University:
Massachusetts Institute of Technology
Course:
15.992 | S-Lab: Laboratory for Sustainable Business
Academic year:

2023
Views:

249

Pages:

45
Author:

advierten86n

Lecture 3 Game Plan Nash equilibrium … in pure strategies & mixed strategies … how NE play arises from rationality … how NE play can arise from evolution Some Prototypical Games Prisoners’ Dilemma price war Example: SUV Price Wars “General Motors Corp. and Ford Motor Co. slapped larger incentives on popular sportutility vehicles, escalating a discounting war in the light-truck category … Ford added a $500 rebate on SUVs, boosting cash discounts to $2,500. The Dearborn, Mich., auto maker followed GM, which earlier in the week began offering $2,500 rebates on many of its SUVs.” -- Wall Street Journal, January 31, 2003 SUV Price Wars: The Game GM Discount Discount Ford Don’t Don’t SUV Price Wars: Outcome Each firm has a unilateral incentive to discount but neither achieves a pricing advantage. Discount Discount Ford Don’t GM Don’t “Red Queen Effect” “It takes all the running you can do to keep in the same place” – Red Queen to Alice From Carroll, Lewis. Alice’s Adventures in Wonderland. Prisoners’ Dilemma SUV Price War is a “prisoners’ dilemma” game: 1. 2. Both firms prefer to Discount regardless of what other does. (Discount is a dominant strategy.) BUT both firms are worse off when they both Discount than if they both Don’t. Prisoners’ Dilemma Game Prisoner 2 Confess Don’t Confess Prisoner 1 Don’t Key features: • Both players have a dominant strategy to Confess • BUT both players better off if they both Don’t Prisoners’ Dilemma Game Prisoner 2 Confess Confess Prisoner 1 Don’t Don’t Reaction Curves in Prisoners’ Dilemma 100% Prisoner 2’s prob. of Confess 50% 0% 0% 50% 100% Prisoner 1’s prob. of Confess Evolution in Prisoners’ Dilemma (One Population) Prob. of Confess in population 0% 25% 100% Row and Col players are drawn from the same population Those who Confess get higher payoff, so Confess dominates the population Some Prototypical Games Prisoners’ Dilemma Loyal Servant price war defensive innovation Soft & Chewy Cookies A cookie store is a bad idea. Besides, the market research reports say America likes crispy cookies, not soft and chewy cookies like yours. -Response to Debbi Fields' idea of starting Mrs. Fields' Cookies, 1977 Soft & Chewy Cookies Supermarket cookies tend to be crispy, not chewy Duncan Hines (owned by P&G) entered with a chewy cookie [1984] How did Nabisco and Keebler respond? Soft & Chewy Wars Nabisco and Keebler rolled out their own soft and chewy varieties: Keebler Soft Batch Nabisco Chips Ahoy! Chewy Soft & Chewy Settlement Duncan Hines brings patentinfringement suit alleging industrial espionage by Keebler, Nabisco and Frito-Lay [1984] Companies agree to pay P&G $125 million, then the most ever reported to settle a patent lawsuit [1989] Soft & Chewy Retreat P&G sells Duncan Hines to Aurora [1997] “This agreement is a win-win. Consumers will still be able to buy great Duncan Hines products, now through Aurora Foods, and we can focus on the strategic opportunities we've established for our food and beverage business.” -Steve Donovan, P&G VP, food and beverages. Defensive Innovation A monopolist’s incentive to innovate increases as it faces innovative entrants. Consider case of product variety • consumers represented as points in a square • they buy whichever product is closest represents consumers who buy from monopolist represents a product of monopolist Product Variety Game Without any entry, the monopolist doesn’t gain from introducing a new product • To keep things simple, we suppose price is fixed represents consumers who buy from monopolist represents a product of monopolist Product Variety Game Now suppose an entrant comes in with a new variety. Now “landing on the entrant” keeps some customers • Incentive to introduce new variety if entry • Will the other firm enter anyway? represents consumers who buy from entrant represents a product of entrant Defensive Innovation: Summary So Far Monopolist Innovate Innovate Entrant Don’t ?? Don’t Case I: Entrant Wants to Innovate Anyway Monopolist Innovate Innovate Entrant Don’t Don’t What Can Conceivably Happen? 