Luciano Méndez-Naya

On shortest path games

Abstract. A class of cooperative TU-games arising from shortest path problems is introduced and analyzed. Some conditions under which a shortest path game is balanced are obtained. Also an axiomatic characterization of the Shapley value for this class of games is provided.

Perfection of Nash equilibria in continuous games

Abstract In this paper we introduce a generalization of Seltens perfect equilibrium for continuous n -person games in normal form. We also study some properties of our new concept as well as its relationship with other equilibria. Some facts that we show contrast significantly with the finite theory.

Zero-Sum Continuous Games with No Compact Support

In this work, we study the mixed extension of the zero-sum two person games, with sets of pure strategies, semi-open on the right side real intervals, and continuous payoff function. It is proved that these games may not have a value and next we offer some conditions for the existence of a value in these games.

Density estimation using game theory

Abstract.In this note we show that the mathematical tools of cooperative game theory allow a successful approach to the statistical problem of estimating a density function. Specifically, any random sample of an absolutely continuous random variable determines a transferable utility game, the Shapley value of which proves to be an estimator of the density function of binned kernel and WARPing types, with good computational and statistical properties.

Weakly strict equilibria in finite normal form games

In this paper we introduce the weakly strict equilibrium for (mixed extensions of) finiten-person games. For those games we prove that our new concept is a strict refinement of the undominated Nash equilibrium concept. We show that their set of weakly strict equilibria is nonempty and coincides with their set of strict equilibria (when the latter is also non-empty) and we study the relation between our refinement and other noncooperative concepts.ZusammenfassungIn dieser Arbeit führen wir das schwach-strikte Gleichgewicht für die gemischte Erweiterung von endlichenn-Personen-Spielen ein. Für diese Spiele zeigen wird, daß dieses Konzept eine echte Verfeinerung des Nash-Gleichgewichts ist. Wir weisen nach, daß die Menge der schwach-strikten Gleichgewichte derartiger Spiele nicht leer ist und mit der Menge der strikten Gleichgewichte übereinstimmt, falls letztere nicht leer ist. Außerdem vergleichen wird das neue Konzept mit anderen in der Literatur vorgeschlagenen Gleichgewichtsbegriffen.

UNILATERAL COMMITMENTS IN FINITELY REPEATED GAMES

In this paper, we consider finitely repeated games (without discounting) in which players can make unilateral commitments (UC) regarding their sets of strategies. More precisely, we suppose that each player can restrict his original set of strategies in a preliminary round of the repeated game. In this round all of the players choose (simultaneously) a subset of their strategy sets. These choices (to whom we refer as UC) are publicly announced before the repeated game starts, and in the repeated game every player is committed to use strategies only from the subset chosen in the preliminary round. We are interested in the Nash equilibria (NE) of the overall game, for which we prove some kind of “folk theorem”. These kinds of UC have already been considered in Fáıña-Med́ın et al. (1998) who proved that, if such a preliminary round is included in a finitely repeated prisoners’ dilemma, then there is a symmetric subgame perfect equilibrium in which both players act cooperatively throughout the post-commitment stages of the game (if the number of repetitions is large enough). Here, we take a much more general framework because: (a) we consider finite repetitions of general n-person strategic games; (b) we analyse both the case in which only the preferences of the players are available and the case in which these preferences are represented by utility functions; and (c) we also study the effect of a preliminary round of commitments on one-shot games. It is clear that UC, as described above, try to catch an idea which is well-known (as testified, e.g. by sentences like “burning one’s boats out”), i.e. in nonzero-sum

Mental Equilibrium and Strategic Emotions

We model mental states as part of an equilibrium notion. In a mental equilibrium each player “selects” an emotional state that determines the player’s preferences over the outcomes of the game. These preferences typically differ from the players’ material preferences. The emotional states interact to play a Nash equilibrium and, in addition, each player’s mental state must be a best response to the mental states of the others (in the sense of maximizing material payoffs). We discuss the concept behind the definition of mental equilibrium and examine it in the context of some of the most popular games discussed in the experimental economics literature. In particular, our approach allows us to identify the mental states (the psychology) that lead players to play various prominent experimental outcomes. We provide necessary and sufficient conditions for mental equilibria to be sustained by material preferences. Finally, we discuss the concept of collective emotions, which is based on the idea that players ca...