices have real empirical and health-related consequences. 3.2 Experimental sessions Experimental sessions were carried out in October 2017 and in April 2018, at the Cologne Laboratory for Experimental Research of the University of Cologne. Subjects in the experiment were mostly students from the University of Cologne, Germany. Participants were invited via the ORSEE platform (Greiner, 2015). In total, 361 subjects participated in the experiment.6 Subjects had an average age of about 24 years, and 55% of them were female. Among the subjects who were students, 131 were in law and social sciences, 22 in medicine, 42 in arts and humanities, 49 in mathematics and natural sciences, 35 in theology. There were 21 in other disciplines or non-students; 61 subjects did not provide their faculty information. The experiment was programmed in zTree (Fischbacher, 2007). Upon arrival, subjects were randomly assigned to cubicles. Initial instructions informed subjects that the experiment consisted of three parts. Detailed instructions of each part would only be given at the start of that part. Each part corresponded to one of the three markets (monopoly, duopoly, and quadropoly). Participants had adequate time to read the instructions. The instructions can be found in Appendix A.1. Participants were allowed to ask clarifying questions, which were answered in private. For each market, subjects needed to answer several control questions. Subjects should understand the price, cost, and bene…t parameters, and how quality choices might a¤ect demands. Each subject must answer all control questions correctly to ensure an adequate understanding before the start of each part of the experiment. The control questions can be found in 6 We dropped three subjects who did not complete their last, monopoly sessions due to technical problems (one subject in condition 3 (D-Q-M), and two in condition 5 (Q-D-M)). However, these three subjects did interact with other subjects before they played their last monopoly session. We have kept data of others who played against these three subjects in duopoly and quadropoly. 15 Appendix A.2. When making a decision, each subject was informed of the incentive-con…guration parameters, as well as pro…ts and the patient bene…ts as functions of the quality that can be one in f0; 1; 2:::; 10g. In monopoly, each subject had 100 patients. In duopoly and quadropoly, a subject had a logistic demand which depended on the quality pro…le of matched subjects. The zTree program provided a calculator, which allowed subjects to input hypothetical own and other players’qualities to calculate the resultant demands (number of patients), pro…ts, and patient bene…ts for all players. A screen shot of the calculator is in Appendix A.3. After subjects played the 8 incentive-con…guration games in a market, they were informed of their and their paired subject’s or subjects’total demands (number of patients), and total patient bene…ts in the 8 games. Data about individual games in each incentive con…guration were not given. Our design gets each of 361 subjects to play 24 games. We have taken steps to guard against “experimenter demand e¤ects” (see, for example, Charness, Gneezy and Kuhn, 2012) by not telling subjects all three markets in advance. We used the common “random-choice”payment method to determine pro…ts and patient bene…ts. One of the 8 incentive-con…guration games in each market would be chosen randomly for determining the subject’s pro…t and the patient bene…ts. The random-choice payment method was implemented for each subject independently. The method is intended to rule out potential income e¤ects or “averaging” behaviors. One subject was randomly chosen to be a monitor. After the experiment, the monitor veri…ed that a money order equal to the total patient bene…t was issued by the Finance Department of the University of Cologne. The money order was payable