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Game Theory

Game Theory. Basic Ideas of Game Theory. Game theory is the general theory of strategic behavior.  Generally depicted in mathematical form.  Plays an important role in modern economics. Rules, Strategies, Payoffs, and Equilibrium. Economic situations are treated as games.

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Game Theory

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  1. Game Theory

  2. Basic Ideas of Game Theory • Game theory is the general theory of strategic behavior.  Generally depicted in mathematical form.  Plays an important role in modern economics.

  3. Rules, Strategies, Payoffs, and Equilibrium • Economic situations are treated as games.  The rules of the game state who can do what, and when they can do it.  A player's strategy is a plan for actions in each possible situation in the game.

  4. Rules, Strategies, Payoffs, and Equilibrium • Economic situations are treated as games.  A player's payoff is the amount that the player wins or loses in a particular situation in a game.  A players has a dominant strategy if that player's best strategy does not depend on what other players do.

  5. Nash Equilibrium • Occurs when each player's strategy is optimal, given the strategies of the other players.  A player's best response (or best strategy) is the strategy that maximizes that player's payoff, given the strategies of other players.  A Nash equilibrium is a situation in which each player makes his or her best response.

  6. Prisoner's Dilemma • Famous example of game theory.  Strategies must be undertaken without the full knowledge of what other players will do.  Players adopt dominant strategies, but they don't necessarily lead to the best outcome.

  7. Prisoner’s Dilemma

  8. Bonnie’s Decision Tree

  9. Economic Applications of Game Theory • Cheating on a cartel • Trade wars between countries • Advertising • Games without dominant strategies

  10. Cheating on a Cartel • Cartel members' possible strategies range from abiding by their agreement to cheating.  Cartel members can charge the monopoly price or a lower price.  Cheating firms can increase profits.  The best strategy is charging the low price.

  11. Cheating on a Cartel

  12. Decision Tree for the Coca Cola Company

  13. Trade Wars Between Countries • Free trade benefits both trading countries. • Tariffs can benefit one trading country.  Imposing tariffs can be a dominant strategy and establish a Nash equilibrium even though it may be inefficient.

  14. Effects of a Tariff on Japanese Televisions P Supply of Japanese Televisions to U.S. Market Price to Buyers with a Tariff $350 A C $100 Tariff $300 E Price with No Tariff B U.S. Demand for Japanese Televisions $250 Price to Sellers with a Tariff Q 600 800 Televisions (thousands per year)

  15. Trade War Payoffs

  16. Decision Tree for the United States

  17. Advertising • The prisoner's dilemma applies to advertising.  All firms advertising tends to equalize the effects.  Everyone would gain if no one advertised.

  18. Advertising Payoffs

  19. Games Without Dominant Strategies • In many games the players have no dominant strategy.  Often a player's strategy depends on the strategies of others.  If a player's best strategy depends on another player's strategy, he has no dominant strategy.

  20. A Game With No Dominant Strategy

  21. Ma’s Decision Tree

  22. Multiple Equilibria • Some games have more than one Nash equilibrium.

  23. Multiple Equilibria • Multiple Nash equilibria means game theorists require extra information to predict what will happen when playing the game.

  24. Payoffs in a Game with Multiple Equilibria

  25. Sequential Games and Credibility • Some games are sequential.

  26. Sequential Games and Credibility • A sequential game is a game in which players make at least some of their decisions at different times.

  27. Sequential Games and Credibility • When the players are a monopoly and a new firm, the new firm faces a number of decisions beginning with whether to enter the industry.

  28. Sequential Games and Credibility • Entry decision determines which side of the decision tree is applicable. • In the second half of the game, the monopoly has the dominant strategy.

  29. Sequential Games and Credibility • A subgame perfect Nash equilibrium is a Nash equilibrium in which every player's strategy is credible. • No player makes incredible threats.

  30. New Firm Chooses New Firm Enters New Firm Does Not Enter Monopoly Chooses Monopoly Chooses High Price Low Price High Price Low Price Monopoly gets $3, New firm gets $2 Monopoly gets $0, New firm gets –$1 Monopoly gets $5, New firm gets $0 Monopoly gets $2, New firm gets $0 ($ millions) A Sequential Game

  31. Payoffs in a Sequential Game of Entry

  32. Commitments • Commitments are valuable.

  33. The Benefit of Commitments • People can benefit from being able to limit their future actions so that they cannot do what they would want to do in the future.

  34. The Benefit of Commitments • A person commits to a future action if they do something now to limit future options or change future incentives so that they will have an incentive to take that action in the future.

  35. The Benefit of Commitments • Commitments can provide valuable benefits by restricting future choices in a way that changes other people's actions to one's own benefit.

  36. Commitment Mechanisms • Committing to future action is often difficult. • The law, social pressures, etiquette, promises and honor all contribute to helping people commit.

  37. Excess Capacity as Commitment • A monopoly firm’s excess capacity may deter the entry of a new firm.

  38. Game With Monopoly Investing in Additional Capacity New Firm Chooses New Firm Enters New Firm Does Not Enter Monopoly Chooses Monopoly Chooses High Price Low Price High Price Low Price Monopoly gets $3, New firm gets $2 Monopoly gets $4, New firm gets –$3 Monopoly gets $5, New firm gets $0 Monopoly gets $4, New firm gets $0 ($ millions)

  39. Commitment in Other Games • Factors such as the capacity to produce help firms honor commitments. • Firms can commit to future actions by convincing government to regulate them.

  40. Repeated Games • A repeated game is a game that the same players play more than once.

  41. Repeated Games • Repeated games differ form one-shot games because people's current actions can depend on the past behavior of other players. • Cooperation is encouraged.

  42. Analysis Of Repeated Games • In the tit-for-tat strategy, players cooperate unless one of them fails to cooperate in some round of the game. • The others do in the next round what the uncooperative player did to them in the last round.

  43. Experimental Evidence On Tit-For-Tat • Evidence indicates tit-for-tat is a winning strategy. • The success of tit-for-tat strategy may lie behind customs and etiquette.

  44. Game Theory End of Chapter 17

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