1. … if both Monopolist and Entrant are rational (only) (Innovate, Innovate) or (Innovate, Don’t) • 2. latter requires monopolist to mistakenly believe that entrant will not innovate … if rationality is common knowledge? (Innovate, Innovate) only since monopolist knows entrant is rational! Loyal Servant Game Servant Safe Route Dangerous Safe Route Master Dangerous Key features: • One player (Master) has dominant strategy • Other player (Servant) wants to do the same thing as Master Loyal Servant Game Servant Safe Route Safe Route Master Dangerous Dangerous Reaction Curves in Loyal Servant Game 100% Servant’s prob. of Safe 50% 0% 0% 50% 100% Master’s prob. of Safe Evolution in Loyal Servant Game (Two Populations) 100% Servant’s prob. of Safe 50% Evolution leads to Nash eqm (Safe, Safe) 0% 0% 50% 100% Master’s prob. of Safe Rationalizable Strategies Strategies are “rationalizable” if they could conceivably be played when 1. 2. players are rational and rationality is common knowledge Suppose each player has a unique rationalizable strategy. Then these strategies form a Nash equilibrium. How to Find Rationalizable Strategies If a strategy is strictly dominated for some player, eliminate it Repeat, eliminating any strictly dominated strategies in reduced game All strategies that remain when you are finished are rationalizable Example: Tourists & Natives Two bars (bar 1, bar 2) compete Can charge price of $2, $4, or $5 6000 tourists pick a bar randomly 4000 natives select the lowest price bar Example 1: each gets 5,000 customers Example 2: Both charge $2 Bar 1 charges $4, Bar 2 charges $5 Bar 1 gets 3000+4000=7,000 customers Bar 2 gets 3000 customers Tourists & Natives Bar 2 $2 $4 $5 $2 10 , 10 14 , 12 14 , 15 Bar 1 $4 12 , 14 20 , 20 28 , 15 $5 15 , 14 15 , 28 25 , 25 in thousands of dollars Successive Elimination of Dominated Strategies Bar 2 $2 $4 $5 $2 10 , 10 14 , 12 14 , 15 Bar 1 $4 12 , 14 20 , 20 28 , 15 $5 15 , 14 15 , 28 25 , 25 Bar 2 $4 $5 $4 20 , 20 28 , 15 Bar 1 $5 15 , 28 25 , 25 Some Prototypical Games Prisoner’s Dilemma Loyal Servant Hunter and Hunted price war defensive innovation audits, bluffing Bluffing in Poker: Set-Up Player A’s hand prior to getting 5th card 3♣ 4♣ 5♣ 6♣ Player A will be drawing on an inside straight flush Player A will have the best hand if: • flush (another club: 9 cards total) or • straight (any 2 or 7: additional 6 cards) Winning Cards 7♣ 8♣ 9♣ 10♣ J♣ Q♣ K♣ A♣ 2♦ 2♥ 2♠ 7♠ 7♥ 7♦ (Road sign: “Deuce of Clubs Ave.”) 2♣ (Sign: “City of Show Low, AZ”) Bluffing Game: Rules Each player has put $100 into the pot After receiving the fifth card, player A will either Raise $100 or Not If Raise, Player B then either Calls (adds $100 more) or Folds (automatically losing $100 already in pot) Player A wins the pot if either A gets winning card or B folds Bluffing Game: Rules Raise Good Card Bad Card Call Fold Not Raise 100, -100 100, -100 Call Fold Not 200, -200 -200, 200 100, -100 -100, 100 successful bluff! Play Bluffing Game! Pair up with a neighbor. Player A will be given a playing card After that, communication allowed Players A,B may say (or show) anything they want to each other Defensive Innovation Case II: Entrant Wouldn’t Innovate Monopolist Innovate Innovate Entrant Don’t Don’t Hunter and Hunted Game Left Left Hunted Right (2,-2) (-2,0) (0,2) (0,0) Hunter Right Key features: • Hunter wants to “catch”; Hunted wants to “avoid” Reaction Curves in Hunter and Hunted Game 100% Hunted’s prob. of Right 50% 0% 0% 50% 100% Hunter’s prob. of Right Evolution in Hunter and Hunted Game 100% Hunted’s prob. of Right 50% Evolving populations may cycle around or 0% 0% 50% 100% fall into the mixed Hunter’s prob. of Right strategy equilibrium, depending on details Side-Blotched Lizard Orange throat, “dominating” Blue throat, “monogamous” Yellow throat, “sneaky” Summary Recognize dominant strategies Take others’ (ir)rationality into account Loyal Servant Game Mixing can be the right way to play Prisoners’ Dilemma Hunter and Hunted Game Next time: more on evolution and introducing sequential moves Online Game #3 (Entrant Game) Play Online Game #3 prior to midnight before next lecture. Note: We are not playing the games in their numerical order!!