Abstract. Experimentalists frequently claim that human subjects in the laboratory violate game-theoretic predictions. It is here argued that this claim is usually premature. The paper elaborates on this theme by way of raising some conceptual and methodological issues in connection with the very definition of a game and of players ’ preferences, in particular with respect to potential context dependence, interpersonal preference dependence, backward induction and incomplete information.

We present an approach to reasoning from statistical and subjective knowledge, which is based on a combination of probabilistic reasoning from conditional constraints with approaches to default reasoning from conditional knowledge bases. More precisely, we introduce the notions of -, lexicographic, and conditional entailment for conditional constraints, which are probabilistic generalizations of Pearl's entailment in system , Lehmann's lexicographic entailment, and Geffner's conditional entailment, respectively. We show that the new formalisms have nice properties. In particular, they show a similar behavior as referenceclass reasoning in a number of uncontroversial examples. The new formalisms, however, also avoid many drawbacks of reference-class reasoning. More precisely, they can handle complex scenarios and even purely probabilistic subjective knowledge as input. Moreover, conclusions are drawn in a global way from all the available knowledge as a whole. We then show that the new formalisms also have nice general nonmonotonic properties. In detail, the new notions of -, lexicographic, and conditional entailment have similar properties as their classical counterparts. In particular, they all satisfy the rationality postulates proposed by Kraus, Lehmann, and Magidor, and they have some general irrelevance and direct inference properties. Moreover, the new notions of - and lexicographic entailment satisfy the property of rational monotonicity. Furthermore, the new notions of -, lexicographic, and conditional entailment are proper generalizations of both their classical counterparts and the classical notion of logical entailment for conditional constraints. Finally, we provide algorithms for reasoning under the new formalisms, and we analyze its computational com...

Preferences among acts are analyzed in the style of L. Savage, but as partially ordered. The rationality postulates considered are weaker than Savage's on three counts. The Sure Thing Principle is derived in this setting. The postulates are shown to lead to a characterization of generalized qualitative probability that includes and blends both traditional qualitative probability and the ranked structures used in logical approaches. 1

Bohr: It was a fascinating paradox. Heisenberg: You actually loved the paradoxes, that’s your problem. You revelled in the contradictions.

Different qualitative models have been proposed for decision under uncertainty in Artificial Intelligence, but they generally fail to satisfy the principle of strict Pareto dominance or principle of "efficiency", in contrast to the classical numerical criterion — expected utility. In [Dubois and Prade, 1995J qualitative criteria based on possibility theory have been proposed, that are appealing but inefficient in the above sense. The question is whether it is possible to reconcile possibilistic criteria and efficiency. The present paper shows that the answer is yes, and that it leads to special kinds of expected utilities. It is also shown that although numerical, these expected utilities remain qualitative: they lead to two different decision procedures based on min, max and reverse operators only, generalizing the leximin and leximax orderings of vectors. 1 Introduction and

This paper proposes a deviation from the von Neumann-Morgenstern (vNM) postulates paradigm in decision theory. It suggests that it may, in certain circumstances, be rational to judge alternatives according to the issues in their main focus. If these issues are deemed as equal, the alternatives will continue to be judged as equal even if they are mixed with different side-effects - side-effects which would not be judged as equal were they to be in the main focus themselves. This contradicts the vNM Independence axiom. Moreover, outcomes of issues in the main focus may completely overshadow the outcomes of the side-issues, so alternatives of the former may be judged as infinitely more (or infinitely less) preferable than those of the latter. This contradicts the vNM Continuity axiom.

The relationship between Popper spaces (conditional probability spaces that satisfy some regularity conditions), lexicographic probability systems (LPS’s) [Blume, Brandenburger, and Dekel 1991a; Blume, Brandenburger, and Dekel 1991b], and nonstandard probability spaces (NPS’s) is considered. If countable additivity is assumed, Popper spaces and a subclass of LPS’s are equivalent; without the assumption of countable additivity, the equivalence no longer holds. If the state space is finite, LPS’s are equivalent to NPS’s. However, if the state space is infinite, NPS’s are shown to be more general than LPS’s. JEL classification numbers: C70; D80; D81; 1

Suppose that each player in a game is rational, each player thinks the other players are rational, and so on. Also, suppose that rationality is taken to incorporate an admissibility requirement–i.e., the avoidance of weakly dominated strategies. Which strategies can be played? We provide an epistemic framework in which to address this question. Specifically, we formulate conditions of “rationality and mth-order assumption of rationality ” (RmAR) and “rationality and common assumption of rationality ” (RCAR). We show: (i) RCAR is characterized by a solution concept called a “self-admissible set; ” (ii) in a “complete ” type structure, RmAR is characterized by the set of strategies that survive m + 1 rounds of elimination of inadmissible strategies; (iii) under a non-triviality condition, RCAR is impossible in a complete structure.

Introduction The standard approach to modeling uncertainty is probability theory. In recent years, researchers, motivated by varying concerns including a dissatisfaction with some of the axioms of probability and a desire to represent information more qualitatively, have introduced a number of generalizations and alternatives to probability, including Dempster-Shafer belief functions [Shafer, 1976] , possibility measures [Dubois and Prade, 1990] , lexicographic probability [Blume et al., 1991] , and many others. Rather than investigating each of these approaches piecemeal, I consider here an approach to representing uncertainty that generalizes them all, and lets us understand their commonalities and differences. A plausibility measure [Friedman and Halpern, 1995] associates with a set a plausibility, which is just an element in a partially ordered space. The only real requirement is that if U is a subset of V , the

The concept of ‘fully permissible sets’ is defined by an algorithm that eliminates strategy subsets. It is characterized as choice sets when there is common certain belief of the event that each player prefer one strategy to another if and only if the former weakly dominates the latter on the set of all opponent strategies or on the union of the choice sets that are deemed possible for the opponent. The concept refines the Dekel–Fudenberg procedure and captures aspects of forward induction.