arXiv subjects

Michele Crescenzi

Publications and source records attributed to Michele Crescenzi.

5 recordsLinked to original sources

arXiv2026

Nested Removal of Strictly Dominated Strategies in Infinite Games

We compare two procedures for the iterated removal of strictly dominated strategies. In the nested procedure, a strategy of a player is removed only if it is dominated by an unremoved strategy. The universal procedure is more comprehensive for it allows the removal of strategies that are dominated by previously removed ones. Outside the class of finite games, the two procedures may lead to different outcomes in that the universal one is always order independent while the other is not. We provide necessary and sufficient conditions for the equivalence of the two procedures. The conditions we give are based on completely bounded subsets of strategy profiles, which are variations of the bounded mechanisms from the literature on full implementation. The two elimination procedures are also shown to be equivalent in quasisupermodular games as well as in games with compact strategy spaces and upper semicontinuous payoff functions. Finally, we give an example of a game in which the nested procedure is order independent but not equivalent to the universal one, thus showing that order independence is not sufficient to guarantee the equivalence of the two elimination procedures.

econ.TH↗

arXiv2025

A choice-based axiomatization of Nash equilibrium

An axiomatic characterization of Nash equilibrium is provided for games in normal form. The Nash equilibrium correspondence is shown to be fully characterized by four simple and intuitive axioms, two of which are inspired by contraction and expansion consistency properties from the literature on abstract choice theory. The axiomatization applies to Nash equilibria in pure and mixed strategies alike, to games with strategy sets of any cardinality, and it does not require that players' preferences have a utility or expected utility representation.

econ.TH↗

arXiv2025

Group knowledge and individual introspection

We study distributed knowledge, which is what privately informed agents come to know by communicating freely with one another and sharing everything they know. Knowledge is not necessarily partitional: agents may be boundedly rational and differ in the ability to form higher-order knowledge. We model the inference making process that leads to distributed knowledge, and we do that by introducing revision operators and revision types. Due to the heterogeneity of reasoning abilities, inference making turns out to be order dependent. We show that there are two qualitatively different cases of how distributed knowledge is attained. In the first, distributed knowledge is determined by any group member who can replicate all the inferences that anyone else in the group makes. This finding is in line with the extant literature. In the second case, no member can replicate all the inferences made within the group. As a result, distributed knowledge is determined by any two group members who can jointly replicate what anyone else infers. This case can be interpreted as a form of wisdom of crowd effect and shows that, contrary to what is generally believed, distributed knowledge cannot always be reduced to the reasoning abilities of a single group member.

econ.TH↗

arXiv2022

Coordination through ambiguous language

We provide a syntactic construction of correlated equilibrium. For any finite game, we study how players coordinate their play on a signal by means of a public strategy whose instructions are expressed in some natural language. Language can be ambiguous in that different players may assign different truth values to the very same formula in the same state of the world. We model ambiguity using the player-dependent logic of Halpern and Kets (2015). We show that, absent any ambiguity, self-enforcing coordination always induces a correlated equilibrium of the underlying game. When language ambiguity is allowed, self-enforcing coordination strategies induce subjective correlated equilibria.

econ.TH↗

arXiv2022

Learning to agree over large state spaces

We study how a consensus emerges in a finite population of like-minded individuals who are asymmetrically informed about the realization of the true state of the world. Agents observe a private signal about the state and then start exchanging messages. Generalizing the classical model of rational dialogues of Geanakoplos and Polemarchakis (1982) and its subsequent extensions, we dispense with the standard assumption that the state space is a probability space and we do not put any bound on the cardinality of the state space itself or the information partitions. We show that a class of rational dialogues can be found that always lead to consensus provided that three main conditions are met. First, everybody must be able to send messages to everybody else, either directly or indirectly. Second, communication must be reciprocal. Finally, agents need to have the opportunity to engage in dialogues of transfinite length.

econ.TH↗