Game Theory for Managers Commitment

Lecture 5 Game Plan „ Qwest Bond Swap „ Chicken Game „ Sequential move games „ „ „ … escaping from the Annoying Servant … escaping from the Prisoners’ Dilemma More on strategic moves „ Pre-emptive moves, threats, and promises Qwest Bond Swap “If Judge Chin allows the offer to go ahead, institutional investors who own bonds will find themselves in a position with some resemblance to the classic ‘prisoners’ dilemma’... If no one tendered, then Qwest would be in the same position as before the offer, and any bondholder would be no worse off. But if a lot of holders tender, those who refuse will be worse off than they were.” - Norris, Floyd. “A Bond Swap Available Only to Big Players,” The New York Times, 18 December 2002. Figure for Q1,Q2 (and Q3) Figure for Q5 Changing the Game “Always be wary of the superstructure of whatever situation you're in. It may just be that the whole game that you're into is something very bogus and you should get out.” - Scott Miller, Game Theory lead guitarist, in: Woelke, Tina. “Where Have You Gone, James Joyce? A Nation Turns Its Lolita Eyes To You.” Non*Stop Banter, December 1988. Game Theory „ Prominent “power paisley pop” band in 80s „ „ formed in 1981 signed by Rational Records „from „ „ „ first album, “Blaze of Glory”… “All I Want is Everything” “Bad Year at UCLA” “Sleeping Through Heaven” Some Prototypical Games „ „ „ „ „ Prisoner’s Dilemma Loyal Servant Hunter and Hunted Assurance Chicken „ „ „ „ „ price war defensive innovation audits, bluffing driving, cooperation negotiation On-Line Game #6 New Market Game Negotiation Game „ Used car dealer says that the lowest possible price is $20,000 • actual cost is $17,000 „ Buyer says that the highest possible price is $18,000 • actual value is $21,000 „ Each player has two strategies: “Give in” or “Not” Negotiation Game Give in Give in Dealer Don’t (2,2) (1,3) (3,1) (0,0) Buyer Don’t in thousands of dollars „ How would you play this game? Mixed Strategies in the Negotiation Game „ (Give In, Don’t) and (Don’t, Give In) are the two pure strategy equilibria „ There is also a mixed strategy equilibrium: Prob(Give In) = 50% „ „ failure to agree 25% of the time! Are any of these equilibria evolutionarily stable? Chicken Game Column Player Swerve Don’t Swerve (2,2) (1,3) (3,1) (0,0) Row Player Don’t „ Key features: „ „ Each wants the other to choose Swerve Both better off if both choose Swerve rather than Don’t Reaction Curves in Chicken Game 100% Col’s prob. of Swerve 50% 0% 0% 50% 100% Row’s prob. of Swerve Evolution in Chicken Game with One Population Prob. of Swerve in population 0% „ „ 50% 100% If initial condition < 50% Swervers, then non-Swervers are relatively better off. Only the mixed strategy equilibrium is evolutionarily stable with one population Evolution in Chicken Game with Two Populations 100% Now Row is drawn from “reds” and Col from “greens”, where these populations evolve separately Col’s prob. of Swerve 50% 0% 0% 50% 100% Row’s prob. of Swerve „ Only the pure strategy equilibria are evolutionarily stable with two populations Sequential Moves in Chicken Game Swerve 2, 2 Don’t 1, 3 Swerve 3, 1 Don’t 0, 0 Swerve Don’t Sequential Moves in Chicken Game Swerve 2, 2 Don’t 1, 3 Swerve 3, 1 Don’t 0, 0 Swerve Don’t „ „ Each player prefers to be first-mover Being first-mover here allows you to “select your favorite equilibrium” Lazy Husband Game „ Husband and wife both work long hours but can’t afford a housekeeper „ Wife happy to do housework if Husband also does, but not if Husband shirks „ Husband has dominant strategy to shirk „ Both prefer that both do housework than that both shirk Loyal Servant Game Servant Safe Safe Master Dangerous Dangerous Special Case: Annoying Servant Game Servant Safe Safe Master Dangerous Dangerous “Story” behind Annoying Servant Game Safe Servant Dangerous Safe Master Dangerous „ „ „ „ Servant wants to be with Master Servant is annoying