Emergent behaviour: Theory and experimentation using the MANA model.
Equilibria in a class of games and topological results implying their existence.
We survey results related to the problem of the existence of equilibria in some classes of infinitely repeated two-person games of incomplete information on one side, first considered by Aumann, Maschler and Stearns. We generalize this setting to a broader one of principal-agent problems. We also discuss topological results needed, presenting them dually (using cohomology in place of homology) and more systematically than in our earlier papers.
Equilibria in constrained concave bimatrix games
We study a generalization of bimatrix games in which not all pairs of players' pure strategies are admissible. It is shown that under some additional convexity assumptions such games have equilibria of a very simple structure, consisting of two probability distributions with at most two-element supports. Next this result is used to get a theorem about the existence of Nash equilibria in bimatrix games with a possibility of payoffs equal to -∞. The first of these results is a discrete counterpart...
Équité et altruisme dans le partage pragmatique
Erweitertes BERNOULLI-Prinzip und Petersburger Spiel
Estrategias óptimas de un juego bipersonal de suma cero y puntos de ensilladura del campo escalar asociado.
Definimos el campo escalar asociado a un juego bipersonal de suma cero. Estudiamos la existencia y unicidad de puntos estacionarios y obtenemos la forma general de los mismos en caso de unicidad. Se establece que todo punto estacionario es de ensilladura.La importancia del estudio anterior queda reflejada al establecer la equivalencia entre las estrategias óptimas simples de un juego y los puntos estacionarios del campo escalar asociado.El Teorema de Shapley-Snow [2] proporciona un método sistemático...
Existence of Nash equilibria in two-person stochastic games of resource extraction
This paper deals with two-person stochastic games of resource extraction under both the discounted and the mean payoff criterion. Under some concavity and additivity assumptions concerning the payoff and the transition probability function a stationary Nash equilibrium is shown to exist. The proof is based on Schauder-Tychonoff's fixed point theorem, applied to a suitable payoff vector space.