1. Econ 545, Spring 2016 Industrial Organization Dynamic Games

2. Dynamic games Goals We are expanding beyond one-shot games. We must think about strategies and payoffs for long-term interactions. We will define and develop an equilibrium concept that works for repeated games. We will discuss how a decision-maker weighs the value of future payoffs relative to present-day payoffs. Broader importance Firms are long-lived and interact repeatedly Many opportunities involve trade-offs between today’s cost and tomorrow benefit (or vice-versa) 2Econ 445: Dynamic Games

3. Sequential and dynamic games Sequential game: A game played with moves taken one-at-a-time. Payoffs received once at end of game. Dynamic (or repeated) game: A game with multiple stages of decisions and payoffs Number of stages may be finite or infinite. Examples: Sequential but not dynamic: Tic-Tac-Toe played once Dynamic simultaneous move: Repeated prisoners dilemma Dynamic with sequential moves: Poker 3Econ 445: Dynamic Games

4. Dynamic strategies and equilibrium Dynamic games have repeated choices and payoffs: Each stage is a small game played simultaneously or sequentially. A strategy for the whole dynamic game is a plan of action to carry through each stage. A strategy is called subgame perfect if a player wants to stick with the strategy at every subgame. We look for a subgame perfect equilibrium, which occurs when all players are playing subgame perfect strategies. 4Econ 445: Dynamic Games

5. Dynamic strategies and equilibrium We solved sequential games using backward induction. Finding a subgame-perfect equilibrium is similar. -Go to the last possible subgame -Find optimal moves within this subgame as if it is the only interaction among players -Go to the second-to-last subgame, using outcome above to “predict” what will happen next. -Continue in this way back to the first subgame … A subgame-perfect strategy is credible because players want to stick with them, just as in sequential games. 5Econ 445: Dynamic Games

6. Example: Fight or accommodate? Firms A and B consider serving a market. Firm A already has a store in the market. Firm B is considering opening a store. Order of actions: 1.B decides whether to enter or not. 2.A decides whether to set very low prices (“fight”) or intermediate prices (“accommodate”). Effects: -If A fights it will be hard on both firms, and B would prefer to be out of the market. -Both firms can exist if A sets intermediate prices. 6Econ 445: Dynamic Games

7. Example: Fight or accommodate? The game so far is a standard sequential game 7Econ 445: Game theory Firm B Firm A 1 3 2 5 0 Enter Fight Accommodate Don’t enter

8. Repeated entry decisions 8Econ 445: Dynamic Games

9. Repeated entry decisions Can A establish a reputation for toughness? If fights in early rounds, maybe it can convince later potential entrants to stay out. Early losses from fighting (payoff of 1 rather than 3) may be justified if it can keep potential entrants out (payoff of 5). Formally: Is it an equilibrium for A to commit fighting, and for all B’s to believe this and stay out? We will use subgame perfect equilibrium to evaluate whether A can credibly make this commitment. 9Econ 445: Dynamic Games

10. Repeated entry decisions 10Econ 445: Dynamic Games

11. Repeated entry decisions 11Econ 445: Dynamic Games

12. Repeated entry decisions 12Econ 445: Dynamic Games

13. Repeated entry decisions 13Econ 445: Dynamic Games

14. Repeated entry decisions This outcome is called the “chain store paradox”. It seems A should be able to benefit from a strong reputation. Once building the reputation no longer matters, firm A can be expected to revert to accommodating behavior. If all players expect this reversion, then at no stage is it optimal for A to invest in its reputation. Some ways to change the game and maybe the outcome: Finite vs Infinite Horizon. Reduced flexibility for A to accommodate B. This can be done through capacity (Q) or price commitments. Hidden information about A’s type. Maybe A has low costs or is crazy. This leads to signaling games we won’t cover in 445. 14Econ 445: Dynamic Games

15. Ex.: Repeated prisoner’s dilemma The chain store game: Firms A and B are at odds with each other. B’s benefit comes at A’s expense and vice versa. The prisoner’s dilemma has: A one-shot equilibrium of (Confess, Confess) that is bad for both prisoners. A pair of actions, (Don’t confess, Don’t confess) that minimizes total jail time for both prisoners. If two criminals play the prisoner’s dilemma repeatedly over time, is it more likely for the prisoners to establish the “good” actions as an equilibrium? Does this resemble any oligopoly payoffs/interaction? 15Econ 445: Dynamic Games

16. Discounting 16Econ 445: Dynamic Games

17. Discounting 17Econ 445: Dynamic Games

18. Discounting 18Econ 445: Dynamic Games

19. Discounting examples 19Econ 445: Dynamic Games

20. Conclusions We have covered: Subgames and subgame perfect equilibrium. When and how can a incumbent prevent entry? Discounting future payoffs. What is upcoming: Incentives to form cartels and incentives to cheat within cartels. Antitrust policy in response to firms’ dynamic strategies. 20Econ 445: Dynamic Games