to an organization, Christo¤ el Blindenmission, which supports ophthalmologists performing cataract surgeries in a hospital in Masvingo, Zimbabwe. The money order was sealed in an envelope, and the monitor and an experiment assistant then deposited the envelope in the nearest mailbox. The monitor was paid an additional e5. Subjects were told in advance that the experimental patient bene…ts would be for real patients, but not for those in a developing country. A similar procedure for making patient bene…ts meaningful to subjects has been applied by, for example, Hennig-Schmidt, Selten and Wiesen (2011), Kesternich, Schumacher and Winter (2015) and Brosig-Koch et al. (2017). Sessions lasted, on average, for about 90 minutes, and subjects earned, on average, about e14.20 (e18.20 16 including show-up fee). The average bene…t per patient was about e8.10. In total, e2,923.60 were transferred to the Christo¤el Blindenmission. Average costs for a cataract operation for adults are about e30, so our experiment supported about 100 surgeries.7 4 Estimation of altruism distributions from experimental data We …rst present data of subjects’ quality choices. Then we describe how we estimate structurally the altruism distribution for each market and in each incentive con…guration. 4.1 Descriptive statistics on subjects’quality choices Table 2 presents some summary statistics of the 361 subjects’quality choices in the 8 incentive-con…guration games in the 3 markets. Clearly, subjects chose higher qualities in duopoly and quadropoly than in monopoly, and the standard deviations of subjects’ quality choices were also much smaller. Raising the intensity of competition from duopoly to quadropoly increases qualities only slightly more. Within a market, quality variations between the 8 incentive-con…guration games seem quite modest. Table 2: Means and standard deviations Incentive con…gurations Monopoly mean st. dev. (p = 10, c = 0:075, b = 0:5) 4.17 2.99 (p = 10, c = 0:075, b = 1) 4.15 2.99 (p = 10, c = 0:1, b = 0:5) 3.79 2.79 (p = 10, c = 0:1, b = 1) 3.73 2.80 (p = 15, c = 0:075, b = 0:5) 4.82 3.43 (p = 15, c = 0:075, b = 1) 4.83 3.41 (p = 15, c = 0:1, b = 0:5) 4.51 3.27 (p = 15, c = 0:1, b = 1) 4.44 3.19 Total 4.31 3.14 of subjects’quality choices Duopoly Quadropoly mean st. dev. mean st. dev. 7.75 1.58 8.26 1.40 7.98 1.59 8.31 1.56 6.94 1.35 7.34 1.34 7.09 1.52 7.46 1.34 8.82 1.53 9.09 1.32 8.98 1.60 9.15 1.43 8.19 1.63 8.55 1.47 8.40 1.62 8.65 1.61 8.02 1.70 8.35 1.57 For each of the 24 games, we draw the quality histograms; they are in Figures 1 to 3, and the actual frequency of each quality between 0 and 10 is written at the top of each vertical bar. These frequencies will be used for estimating subjects’altruism parameter. 7 For more on activities of the Christo¤el Blindenmission related to www.cbm.de/spendenCBM_Spenden_Sie_fuer_Operationen_am_Grauen_Star-494570.html. 17 cataract, see Figure 1: Quality histograms in monopoly 18 Figure 2: Quality histograms in duopoly 19 Figure 3: Quality histograms in quadropoly 20 Clearly, the 24 histograms show higher qualities in duopoly and quadropoly than monopoly. Nevertheless, the di¤erence between duopoly and quadropoly does not appear to be very signi…cant. Quality frequencies are needed for the estimation of altruism parameters, to which we now turn. 4.2 Nonparametric estimation of altruism distribution by Bayes-Nash equilibria We adapt a nonparametric estimation method developed by Guerre, Perrigne and Vuong (2000) (abbreviated to GPV) for …rst-price auctions. We use duopoly to illustrate the adaptation. First, from the equilibrium strategy q in (9), we invert and obtain and incentive parameters: 8 > > > < = > > > : in terms of the equilibrium quality q ( ), the utility function U , Z cq ( ) ) 0 2cq ( )U (p Z cq ( )2 ) U (p 8 > > > < b Z > > > +bq ( ) : 2 9 > > > = S(q ( ); q (x))dF (x) > > S(q ( ); q (x))]dF (x) > ; 9 : > > > S(q ( ); q (x))dF (x) = bS(q ( ); q (x))[1 Z bS(q ( ); q (x))[1 (11) > > S(q ( ); q (x))]dF (x) > ; Given an equilibrium q , the uncertainty concerning a rival subject’s altruism is equivalent to the uncertainty of the rival’s quality choices. From Remark 1, we can replace the altruism distribution F by the equilibrium quality distribution G . Then, using q to denote the equilibrium quality chosen by the subject with altruism parameter , we rewrite (11) as 0 2cqU (p = Z 10 Z 10 2 S(q; x)dG (x) U (p cq ) bS(q; x)[1 S(q; x)]dG (x) cq ) 0 0 : Z 10 Z 10 b S(q; x)dG (x) + bq bS(q; x)[1 S(q; x)]dG (x) 2 0 (12) 0 This says that given an equilibrium q , we can use the equilibrium quality distribution G to express a subject’s altruism parameter in terms of his quality choice q. We estimate the their values from subjects’quality choices. The estimated distribution by recovering can be thought of a nonlinear map of the chosen quality q, and the equilibrium quality distribution G , given the game’s parameters. The argument suggests that we adapt the GPV two-step method as follows. In Step 1, the densities of equilibrium quality distribution G are estimated by the empirical quality densities in each market-incentivecon…guration constellation. Let gb(x) denote the empirical quality densities; it is the fraction of subjects (out 21 of the total of 361) who have chosen quality x = 0; 1; :::; 10. We use gb(x) to estimate the G ’densities. The empirical densities of the 24 games are those in Figures 1 to 3. The term Z 10 S(q; x)dG (x) in (12) is now estimated by 0 10 X S(q; x)b g (x); similarly, the term 10 X bS(q; x)[1 10 bS(q; x)[1 0 x=0 S(q; x)]dG (x) in (12) is estimated by Z S(q; x)]b g (x). For each subject i = 1; :::; 361, we use x=0 (12) to calculate: 2cqi U 0 (p cqi2 ) 10 P S(qi ; x)b g (x) U (p b 10 P S(qi ; x)b g (x) + bqi x=0 which is an estimate of subject i’s bS(qi ; x)[1 S(qi ; x)]b g (x) x=0 x=0 ^i = 10 P cqi2 ) 10 P bS(qi ; x)[1 ; (13) S(qi ; x)]b g (x) x=0 . In Step 2, we use the sample of estimated ’s to estimate nonpara- metrically the altruism distribution: 361 1 X If ^i Fb(a) = 361 i=1 ag: (14) where I is the indicator function that takes the value 1 when the condition inside the curly brackets is satis…ed, and 0 otherwise. The estimation procedures are similar for monopoly and quadropoly. In monopoly, we use the …rstorder condition (4) to recover a subject’s value from his quality choice in any given incentive-market con…guration. In other words, in the …rst step, for each i = 1; :::; 361, we compute ^i = 2cqi U 0 (p b cqi2 ) : Then these estimated ’s are used to estimate the distribution of altruism in the second step. For quadropoly, in the …rst step, we compute the following 2cqi U 0 (p cqi2 ) 10 P x;y;z=0 ^i = b 10 P x;y;z=0 S(qi ; x; y; z)b l(x)b l(y)b l(z) S(qi ; x; y; z)b l(x)b l(y)b l(z) + bqi U (p cqi2 ) 10 P bS(qi ; x; y; z)[1 x;y;z=0 10 P bS(qi ; x; y; z)[1 x;y;z=0 S(qi ; x; y; z)]b l(x)b l(y)b l(z) S(qi ; x; y; z)]b l(x)b l(y)b l(z) where b l(x); x = 0; 1; :::; 10 is the empirical density function of quality in quadropoly. In the second step, these estimated ’s are used to estimate the altruism distribution K. Ours is a Bayesian game with independent values. Given preferences and the uniqueness of the symmetric equilibrium, our model is identi…ed by the equilibrium quality being monotone in altruism. The basic games 22 ; and identi…cation are the same as in GPV, whose two-step estimator for bidders’valuation distribution in …rst-price auctions is consistent and asymptotically e¢ cient. These results depend on the assumption that the unknown valuation distribution is smooth. However, subjects in our game choose from only 11 possible qualities. We therefore can only estimate the unknown altruism distribution by histograms with 11 possible values. Even with more subjects, we would be unable to approximate a smooth distribution with histograms with a limited number of values. 