Essays in Game Theory

Open Access
Author:
Lee, Byung Soo
Graduate Program:
Economics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
March 08, 2010
Committee Members:
  • Edward James Green, Dissertation Advisor
  • Edward James Green, Committee Chair
  • Kalyan Chatterjee, Committee Member
  • Tymofiy Mylovanov, Committee Member
  • Stephen George Simpson, Committee Member
Keywords:
  • extensive-form rationalizability
  • forward induction
  • iterated admissibility
  • game theory
  • complete type structures
  • epistemic condition
Abstract:
Chapter 1:<br/> I modify two-player simultaneous-move games with a unique payoff-dominant strategy profile by allowing each player to publicly discard any of her original strategic options in turn before play begins. In this setting, I show that extensive-form rationalizable (EFR) profiles, as defined in Pearce (1984), have payoff-dominant outcomes. Furthermore, a strategy profile in which no player makes any commitments is EFR. Thus, the model is interpreted as one of payoff-dominant focal-point formation via forward induction, which is captured by EFR. The result is analogous to that in Ben-Porath and Dekel’s (1992) model of money-burning games. That the order of beliefs required to obtain payoff-dominant outcomes is uniformly bounded at three across all games is an advantage of the model in this paper over the money-burning approach, which may require the use of arbitrarily high orders of beliefs to obtain the same result. A limitation of this paper, which is also shared by the money-burning model, is that the prediction of payoff-dominant play is not robust to the addition of players. <br/> <br/> Chapter 2: <br/> I provide an epistemic characterization of iterated elimination of inadmissible---that is, weakly dominated---strategies. Along the way, I show that for each finite game there exists a large class of complete lexicographic type structures that admit rationality and common assumption of rationality (RCAR), and provide a versatile methodology for constructing them. This answers a question posed in Brandenburger, Friedenberg, and Keisler (2008) (BFK). Solving a long-standing puzzle of Samuelson (1992), BFK gave an epistemic characterization of finite rounds of elimination of inadmissible strategies. However, they also gave a negative result showing that RCAR is impossible in a complete lexicographic type structure with continuous mappings. This seemed to cast doubt on the possibility of RCAR as a natural candidate for the desired epistemic condition, but our results revive this possibility. I examine the differences between our positive result and their negative result in isolation, and arrive at the surprising conclusion that a lexicographic type structure contains more information than previously thought.