Finite Stage Centipede Game and Other Finite Two Player Dynamic Games with Bounded Rationality

Abstract

Subgame Perfect Nash Equilibrium (SPNE), as a predictive theory, has been found to be inconsistent with experimental evidence in many dynamic games. This working paper introduces bounded rationality of varying degrees through a distribution of the types of each player in finite dynamic games, and checks if that rationalizes observed/”intuitive” behavior. Each of these types has a different degree of limited foresight which causes them to be bounded rational. In this scenario, the solution concept applied is a self developed variation of the Perfect Bayesian Nash Equilibrium. This analysis with presence of bounded rational player types gives justification for strategies that are suboptimal in the sense of subgame perfection serving as equilibrium strategies even when two rational players interact. A specific analysis of the Centipede Game (which is cited as one of the major critiques of subgame perfection) using this modeling of bounded rationality brings forth results more compatible with experimental evidence -- even with arbitrarily small ex-ante probability on the different bounded rational types of a player, given large enough “k” stages in the Centipede Game, we have equilibrium cooperation till the (k-2)th stage.