hat Dynamic Games and Equilibrium Dynamic games can be represented in normal form. Consider the entry game of lecture 10. (-1,0 (12) (0.5) 2 There are two pure Nash equilibria-(DE, F) and E, DF). In fact, there are infinitely many mixed equilibria also- where the entrant plays DE and the monopolist plays F with at least probability half. Market- What Nerty Credibility However, working from the back of the game in extensive form, the entrant will always choose to enter given they now that if they do. the monopolist will not fight. The threat to fight is not credible. An equilibrium is subgame perfect if it is a Nash equilibrium of each subgame and of the whole game a subgame is simply a game starting at any particular node. Subgame perfection rules out incredible threats. The only subgame perfect equilibrium in this game is E, DFJ. This is a refinement of Nash equilibrium. Can the monopolist ever deter entry? If the game is repeated many (many)times then, yes fighting in the above game, collusion in oligopoly and even cooperation in the repeated prisoners'dilemma.Market — What Next? 11 Dynamic Games and Equilibrium • Dynamic games can be represented in normal form. Consider the entry game of lecture 10. .............................................................................................................................................................................................................................................................................................. .............................................................................................................................................................................................................................................................................................. ............................................................................................................................................................................................................................................................................................... • .............................................................................................................................................................................................................................................................................................. • • • • E M Fight Don’t Fight Enter Don’t Enter (0, 5) (1, 2) (−1, 0) F DF E 0 −1 2 1 DE 5 0 5 0 • There are two pure Nash equilibria — {DE, F} and {E, DF}. In fact, there are infinitely many mixed equilibria also — where the entrant plays DE and the monopolist plays F with at least probability half. Market — What Next? 12 Credibility • However, working from the back of the game in extensive form, the entrant will always choose to enter given they know that if they do, the monopolist will not fight. The threat to fight is not credible. • An equilibrium is subgame perfect if it is a Nash equilibrium of each subgame and of the whole game. • A subgame is simply a game starting at any particular node. Subgame perfection rules out incredible threats. • The only subgame perfect equilibrium in this game is {E, DF}. This is a refinement of Nash equilibrium. • Can the monopolist ever deter entry? If the game is repeated many (many) times then, yes. • The folk theorems prove that in an infinitely repeated game almost anything is subgame perfect. For example, fighting in the above game, collusion in oligopoly and even cooperation in the repeated prisoners’ dilemma