This thesis contributes to a re-examination and extension of the equilibrium concept in normal and extensive form games. The equilibrium concept is a solution concept for games that is consistent with individual rationality and various assumptions about players' knowledge about the nature of their strategic interaction. The thesis argues that further consistency conditions can be imposed on a rational solution concept. By its very nature, a rational solution concept implicitly defines which strategies are non-rational. A rational player's beliefs about play by non-rational opponents should be consistent with this implicit definition of non-rational play. The thesis shows that equilibrium concepts that satisfy additional consistency requirements can be formulated in Choquet-expected utility theory, i.e. non-expected utility theory with non-additive or set-valued beliefs, together with an empirical assumption about players' attitude toward uncertainty. Chapter 1 introduces the background of this thesis. We present the conceptual problems in the foundations of game theory that motivate our approach. We then survey the decision-theoretic foundations of Choquet-expected utility theory and game-theoretic applications of Choquet-expected utility theory that are related to the present approach. Chapter 2 formulates this equilibrium concept for normal form games. This concept, called Choquet-Nash Equilibrium, is shown to be a generalization of Nash Equilibrium in normal form games. We establish an existence result for finite games, derive various properties of equilibria and establish robustness results for Nash equilibria. Chapter 3 extends the analysis to extensive games. We present the equivalent of subgame-perfect equilibrium, called perfect Choquet Equilibrium, for extensive games. Our main finding here is that perfect Choquet equilibrium does not generalize, but is qualitatively different from subgame-perfect equilibrium. Finally, in chapter 4 we examine the centipede game. It is shown that the plausible assumption of bounded uncertainty aversion leads to an 'interior' equilibrium of the centipede game.

The epistemic program in game theory uses formal models of interactive reasoning to provide foundations for various game-theoretic solution concepts. Much of this work is based around the (static) Aumann structure model of interactive epistemology, but more recently dynamic models of interactive reasoning have been developed, most notably by Stalnaker (Economics and Philosophy 1996) and Battigalli and Siniscalchi (Journal of Economic Theory 1999), and used to analyze rational play in extensive form games. But while the properties of Aumann structures are well un- derstood, without a formal language in which belief and belief revision statements can be expressed, it is unclear exactly what are the properties of these dynamic models. In chapter 1, "Dynamic In- teractive Epistemology", we investigate this question by defining such a language. A semantics and syntax are presented, with soundness and completeness theorems linking the two. Chapter 2, "Algorithmic Characterization of Ratioalizability in Extensive Form Games", uses the framework of chapter 1 to construct a dynamic epistemic model for extensive form games, which generates a hierarchy of beliefs for each player over her opponents' strategies and beliefs, and tells us how those beliefs will be revised as the game proceeds. We use the model to analyze the implications of the assumption that the players possess common (true) belief in rationality, thus extending the concept of rationalizability to extensive form games. Chapter 3, "The Equivalence of Bayes and Causal Rationality in Games", takes as its starting point a seminal paper of Aumann (Econometrica 1987), which showed how the choices of rational players could be analyzed in a unified state space framework. His innovation was to include the choices of the players in the description of the states, thus abolishing Savage's distinction between acts and consequences. But this simplification comes at a price: Aumann's notion of Bayes ratio­ nality does not allow players to evaluate what would happen were they to deviate from their actual choices. We show how the addition of a causal structure to the framework enables us to analyze such counterfactual statements, and use it to introduce a notion of causal rationality. Under a plausible causal independence condition, the two notions are shown to be equivalent. If we are prepared to accept this condition we can dispense with the causal apparatus and retain Aumann's original framework. In chapter 4, "The Deception of the Greeks", it is argued that the standard model of an extensive form game rules out an important phenomenon in situations of strategic interaction: deception. Using examples from the world of ancient Greece and from modern-day Wall Street, we show how the model can be generalized to incorporate this phenomenon. Deception takes place when the action observed by a player is different from the action actually taken. The standard model does allow imperfect information (modeled by non-singleton information sets), but not deception: the actual action taken is never ruled out. Our extension of extensive form games relaxes the assumption that the information sets partition the set of nodes, so that the set of nodes considered possible after a certain action is taken might not include the actual node. We discuss the implications of this relaxation, and show that in certain games deception is inconsistent with common knowledge of rationality even along the backward induction path.

