Cooperative games in strategic form

In this paper we view bargaining and cooperation as an interaction superimposed on a strategic form game. A multistage bargaining procedure for N players, the proposer commitment procedure, is presented. It is inspired by Nash s two-player variable-threat model; a key feature is the commitment to threats. We establish links to classical cooperative game theory solutions, such as the Shapley value in the transferable utility case. However, we show that even in standard pure exchange economies the traditional coalitional function may not be adequate when utilities are not transferable.

A general class of adaptative strategies

We exhibit and characterize an entire class of simple adaptive strategies,in the repeated play of a game, having the Hannan-consistency property: In the long-run, the player is guaranteed an average payoff as large as the best-reply payoff to the empirical distribution of play of the otherplayers; i.e., there is no "regret." Smooth fictitious play (Fudenberg and Levine [1995]) and regret-matching (Hart and Mas-Colell [1998]) areparticular cases. The motivation and application of this work come from the study of procedures whose empirical distribution of play is, in thelong-run, (almost) a correlated equilibrium. The basic tool for the analysis is a generalization of Blackwell's [1956a] approachability strategy for games with vector payoffs.

Stochastic uncoupled dynamics and Nash equilibrium

In this paper we consider dynamic processes, in repeated games, that are subject to the natural informational restriction of uncoupledness. We study the almost sure convergence to Nash equilibria, and present a number of possibility and impossibility results. Basically, we show that if in addition to random moves some recall is introduced, then successful search procedures that are uncoupled can be devised. In particular, to get almost sure convergence to pure Nash equilibria when these exist, it su±ces to recall the last two periods of play.

Finite horizon bargaining and the consistent field

This paper explores the relationships between noncooperative bargaining games and the consistent value for non-transferable utility (NTU) cooperative games. A dynamic approach to the consistent value for NTU games is introduced: the consistent vector field. The main contribution of the paper is to show that the consistent field is intimately related to the concept of subgame perfection for finite horizon noncooperative bargaining games, as the horizon goes to infinity and the cost of delay goes to zero. The solutions of the dynamic system associated to the consistent field characterize the subgame perfect equilibrium payoffs of the noncooperative bargaining games. We show that for transferable utility, hyperplane and pure bargaining games, the dynamics of the consistent fields converge globally to the unique consistent value. However, in the general NTU case, the dynamics of the consistent field can be complex. An example is constructed where the consistent field has cyclic solutions; moreover, the finite horizon subgame perfect equilibria do not approach the consistent value.

A simple adaptive procedure leading to correlated equilibrium

We propose a simple adaptive procedure for playing a game. In thisprocedure, players depart from their current play with probabilities thatare proportional to measures of regret for not having used other strategies(these measures are updated every period). It is shown that our adaptiveprocedure guaranties that with probability one, the sample distributionsof play converge to the set of correlated equilibria of the game. Tocompute these regret measures, a player needs to know his payoff functionand the history of play. We also offer a variation where every playerknows only his own realized payoff history (but not his payoff function).

Autoecología de los hayedos catalanes

Este estudio está basado en el muestreo de campo y posterior análisis de 24 parcelas de hayedo seleccionadas mediante una estratificación de su área de distribución basada en la clasificación CLATERES de la Ecorregión Catalano-Aragonesa. En cada parcela se han evaluado 3 parámetros fisiográficos, 15 climáticos y 18 edáficos, a partir de los cuales se han establecido sus valores paramétricos centrales y marginales que permiten definir los hábitats fisiográfico, climático y edáfico de las masas de Fagus sylvatica L. en Cataluña. Los hayedos catalanes se presentan sobre substratos litológicos muy diversos (plutonitas, vulcanitas, metamorfitas y sedimentitas, tanto ácidas como básicas), con texturas predominantes francas, franco-arenosas o franco-limosas. Los suelos, según FAO, son mayoritariamente cambisoles. A pesar de que la capacidad de retención de agua de sus suelos es escasa, la sequía fisiológica es reducida. Los humus predominantemente pertenecen a los tipos mull forestal y mull cálcico. Además, se presentan una serie de parámetros selvícolas ( Densidad de pies y densidad de chirpiales, Area basimétrica, Altura Total dominante, Índices de Hart-Becking, Índice de Calidad de Estación y Edad de la masa) que al correlacionarlos con los ecológicos nos ha permitido comprobar que los mejores hayedos se encuentran en las localizaciones más térmicas, en las que incluso se podría producir sequía fisiológica si no fuera por que existen suficientes precipitaciones estivales.