4.3 Estimates of altruism distributions We assume that the utility function U is linear: U (x) = x. In this case, between patient bene…t bq and pro…t p is the marginal rate of substitution cq 2 . Our main results will be based on this structural assumption. When U is linear, for monopoly we have = 2cq ; b (15) for duopoly, we have 2cq = Z Z 10 S(q; x)dG(x) (p cq 2 ) bS(q; x)[1 S(q; x)]dG(x) 0 0 : Z 10 Z 10 b S(q; x)dG(x) + bq bS(q; x)[1 S(q; x)]dG(x) 10 0 (16) 0 For brevity, we do not write down the corresponding expression for under quadropoly. We have also used the alternate assumption of the utility function exhibiting a constant coe¢ cient of absolute risk aversion.8 The estimation results for U (x) 1 exp( rx) are in Appendix B. There we set the coe¢ cient of absolute risk aversion r at 0:10. (We have also obtained results for r set at 0:05 and 0:15. Results turn out to be similar and are available from the authors.) The drawback is that the marginal rate of substitution between patient bene…t and pro…t varies with the quality level, so the estimated value of is not so easy to interpret. We …rst present summary statistics of the estimated altruism distributions. Table 3 lists the means of the estimated distributions in monopoly. We use these estimated monopoly means as normalization. In 8 CARA is a common functional form for risk preferences in the literature. See, for example, Barseghyan et al., 2018. It has been used for estimating risk preferences from individual-level data in contexts such as property insurance (Cohen and Einav, 2007; Barseghyan et al., 2016), game shows (Beetsma and Schotman, 2001; Andersen et al., 2008), and health insurance (Einav et al., 2013; Handel and Kolstad, 2015). In experiments, the CARA speci…cation also has been used for estimating risk preferences (Harrison and Rutström, 2008). 23 Table 3: Estimated means of in monopoly Incentive con…gurations mean (p = 10, c = 0:075, b = 0:5) 1.252 (p = 10, c = 0:075, b = 1) 0.622 (p = 10, c = 0:1, b = 0:5) 1.515 (p = 10, c = 0:1, b = 1) 0.746 (p = 15, c = 0:075, b = 0:5) 1.446 (p = 15, c = 0:075, b = 1) 0.725 (p = 15, c = 0:1, b = 0:5) 1.805 (p = 15, c = 0:1, b = 1) 0.889 duopoly and quadropoly, for each incentive con…guration, we subtract the estimated monopoly mean from each estimated . This normalization uses the estimated monopoly mean as the origin. In Table 4, we present the normalized means and standard deviations of the 24 altruism distributions. Due to the normalization, each reported monopoly the magnitude distribution in Table 4 has a zero mean. Across a row in Table 4, for example, 1:335 for the duopoly mean in incentive con…guration (p = 10, c = 0:075, b = 0:5) says that when the market changes from monopoly to duopoly, the average altruism parameter has decreased by 1:335. Table 4: Normalized means and standard Incentive con…gurations Monopoly mean st. dev. (p = 10, c = 0:075, b = 0:5) 0 0.898 (p = 10, c = 0:075, b = 1) 0 0.448 (p = 10, c = 0:1, b = 0:5) 0 1.117 (p = 10, c = 0:1, b = 1) 0 0.559 (p = 15, c = 0:075, b = 0:5) 0 1.028 (p = 15, c = 0:075, b = 1) 0 0.512 (p = 15, c = 0:1, b = 0:5) 0 1.308 (p = 15, c = 0:1, b = 1) 0 0.638 deviations of distributions Duopoly Quadropoly mean st. dev. mean st. dev. -1.335 0.939 -1.579 0.766 -0.812 0.612 -0.985 0.657 -1.378 0.903 -2.233 1.710 -0.882 0.725 -1.069 0.822 -1.980 0.928 -2.382 0.980 -1.244 0.767 -1.471 1.138 -2.001 1.327 -2.428 1.147 -1.207 0.827 -1.485 1.016 The striking observation is that across each row, the average altruism has decreased from monopoly to duopoly, and then decreased further more from duopoly to quadropoly! This is clear evidence that competition reduces altruism on average. Standard deviations also tend to be di¤erent, but the pattern is not so homogenous. We now present the estimated ’s and their frequencies. Each of the