Copyright (c) 2008 All rights reserved. http://works.bepress.com/muhamet_yildiz Recent documents in Muhamet Yildiz en-us Thu, 03 Jan 2008 11:27:50 PST 3600 http://works.bepress.com/muhamet_yildiz/9 http://works.bepress.com/muhamet_yildiz/9 Fri, 09 Feb 2007 13:41:56 PST Rationalizability is a central solution concept of game theory. Economic models often have many rationalizable outcomes, motivating economists to use refinements of rationalizability, including equilibrium refinements. In this paper we try to achieve a general understanding of when this multiplicity occurs and how we should deal with it. Assuming that the set of possible payoff functions and belief structures is sufficiently rich, we establish a revealing structure of the correspondence of beliefs to sets of rationalizable outcomes. We show that, for any rationalizable action a of any type, we can perturb the beliefs of the type in such a way that a is uniquely rationalizable for the new type. This unique outcome will be robust to further small changes. When multiplicity occurs, then, we are in a "knife-edge" case where the unique rationalizable outcome changes, sandwiched between open sets of types where each of the rationalizable actions is uniquely rationalizable. As an immediate application of this result, we characterize, for any refinement of rationalizability, the predictions that are robust to small misspecifications of interim beliefs. These are only those predictions that are true for all rationalizable strategies, i.e., the predictions that could have been made without the refinement. Jonathan Weinstein Game Theory http://works.bepress.com/muhamet_yildiz/8 http://works.bepress.com/muhamet_yildiz/8 Fri, 09 Feb 2007 13:39:39 PST In some games, the impact of higher-order uncertainty is very large, implying that present economic theories may rely critically on the strong common knowledge assumptions they make. Focusing on normal-form games in which the players' action spaces are compact metric spaces, we show that our key condition, called "global stability under uncertainty," implies that the maximum change in equilibrium actions due to changes in players' beliefs at orders higher than k is exponentially decreasing in k. Therefore, given any need for precision, we can approximate equilibrium actions by specifying only finitely many orders of beliefs. Jonathan Weinstein Game Theory http://works.bepress.com/muhamet_yildiz/7 http://works.bepress.com/muhamet_yildiz/7 Fri, 09 Feb 2007 13:35:20 PST Given any two-person economy, consider an alternating-offer bargaining game with complete information where the proposers offer prices, and the responders either choose the amount of trade at the offered prices or reject the offer. We provide conditions under which the outcomes of all subgame-perfect equilibria converge to theWalrasian equilibrium (the price and the allocation) as the discount rates approach 1. Therefore, price-taking behavior can be achieved with only two agents. Muhamet Yildiz Bargaining http://works.bepress.com/muhamet_yildiz/6 http://works.bepress.com/muhamet_yildiz/6 Fri, 09 Feb 2007 12:36:07 PST Towards developing a theory of systematic biases about strategies, I analyze strategic implications of a particular bias: wishful thinking about the strategies. I identify a player as a wishful thinker if she hopes to enjoy the highest payoff that is consistent with her information about the others' strategies. I develop a straightforward elimination process that characterizes the strategy profiles that are consistent with wishful thinking, mutual knowledge of wishful thinking, and so on. Every pure-strategy Nash equilibrium is consistent with common knowledge of wishful thinking. For generic two-person games, I further show that the pure Nash equilibrium strategies are the only strategies that are consistent with common knowledge of wishful thinking. My analysis also illustrates how one can characterize the strategic implications of general decision rules using the tools of game theory. Muhamet Yildiz Game Theory http://works.bepress.com/muhamet_yildiz/5 http://works.bepress.com/muhamet_yildiz/5 Fri, 09 Feb 2007 12:19:29 PST I analyze a sequential bargaining model in which players are optimistic about their bargaining power (measured as the probability of making offers), but learn as they play the game. I show that there exists a uniquely predetermined settlement date, such that in equilibrium the players always reach an agreement at that date, but never reach one before it. Given any discount rate, if the learning is sufficiently slow, the players agree immediately. I show that, for any speed of learning, the agreement is delayed arbitrarily long, provided that the players are sufficiently patient. Therefore, although excessive optimism alone cannot cause delay, it can cause long delays if the players are expected to learn. Muhamet Yildiz Bargaining http://works.bepress.com/muhamet_yildiz/4 http://works.bepress.com/muhamet_yildiz/4 Fri, 09 Feb 2007 12:00:48 PST In sequential bargaining models without outside options, each player's bargaining power is ultimately determined by which player will make an offer and when. This paper analyzes a sequential bargaining model in which players may hold different beliefs about which player will make an offer and when. Excessive optimism about making offers in the future can cause delays in agreement. The main result states that, despite this, if players will remain sufficiently optimistic for a sufficiently long future, then in equilibrium they will agree immediately. This result is also extended to other canonical models of optimism. Muhamet Yildiz Bargaining http://works.bepress.com/muhamet_yildiz/1 http://works.bepress.com/muhamet_yildiz/1 Fri, 09 Feb 2007 11:45:13 PST We analyze the subgame-perfect equilibria of a game where two agents bargain in order to share the risk in their assets that will pay dividends once at some fixed date. The uncertainty about the size of the dividends is resolved gradually by the payment date and each agent has his own view about how the uncertainty will be resolved. As agents become less uncertain about the dividends, some contracts become unacceptable to some party to such an extent that at the payment date no trade is possible. The set of contracts is assumed to be rich enough to generate all the Pareto-optimal allocations. We show that there exists a unique equilibrium allocation, and it is Pareto-optimal. Immediate agreement is always an equilibrium outcome; under certain conditions, we further show that in equilibrium there cannot be a delay. In this model, the equilibrium shares depend on how the uncertainty is resolved, and an agent can lose when his opponent becomes more risk-averse. Finally, we characterize the conditions under which every Pareto-optimal and individually rational allocation is obtainable via some bargaining procedure as the unique equilibrium outcome. Muhamet Yildiz Bargaining