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Game Theory Part II

This slide explain about Game Theory. this slide is divided into five parts. this is the first part.

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Game Theory Part II

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  1. Chapter 12 Strategy and Game Theory (Part II) © 2004 Thomson Learning/South-Western

  2. Two Simple Games • Table 12.2 (b) shows a game where a husband (A) and wife (B) have different preferences for a vacation (A prefers mountains, B prefers the seaside) • However, both players prefer a vacation together (where both players receive positive utility) than one spent apart (where neither players receives positive utility).

  3. TABLE 12.2 (b): Battle of the Sexes--Two Nash Equilibria

  4. Two Simple Games • At the strategy (A: Mountain, B: Mountain), neither player can gain by knowing the other’s strategy. • The same is true with the strategy (A: Seaside, B: Seaside). • Thus, this game has two Nash equilibria.

  5. APPLICATION 12.1: Nash Equilibrium on the Beach • Applications of the Nash equilibrium concept have been used to analyze where firms choose to operate. • The concept can be used to analyze where firm’s locate geographically. • The concept can also be used to analyze where firm’s locate in the spectrum of specific types of products.

  6. APPLICATION 12.1: Nash Equilibrium on the Beach • Hotelling’s Beach • Hotelling looked at the pricing of ice cream sellers along a linear beach. • If people are evenly spread over the length of the beach, he showed that each seller had an advantage selling to nearby consumers who incur lower (walking) costs. • The Nash equilibrium concept can be used to show the optimal location for each seller.

  7. APPLICATION 12.1: Nash Equilibrium on the Beach • Milk Marketing in Japan • In southern Japan, four local marketing boards regulate the sale of milk. • It appears that each must take into account what the other boards are doing, since milk can be shipped between regions. • A Nash equilibrium similar to the Cournot model found prices about 30 percent above competitive levels.

  8. APPLICATION 12.1: Nash Equilibrium on the Beach • Television Scheduling • Firms can also choose where to locate along the spectrum that represents consumers’ preferences for characteristics of a product. • Firms must take into account what other firms are doing, so game theory applies. • In television, viewers’ preferences are defined along two dimensions--program content and broadcast timing.

  9. APPLICATION 12.1: Nash Equilibrium on the Beach • In general, the Nash equilibrium tended to focus on central locations • There is much duplication of both program types and schedule timing • This has left “room” for specialized cable channels to attract viewers with special preferences for content or viewing times. • Sometimes the equilibria tend to be stable (soap operas and sitcoms) and sometimes unstable (local news programming).

  10. The Prisoner’s Dilemma • The Prisoner’s Dilemma is a game in which the optimal outcome for the players is unstable. • The name comes from the following situation. • Two people are arrested for a crime. • The district attorney has little evidence but is anxious to extract a confession.

  11. The Prisoner’s Dilemma • The DA separates the suspects and tells each, “If you confess and your companion doesn’t, I can promise you a six-month sentence, whereas your companion will get ten years. If you both confess, you will each get a three year sentence.” • Each suspect knows that if neither confess, they will be tried for a lesser crime and will receive two-year sentences.

  12. The Prisoner’s Dilemma • The normal form of the game is shown in Table 12.3. • The confess strategy dominates for both players so it is a Nash equilibria. • However, an agreement not to confess would reduce their prison terms by one year each. • This agreement would appear to be the rational solution.

  13. TABLE 12.3: The Prisoner’s Dilemma

  14. The Prisoner’s Dilemma • The “rational” solution is not stable, however, since each player has an incentive to cheat. • Hence the dilemma: • Outcomes that appear to be optimal are not stable and cheating will usually prevail.

  15. Prisoner’s Dilemma Applications • Table 12.4 contains an illustration in the advertising context. • The Nash equilibria (A: H, B: H) is unstable since greater profits could be earned if they mutually agreed to low advertising. • Similar situations include airlines giving “bonus mileage” or farmers unwilling to restrict output. • The inability of cartels to enforce agreements can result in competitive like outcomes.

  16. Table 12.4: An Advertising Game with a Desirable Outcome That is Unstable

  17. Cooperation and Repetition • In the version of the advertising game shown in Table 12.5, the adoption of strategy H by firm A has disastrous consequences for B (-50 if L is chosen, -25 if H is chosen). • Without communication, the Nash equilibrium is (A: H, B: H) which results in profits of +15 for A and +10 for B.

  18. TABLE 12.5: A Threat Game in Advertising

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