estimate is a nonlinear transfor- mation of the chosen quality and the empirical quality distribution, and market and incentive-con…guration parameters. The frequency for each estimate is the same as the quality frequency, which are in Figures 1 to 24 3, so we do not write the frequencies again. We maintain the normalization by measuring estimates from the means, which are in Table 3. In Table 5, we list the normalized estimated normalized ’s corresponding to each quality between 0 and 10. Table 5: Estimated monopoly values, normalized at mean q=0 q=1 q=2 q=3 q=4 q=5 q=6 q=7 q=8 q=9 (p = 10, c = 0:075, b = 0:5) -1.252 -0.952 -0.652 -0.352 -0.052 0.248 0.548 0.848 1.148 1.448 q = 10 1.748 (p = 10, c = 0:075, b = 1) -0.622 -0.472 -0.322 -0.172 -0.022 0.128 0.278 0.428 0.578 0.728 0.878 (p = 10, c = 0:1, b = 0:5) -1.515 -1.115 -0.715 -0.315 0.085 0.485 0.885 1.285 1.685 2.085 2.485 (p = 10, c = 0:1, b = 1) -0.746 -0.546 -0.346 -0.146 0.054 0.254 0.454 0.654 0.854 1.054 1.254 (p = 15, c = 0:075, b = 0:5) -1.446 -1.146 -0.846 -0.546 -0.246 0.054 0.354 0.654 0.954 1.254 1.554 (p = 15, c = 0:075, b = 1) -0.725 -0.575 -0.425 -0.275 -0.125 0.025 0.175 0.325 0.475 0.625 0.775 (p = 15, c = 0:1, b = 0:5) -1.805 -1.405 -1.005 -0.605 -0.205 0.195 0.595 0.995 1.395 1.795 2.195 (p = 15, c = 0:1, b = 1) -0.889 -0.689 -0.489 -0.089 0.111 0.311 0.511 0.711 0.911 1.111 -0.289 The frequencies of these normalized estimated ’s are in the following histograms in Figure 4. In these histograms, and later ones to be presented, we do not use identical scales on the horizontal axis. The eight histograms exhibit various properties. Due to the nonlinear transformation from the observed qualities to the estimated , the actual values di¤er considerably across di¤erent incentive con…gurations. However, these histograms show that altruism distributions are diverse. 25 Figure 4: Histograms of estimated in each incentive con…guration in monopoly 26 Next, we turn to estimated duopoly Table 6; we do not report those (again normalized by the corresponding monopoly mean) in when the corresponding quality was chosen by none of the subjects. The corresponding histograms are in Figure 5. The frequency for each estimate is the same as the corresponding quality frequency, which is in Figure 2. Table 6: Estimated duopoly values, normalized at monopoly mean q=0 q=1 q=2 q=3 q=4 q=5 q=6 q=7 q=8 q=9 (p = 10, c = 0:075, b = 0:5) -10.486 -5.422 -4.272 -3.430 -2.758 -2.186 -1.668 -1.177 -0.689 q = 10 -0.187 (p = 10, c = 0:075, b = 1) -8.148 -3.359 -2.603 -2.079 -1.682 -1.359 -1.071 -0.792 -0.506 -0.187 (p = 10, c = 0:1, b = 0:5) -7.4 - -4.289 -3.364 -2.608 -1.942 -1.321 -0.710 -0.088 0.559 (p = 10, c = 0:1, b = 1) -8.824 -4.912 - -2.613 -2.038 -1.607 -1.244 -0.900 -0.542 -0.141 0.332 (p = 15, c = 0:075, b = 0:5) -6.430 -5.252 -4.349 -3.613 -2.979 -2.403 -1.851 -1.296 (p = 15, c = 0:075, b = 1) -11.376 -6.272 -4.496 -3.569 -2.923 -2.443 -2.079 -1.772 -1.489 -1.213 -0.900 (p = 15, c = 0:1, b = 0:5) -15.714 - -6.486 -5.255 -4.284 -3.468 -2.744 -2.071 -1.412 -0.741 (p = 15, c = 0:1, b = 1) -11.589 - -3.956 -3.156 -2.551 -2.082 -1.688 -1.326 -0.967 -0.568 27 Figure 5: Histograms of estimated in each incentive con…guration in duopoly 28 The estimated values of are very di¤erent from those in monopoly. The range has become much wider. From the histograms, we see that the higher values of estimated ’s have higher densities, but all of these higher values are below the corresponding monopoly mean. Subjects have become much less altruistic. Besides the stronger concentration, the Table 7 presents the (normalized) frequency for each distributions appear to be strongly left-skewed in duopoly. estimates for quadropoly, and Figure 6 presents the histogram. The estimate is the same as the corresponding quality frequency, which is in Figure 3. Similar to duopoly, The quadropoly distributions show a stronger concentration