Eco514-Game Theory lecture 16: Applications of Sequential and Perfect Bayesian equilibrium Marciano siniscalchi November 16. 1999 Introduction The purpose of this lecture is to help you familiarize with the workings of sequential equi- librium and"sequential equilibrium lite", i.e. perfect Bayesian equilibrium The main focus is the "reputation"result of Kreps and Wilson(1982). You should refer to OR for details and definitions: I am following the textbook quite closely We have already mentioned the Entry Deterrence game. Now consider a K-fold repetition of the game in which an incumbent faces a sequence of K(potential) entrants. It is clear hat, in the subgame in which the last entrant gets a chance to play, the incumbent will Concede. But then, by backward induction, he will also Concede at any previous round This conclusion seems unpalatable. One would expect the chain-store to fight a few times early on so as to deter further entry; yet, this simply cannot occur in equilibrium The Chain-Store Game with Imperfect Information Kreps and Wilson suggest the following way out of the Chain Store Paradox. Assume that with some small probability e >0, the incumbent is"Tough: that is, she really enjoys beating up entrants Consider the behavior of a"Regular"incumbent; clearly, when she faces the last entrant she will Concede if the latter moves In. However, in previous rounds, she may threaten to Fight entry; in this case, if the current entrant moves In and is met with a fight, the following entrant does not learn whether the incumbent is Regular or Tough, because both Fight enty Hence, the posterior probability that the incumbent is Tough remains constant at E, and if this value is such that the following Entrant prefers not to Enter, the incumbent's threat is credibleEco514—Game Theory Lecture 16: Applications of Sequential and Perfect Bayesian Equilibrium Marciano Siniscalchi November 16, 1999 Introduction The purpose of this lecture is to help you familiarize with the workings of sequential equi￾librium and “sequential equilibrium lite”, i.e. perfect Bayesian equilibrium. The main focus is the “reputation” result of Kreps and Wilson (1982). You should refer to OR for details and definitions: I am following the textbook quite closely. We have already mentioned the Entry Deterrence game. Now consider a K-fold repetition of the game in which an incumbent faces a sequence of K (potential) entrants. It is clear that, in the subgame in which the last entrant gets a chance to play, the incumbent will Concede. But then, by backward induction, he will also Concede at any previous round. This conclusion seems unpalatable. One would expect the chain-store to fight a few times early on so as to deter further entry; yet, this simply cannot occur in equilibrium. The Chain-Store Game with Imperfect Information Kreps and Wilson suggest the following way out of the Chain Store Paradox. Assume that, with some small probability  > 0, the incumbent is “Tough”: that is, she really enjoys beating up entrants. Consider the behavior of a “Regular” incumbent; clearly, when she faces the last entrant, she will Concede if the latter moves In. However, in previous rounds, she may threaten to Fight entry; in this case, if the current entrant moves In and is met with a fight, the following entrant does not learn whether the incumbent is Regular or Tough, because both Fight entry. Hence, the posterior probability that the incumbent is Tough remains constant at , and if this value is such that the following Entrant prefers not to Enter, the incumbent’s threat is credible. 1