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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.

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

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

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

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

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

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

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

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

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

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

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