Economics 703 Advanced Microeconomics Prof. Peter Cramton Lecture Note 4: Refinement A. Subgame Perfection Revisited

The refinements of the Nash equilibrium concept surveyed in this section are all attempts to extend the spirit of Selten's [1965] definition of subgame perfection to games with imperfect information. To begin, we review the effect of subgame perfection in games of perfect information and the problems that arise with imperfect information. Extensive Form The normal form reveals that both (L,r) and (R,l) are Nash equilibria, but the former relies on an incredible threat by player 2: 2 threatens to play r if player 1 gives 2 the move; this would be bad for 1, so 1 plays L, but it also would be bad for 2. Given the opportunity to move, 2 prefers to play l, so (R,l) is the only sensible Nash equilibrium. 1 These notes are based without restraint on notes by Robert Gibbons, MIT.