Brodgar Downhole Gauge Analysis with Deconvolution

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Explicit Formulas for Repeated Games with Absorbing States

Explicit formulas for the asymptotic value and the asymptotic minmax of finite discounted absorbing games are provided. New simple proofs for the existence of the limits when the players are more and more patient (i.e. when the discount factor goes zero) are given. Similar characterizations for stationary Nash equilibrium payoffs are obtained. The results may be extended to absorbing games with compact action sets and jointly continuous payoff functions.Repeated games, stochastic games, value, minmax, Nash equilibrium

Coalitional Equilibria of Strategic Games

Let N be a set of players, C the set of permissible coalitions and G an N-playerstrategic game. A profile is a coalitional-equilibrium if no coalition permissible coalition in C has a unilateral deviation that profits to all its members. Nash-equilibria consider only single player coalitions and Aumann strong-equilibria permit all coalitions to deviate. A new fixed point theorem allows to obtain a condition for the existence of coalitional equilibria that covers Glicksberg for the existence of Nash-equilibria and is related to Ichiishi's condition for the existence of Aumann strong-equilibria.Fixed point theorems, maximum of non-transitive preferences, Nash and strong equilibria, coalitional equilibria

Irreversible Games with Incomplete Information: The Asymptotic Value

Les jeux irréversibles sont des jeux stochastiques où une fois un état est quitté, il n'est plus jamais revisité. Cette classe contient les jeux absorbants. Cet article démontre l'existence et une caractérisation de la valeur asymptotique pour tout jeu irréversible fini à information incomplète des deux côtés. Cela généralise Mertens et Zamir 1971 pour les jeux répétés à information incomplète des deux côtés et Rosenberg 2000 pour les jeux absorbants à information incomplète d'un côté.Jeux stochastiques; jeux répétés; information incomplète; valeur asymptotique; principe de comparaison; inégalités variationelles

Equilibrium in Two-Player Non-Zero-Sum Dynkin Games in Continuous Time

We prove that every two-player non-zero-sum Dynkin game in continuous time admits an epsilon-equilibrium in randomized stopping times. We provide a condition that ensures the existence of an epsilon-equilibrium in non-randomized stopping times

Inertial game dynamics and applications to constrained optimization

Aiming to provide a new class of game dynamics with good long-term rationality properties, we derive a second-order inertial system that builds on the widely studied "heavy ball with friction" optimization method. By exploiting a well-known link between the replicator dynamics and the Shahshahani geometry on the space of mixed strategies, the dynamics are stated in a Riemannian geometric framework where trajectories are accelerated by the players' unilateral payoff gradients and they slow down near Nash equilibria. Surprisingly (and in stark contrast to another second-order variant of the replicator dynamics), the inertial replicator dynamics are not well-posed; on the other hand, it is possible to obtain a well-posed system by endowing the mixed strategy space with a different Hessian-Riemannian (HR) metric structure, and we characterize those HR geometries that do so. In the single-agent version of the dynamics (corresponding to constrained optimization over simplex-like objects), we show that regular maximum points of smooth functions attract all nearby solution orbits with low initial speed. More generally, we establish an inertial variant of the so-called "folk theorem" of evolutionary game theory and we show that strict equilibria are attracting in asymmetric (multi-population) games - provided of course that the dynamics are well-posed. A similar asymptotic stability result is obtained for evolutionarily stable strategies in symmetric (single- population) games.Comment: 30 pages, 4 figures; significantly revised paper structure and added new material on Euclidean embeddings and evolutionarily stable strategie

Stopping games in continuous time

We study two-player zero-sum stopping games in continuous time and infinite horizon. We prove that the value in randomized stopping times exists as soon as the payoff processes are right-continuous. In particular, as opposed to existing literature, we do not assume any conditions on the relations between the payoff processes. We also show that both players have simple epsilon- optimal randomized stopping times; namely, randomized stopping times which are small perturbations of non-randomized stopping times.Comment: 21 page