Chapter 10: Games and Strategic Behavior

1. Chapter 10: Games and Strategic Behavior • Game theory attempts to mathematically capture behavior in strategic situations, in which an individual's success in making choices depends on the choices of others. (Wikipedia) • The actions taken by monopolistic competitors or oligopolies are interdependent, so are their payoffs.

2. Game Theory • Basic elements of a game • The players • Their available strategies, actions, or decisions • The payoff to each player for each possible action • A dominant strategy is one that yields a higher payoff no matter what the other player does • Dominated strategy is any other strategy available to a player who has a dominant strategy

3. Example: American and United – Scenario 1 • Players: United and American Airlines supplying service between Chicago and St. Louis • No other carriers • Strategies: Increase advertising by $1,000 or not • Assumption • All payoffs are known to all parties

4. Payoff Matrix • Payoff is symmetric • Dominant strategy is raise advertising spending • Both companies are worse off • Payoff is symmetric • Dominant strategy is raise advertising spending • Both companies are worse off

5. Equilibrium in a Game • In an equilibrium, each player of the game has adopted a strategy that they are unlikely to change. • Nash equilibrium is any combination of strategies in which each player’s strategy is her or his best choice, given the other player’s strategies • Equilibrium occurs when each player follows his dominant strategy, if it exists • Equilibrium does not require a dominant strategy

6. American and United – Scenario 2 Lower-Left cell is a Nash equilibrium • Same situation • Different payoffs; non-symmetric • America raises spending • United anticipates American action; does not raise

7. Prisoner's Dilemma Dominant strategy Optimal strategy • The prisoner's dilemma has a dominant strategy • The resulting payoffs are smaller than if each had stayed silent

8. Cartels • A cartel is a coalition of firms that agree to restrict output to increase economic profit • Restrict total output • Allocate quotas to each player

9. Cartel in Action: An Example • Two suppliers of bottled water agree to split the market equally • Price is set at monopoly level • If one party charges less, he gets all of the market • Marginal cost is zero • Agreement is not legally enforceable

10. Bottled Water Cartel • Each party has an incentive to lower the price a little to increase its economic profits • Successive reductions result in price equal to marginal cost

11. Bottled Water Cartel

12. Repeated Prisoner's Dilemma • Two players with repeated interactions • Each has a stake in the future outcomes • Both players benefit from collaboration • Tit-for-tat strategy limits defections • Tit-for-tat strategy says my move in this round is whatever your move was in the last round • If you defected, I defect • Tit-for-tat is rarely observed in the market • This strategy breaks down with more than two players or potential players