Entry Deterrence Players Two firms, entrant and incumbent Order of play Entrant decides to enter or stay out. If entrant enters, incumbent decides to fight or collude. Payoffs 300 at monopoly price, 0 at fighting price. Duopoly reduces profits to 100, split evenly. Entry costs are 10.

Subgame Perfectness A subgame is a game consisting of a singleton decision node, all its successors, and the associated payoffs. The game itself is a subgame A strategy profile is a subgame perfect Nash equilibrium if its relevant action rules are a NE for every subgame. Every SPE is a NE.

Strategies in repeated Prisoner’s Dilemma Grim trigger Start by choosing Deny Continue to choose Deny unless some player has chosen Confess, in which case choose Confess forever after. Tit-for-Tat Start by choosing Deny Choose in period n the action the other player chose in period n-1.

Folk theorem In an infinitely repeated n-player game with finite action sets, any profile of actions is the unique outcome of some subgame perfect equilibrium if: the rate of time preference is sufficiently small, the probability that the game ends in each period is sufficiently small, the set of payoffs that Pareto dominates the minimax payoffs is n-dimensional.