below the normalized monopoly mean and are left-skewed, as in duopoly. Table 7: Estimated quadropoly q=0 q=1 q=2 q=3 q=4 (p = 10, c = 0:075, b = 0:5) -11.194 -3.733 values, normalized at monopoly mean q=5 q=6 q=7 q=8 q=9 q = 10 -3.079 -2.540 -2.073 -1.648 -1.245 -0.845 (p = 10, c = 0:075, b = 1) -10.619 -3.753 -2.838 -2.258 -1.843 -1.521 -1.253 -1.015 -0.788 -0.550 (p = 10, c = 0:1, b = 0:5) -21.505 -11.209 -7.642 - -4.539 -3.651 -2.941 -2.322 -1.730 -1.095 -0.331 -2.866 -2.258 -1.815 -1.460 -1.154 -0.864 -0.560 -0.197 - -5.598 -4.707 -3.992 -3.390 -2.860 -2.374 -1.908 (p = 15, c = 0:075, b = 1) -15.717 - -4.191 -3.362 -2.783 -2.346 -1.995 -1.698 -1.429 -1.163 (p = 15, c = 0:1, b = 0:5) -16.729 - -6.908 -5.671 -4.721 -3.944 -3.277 -2.678 -2.117 -1.566 (p = 15, c = 0:1, b = 1) -15.883 -8.235 -5.619 -4.259 -3.403 -2.796 -2.329 -1.947 -1.614 -1.305 -0.987 (p = 10, c = 0:1, b = 1) -10.742 (p = 15, c = 0:075, b = 0:5) -16.391 - 29 Figure 6: Histograms of estimated in each incentive con…guration in quadropoly 30 Estimations show that the di¤erences between the monopoly quadropoly distributions and the duopoly and distributions are quite striking. Whereas preferences tend to exhibit diversity in monopoly, they are less diverse in duopoly, and becoming less so in quadropoly. Densities of estimated ’s tend to vary quite a lot in monopoly, but a lot less so in duopoly and quadropoly. Moreover, estimated distributions tend to be left-skewed and being more concentrated at the high end of the distribution. 4.4 Counterfactual monopoly qualities from estimated duopoly and quadropoly altruism Whereas Table 2 and Figures 1 to 3 report the outcomes, our structural estimation of distributions in 4.2 can separately identify the e¤ects (i) due to preferences change and (ii) due to market-incentive changes. However, results in Subsections 4.2 and 4.3 are obtained without explicit derivations of Bayes-Nash equilibria. One could not easily compute duopoly or quadropoly equilibrium quality distributions under the counterfactual that preference distributions remained unchanged at the monopoly con…guration. Instead, we perform counterfactual of the following sort. We use the estimated altruism distributions in an incentive con…guration in duopoly or quadropoly. to calculate the optimal qualities under monopoly. That is, we take values and their frequencies from Tables 6 and 7 and feed them into the monopoly …rst- order condition (4) to calculate optimal qualities. The next two …gures show the counterfactual histograms of monopoly qualities when ’s are those identi…ed in duopoly and quadropoly. In each counterfactual computation, the optimal qualities need not be integers, and we have limited the optimal qualities to be nonnegative. (Those estimated in duopoly and quadropoly that are negative have been replaced by 0 to ensure a nonnegative optimal monopoly quality.) 31 Figure 7: Counterfactual monopoly quality histogram from duopoly altruism 32 Figure 8: Counterfactual monopoly quality histogram from quadropoly altruism 33 Di¤erences between empirical monopoly qualities and counterfactual qualities are striking. Histograms in Figures 7 and 8 have no resemblance to those in the empirical quality distributions in Figure 1. This indeed indicates that markets and incentives do change preferences. 