Preface

Choice-Theoretic Deontic Logic

Rational choice theorists and deontic logicians both study actions, yet they use very different approaches. This paper introduces some choice-theoretic concepts, namely those of feasible options, choice contexts, choice functions, rankings of options, and reasons structures, into deontic logic. We use these concepts to define a simple "choice-theoretic" language for deontic logic, and consider four different "choice-theoretic" semantics for that language, which we call "basic", "behavioural", "ranking-based", and "reason-based semantics". We compare these semantics in terms of the strength of their entailment relations and characterize precisely the differences in strength between weaker and stronger ones among these semantics.

No Trade and Yes Trade Theorems for Heterogeneous Priors

There is a widespread belief that because a classic theorem shows that common priors imply no trade, it follows that lack of common priors is sufficient to guarantee trade. We show, however, that even under non-common priors the classical no trade theorem obtains. Speculative trade does become mutually acceptable if traders put at least slight probability on the trading partner being irrational. Our model, thus, provides a generalization of the result of Neeman (1996) for the case of heterogeneous priors. We also derive bounds on disagreements in the case of heterogeneous priors and p-common beliefs.

Common Belief in Rationality in Psychological Games

Belief-dependent motivations and emotional mechanisms such as surprise, anxiety, anger, guilt, and intention-based reciprocity pervade real-life human interaction. At the same time, traditional game theory has experienced huge difficulties trying to capture them adequately. Psychological game theory, initially introduced by Geanakoplos et al. (1989), has proven to be a useful modeling framework for these and many more psychological phenomena. In this paper, we use the epistemic approach to psychological games to systematically study common belief in rationality, also known as correlated rationalizability. We show that common belief in rationality is possible in any game that preserves optimality at infinity, a mild requirement that nests all previously known existence conditions. Also, we provide an example showing that common belief in rationality might be impossible in games where optimality is not preserved at infinity. We then develop an iterative procedure that, for a given psychological game, determines all rationalizable choices. In addition, we explore classes of psychological games that allow for a simplified procedure.

Why Forward Induction Leads to the Backward Induction Outcome: A New Proof for Battigalli's Theorem

Battigalli (1997) has shown that in dynamic games with perfect information and without relevant ties, the forward induction concept of extensive-form rationalizability yields the backward induction outcome. In this paper we provide a new proof for this remarkable result, based on four steps. We first show that extensive-form rationalizability can be characterized by the iterated application of a special reduction operator, the strong belief reduction operator. We next prove that this operator satisfies a mild version of monotonicity, which we call monotonicity on reachable histories. This property is used to show that for this operator, every possible order of elimination leads to the same set of outcomes. We finally show that backward induction yields a possible order of elimination for the strong belief reduction operator. These four properties together imply Battigalli's theorem.