The first chapter introduces the topic of coalition structures and stresses its importance and impact on game theory. Additionally, it presents and motivates the significance of the three following chapters. / The second chapter investigates how rational individuals partition themselves into different coalitions. We propose a notion that determines simultaneously the coalition structures that are likely to prevail in a game, as well as the feasible payoff configurations associated with them. Our solution concept is built in the spirit of von Neumann and Morgenstern stability, but it overcomes the overoptimism associated with it when employed in our context. Moreover, in doing so, we achieve consistency and resolve the problem of myopia embedded in previous notions. We prove existence for a general class of games, and investigate the efficiency of our solution. / The third chapter ascertains which partitions of players will emerge and what actions will these players choose under each partition, when they can negotiate with each other and their actions have externalities. Naturally, the environment is depicted by a normal form game. The solution is a collection of pairs, each consisting of a coalition structure and a strategy profile. Although this chapter addresses the same question the Ray and Vohra (1997) paper did, it does so in a manner that overcomes the problems embedded in their approach. In particular, we assume that once a coalition deviates it fears the worst, given that the non-members do the best for themselves. In doing so, we improve upon previous solution concepts (e.g. strong and coalition-proof Nash equilibria) by NOT assuming that all other players will stay put. Yet, unlike the Ray and Vohra approach, we do not endow the deviating coalition with the power of imposing its will on all of the other players. A general solution concept is defined and its properties (efficiency, etc.) and applications are discussed. / The fourth chapter analyzes cartel stability when firms are farsighted. It studies a price leadership model a la D'Aspremont et al. (1983), where the dominant cartel acts as a leader by determining the market price, while the fringe behaves competitively. According to D'Aspremont et al.'s notion of cartel stability, a firm will not remain in a cartel as long as it prefers the outcome where it is the only member leaving the cartel for the fringe. Such an approach implies that the firm is myopic since it ignores whether the outcome of its deviation is stable itself. Our notion captures foresight by employing a solution concept built in the spirit of von Neumann and Morgenstern stable set, yet adopting an indirect dominance a la Harsanyi. We show that there always exists a unique, non-empty set of stable cartels.

One way to create a champion level poker agent is to compute a Nash Equilibrium in an abstract version of the poker game. The resulting strategy is then used to play in the full game. With this approach, translation is required between the full and abstract games in order to use the abstract strategy. In limit poker this translation step is defined when the abstraction is chosen. However, when considering no-limit poker the translation process becomes more complicated. We formally describe the process of translation and investigate its consequences. We examine how the current method, hard translation, can result in exploitable agents and introduce a new probabilistic method, soft translation, that produces more robust players. We also investigate how switching between strategies with different underlying abstractions affects the performance of an agent.

Thesis (Ph. D.)--University of Wyoming, 2005. / Title from PDF title page (viewed on Nov. 5, 2007). Includes bibliographical references (p. 125-129).

Thesis (Ph. D.)--University of Adelaide, Dept. of Applied Mathematics, 1999. / Includes bibliographical references (leaves 158-166).

Thesis (Ph.D.)--University of Melbourne, 2006. / Typescript. Includes bibliographical references (leaves 222-236).

Thesis (M.S. in Operations Research)--Naval Postgraduate School, June 2009. / Thesis Advisor(s): Lin, Kyle Y. "June 2009." Description based on title screen as viewed on July 13, 2009. DTIC Identifiers: RCIED (Radio Controlled Improvised Explosive Devices). Author(s) subject terms: Game Theory, Zero-Sum Game, Radio Controlled Improvised Explosive Device Loadset, RCIED Loadset, Active Jamming Loadset, Optimizing Active Jamming Loadset. Includes bibliographical references (p. 73-75). Also available in print.

Thesis (M.S. in Applied Mathematics)--Naval Postgraduate School, June 2009. / Thesis Advisor(s): Owen, Guillermo ; Borges, Carlos. "June 2009." Description based on title screen as viewed on 13 July 2009. Author(s) subject terms: Game Theory, Bimatrix, modeling, convoy routing, Nash Equilibrium, search, ambush. Includes bibliographical references (p. 39). Also available in print.

Thesis (M.S.)--Brigham Young University. School of Technology, 2004. / Includes bibliographical references (p. 71-76).