5 Reduced-form analysis of experimental data In the previous section, we have focussed on the altruism distribution estimation. Here, we turn our attention to reduced-form analysis of subjects’ quality choices. Table 2 already describes the 24 quality means and standard deviations for the 3 markets and 8 incentive con…gurations, and Figures 1 to 3 show the quality histograms. Here, we …rst present some aggregated descriptive statistics, and then regression results. A subject makes 8 quality choices in each market. Of these 8, four of them are made with one …xed incentive-con…guration parameter. For example, under monopoly at p = 10, a subject chooses 4 qualities, while cost and patient-bene…t parameters vary between low and high. We record the average of these 4 qualities for each subject, and then we …nd the average of all 361 subjects (the average of a total of 1; 444 quality choices). In Table 8, the …rst entry 3:959 records the population mean of subjects’average quality choices at p = 10, and 2:900 is the corresponding standard deviation. Across that row, when the price is set at 15, the higher level, the mean becomes 4:652, and the standard deviation becomes 3:327. The relative di¤erence, 0:175, equals (4:652 3:959)=3:959. The rest of Table 8 presents the quality-choice averages for each parameter in each market.9 From the …rst three rows with data entries in Table 8, average quality is higher in each market when the price is set at the higher level, but the relative di¤erence declines as the market becomes more competitive. From the second set of data entries, average quality becomes lower when cost is set at the higher level, although the relative di¤erence remains almost the same across markets. For patient bene…ts, quality averages exhibit a di¤erent pattern. For monopoly, a higher patient bene…t results in a slightly lower average quality, whereas for duopoly and quadropoly, a high patient bene…t results in slightly higher quality averages. But in all three markets, the relative di¤erence seems very small. 9 Table 8 aggregates the information in Table 2, which contains quality-choice means and standard deviations in each incentive-con…guration-market constellation. 34 Table 8: Descriptives on the variations in price, Low parameter level (N=1,444, per market) Parameter Mean st. dev. Price (p = 10; p = 15) Monopoly 3.959 2.900 Duopoly 7.442 1.573 Quadropoly 7.841 1.479 costs, and patient bene…t High parameter level (N=1,444, per market) Mean st. dev. Relative di¤erence 4.652 8.595 8.862 3.327 1.625 1.484 0.175 0.155 0.130 Cost (c = 0:075; c = 0:1) Monopoly Duopoly Quadropoly 4.493 8.380 8.704 3.227 1.660 1.489 4.118 7.657 8.000 3.038 1.662 1.564 -0.083 -0.086 -0.081 Patient bene…t (b = 0:5; b = 1) Monopoly Duopoly Quadropoly 4.323 7.925 8.310 3.150 1.668 1.523 4.287 8.112 8.393 3.128 1.726 1.608 -0.008 0.024 0.010 We next use ordinary least square regressions to study the e¤ect of market competition and incentivecon…gurations: qi = + 1D + 2Q + 1 P rice + 2 Cost + 3 Benef it where qi , the dependent variable, is subject i’s quality choice, and + Xi + "i (17) is the intercept. Experimental manip- ulations are de…ned by a set of dummies. Regarding monopoly as the reference market, we use the dummy variables D and Q to represent duopoly and quadropoly, respectively; a dummy is set to 1 when the quality on the left-hand side has been chosen under the corresponding market condition. The P rice, Cost and Benef it variables are also dummies. The variable P rice takes the value of 1 when price p is equal to the high level of 15; it takes the value at 0 otherwise. Similarly, Cost takes the value of 1 when c = 0:1, and Benef it takes the value of 1 when patient bene…t b = 1; otherwise, they are 0. Equation (17) includes a vector of additional control Xi of market orders (see Table 1) and session dummies, and …nally "i is an error term. Model (1) of Table 9 presents the estimation results. In Model (2), we add markets and incentive con…gurations interaction terms. From Table 9, quality is signi…cantly higher in duopoly and quadropoly compared to monopoly, and the 35 magnitudes are similar in both models. Wald tests indicate a highly signi…cant di¤erence between Duopoly and Quadropoly (p < 0:001). For incentive con…gurations with a high price, a low cost, and a high patient bene…ts, qualities are signi…cantly higher; see Model (1). With interaction terms in Model (2), the e¤ects of price and cost remain qualitatively similar