Æ Master likes (S,D) most Dangerous route not passable alone Æ Master prefers (S,S) over (D,S) Servant might “accidentally” fall off the cliff Æ Master prefers (D,D) over (S,S) Lazy Husband Game Work Work Wife Shirk (2,2) (-1,1) (3,-1) (0,0) Husband Shirk „ What should Husband do? Lazy Husband Game Work 2, 2 Shirk -1, 1 Work 3, -1 Shirk 0, 0 Work Shirk Not Dominant Anymore … Work 2, 2 Shirk -1, 1 Work 3, -1 Shirk 0, 0 Work Shirk „ Husband commits not to Shirk “What’s For Dinner?” „ Child decides whether to eat veggies „ „ „ wants to not eat veggies wants very much to eat dessert Parent decides if dessert will be served „ „ wants Child to be happy wants very much for Child to eat veggies Payoffs in Dinner Game Parent Dessert Not Veggies Child Not „ In simultaneous move version, both have dominant strategies: No Veggies and Dessert Dinner w/ Sequential Moves Dessert 3, 4 Not 1, 3 =3 Dessert 4, 2 =2 Veggie Not Not „ 2, 1 =4 =1 No Veggies & Dessert is unique subgameperfect equilibrium when Child moves first Strategic Moves at Dinner „ Does moving first help Parent? „ What should Parent do? “You don’t get dessert unless you eat veggies” „ Parent can improve outcome by committing to a response rule „ “Threat” = response rule that punishes others if they do not cooperate with you, in a way that goes against your own incentives „ “Promise” = response rule that rewards others if they do cooperate, in a way that goes against your own incentives “You don’t get dessert unless you eat veggies” „ This is a “threat” in our game „ „ Parent will act against incentive to give Dessert if Child doesn’t eat veggies Would be a “promise” if Parent would normally not give Dessert even if Child ate veggies Threats and Promises „ A school bully says to me: “I will beat you up if you come to school” This is a fact, not a “threat”!! „ Saying this will not change whether I decide to go to school „ „ To be effective, promised or threatened actions must go against one’s own incentives Students’ Dilemma „ 1. 2. 3. Two students in a class. Professor announces an unusual “final exam”: “If neither of you shows up to class tomorrow, you both get A’s. “If both of you show up, you both get B’s. “If one of you shows up, that person gets an A plus TAship for next year, while the other person gets an F.” • both students would like the TAship „ How can the students escape this Prisoners’ Dilemma? Escaping the Prisoners’ Dilemma “I won’t confess if you don’t but I will confess if you do” „ Is this a promise or a threat? „ If credible, what is its effect? Warnings and Assurances „ Just stating what you will do without commitment is called a “warning” or “assurance” „ Warnings and assurances are effective for coordinating behavior when there are multiple Nash equilibria „ To be effective, warnings or assurances must be consistent with one’s own incentives Talk is Cheap … Boeing Co. “announced it was building a plane with 600 to 800 seats, the biggest and most expensive airliner ever. Some in the industry suggest Boeing’s move is a bluff to preempt Airbus from going ahead with a similar plane.” - Rothman, Andrea, and Dori Jones. “Boeing Launches a Stealth Attach on Airbus,” Business Week, 18 January 1993. … And Getting Cheaper Airbus announces commercial launch of the A3XX, the largest civil aircraft ever. “Boeing … has said that there is no market for such a large plane and has decided to modernize its trustworthy 747 family of planes rather than build its own megaseater.” - Seward, Deborah. “Airbus Announces Launch of A3XX Superjumbo Jet.” Associated Press, 23 June 2000. Reagan Tax Plan Repubs Support Reagan Completely Mostly Support Reagan Dems Attack Reagan Compromise Senate vs. House „ Senate Dems hoped for compromise by not attacking Reagan … but Repubs didn’t yield „ Can House Dems do anything to get a better outcome? In-Class Game Next Time „ Please prepare for “Dynamic Pricing Game” to be played next class „ See handout