but the magnitudes have declined. The average bene…t e¤ect becomes insigni…cant; this suggests that the patient-bene…t e¤ect may be market speci…c. Using Wald tests, we …nd that market e¤ects are signi…cantly larger than market-con…guration e¤ects (at p < 0:001). Model Duopoly (D) Quadropoly (Q) High price (= 1 if p = 15) High cost (= 1 if c = 0:1) High bene…t (= 1 if b = 1) Duopoly High price Quadropoly Duopoly High price High cost High bene…t Quadropoly High bene…t Market order and session dummies Constant (2) 3.545*** (0.157) 3.987*** (0.156) 0.693*** (0.050) -0.375*** (0.046) -0.036 (0.043) 0.461*** (0.066) 0.328*** (0.061) -0.348*** (0.056) -0.328*** (0.055) 0.224*** (0.056) 0.119** (0.055) High cost Quadropoly Duopoly Table 9: Quality regressions (1) 3.713*** (0.158) 4.046*** (0.157) 0.955*** (0.029) -0.601*** (0.024) 0.078*** (0.024) Yes Yes 3.971*** (0.400) 4.047*** (0.399) Observations 8,664 8,664 Subjects 361 361 R2 0.445 0.447 Notes: OLS; robust standard errors clustered for subjects in brackets; *** for p < 0:01; ** for p < 0:05 36 From in Models (1) and (2) results, more intense market competition has implemented higher equilibrium qualities. An interpretation of an unquali…ed success of competition (under regulated prices) on implementing higher qualities, however, is misguided. Bayes-Nash equilibrium qualities depend on preferences, markets, and incentive con…gurations. Our structural estimation supports reduction in altruism, which generally reduces subjects’ qualities in equilibrium. The scenario is more appropriately described as a tug of war— between altruism reduction and competition-incentive disciplinary powers. In our setting, competitionincentive powers have won over altruism reduction. 6 Concluding remarks Using behavioral data from an experiment in a health frame, we show that the altruistic preferences are a¤ected by markets and incentives. We model subjects’preferences through a linear utility function whose marginal rate of substitution is interpreted as the degree of altruism. Subjects play a simultaneous-move incomplete information game when they compete with each other. Using the experimental data, we estimate the altruism distribution in each market-incentive environment. The estimation results show that subjects are less altruistic when they have to compete against each other. Although our conclusion is that altruism has changed, we have maintained certain assumptions, both in the theoretical model and in the experiment. The structural model does require some consistency in preferences between di¤erent markets and incentive con…gurations. So to speak, we can estimate changing preferences only if those changes are not so drastic. We narrow down our study to one altruism parameter. The assumption that individuals are interested only in pro…ts and patient bene…ts is maintained throughout. We would not be a position to test if subjects would become spiteful, winning oriented, or fair-minded when they participate in duopoly or quadropoly. Our design does minimize these contaminations, however. We have only told subjects very sparse outcome information. Subjects never have learned that they have been “disadvantaged” by the rival, that their qualities have been higher or lower than rivals’, or that their choices turn out to be similar or very di¤erent from the population averages. We have limited subjects’ ability to learn about each other by implementing a simultaneous-move game. Interaction between subjects 37 and learning about the population are both impossible in our design. Every attempt has been made to ensure that a subject is playing against another randomly drawn subject, and only once. Our goal simply is to make the point that economic institutions may a¤ect preferences in nontrivial ways. Economic institutions may shape preferences just as climate, cultural-historical events, physiology, and genetics. 38