A game model referring to the control of independent discrete time stochastic processes
A game of fair division in the normal form
A note on robust Nash equilibria with uncertainties
In this short note, we investigate the framework where agents or players have some uncertainties upon their payoffs or losses, the behavior (or the type, number or any other characteristics) of other players. More specifically, we introduce an extension of the concept of Nash equilibria that generalize different solution concepts called by their authors, and depending on the context, either as robust, ambiguous, partially specified or with uncertainty aversion. We provide a simple necessary and...
A note on the first occurrence of strings.
A symbolic shortest path algorithm for computing subgame-perfect Nash equilibria
Consider games where players wish to minimize the cost to reach some state. A subgame-perfect Nash equilibrium can be regarded as a collection of optimal paths on such games. Similarly, the well-known state-labeling algorithm used in model checking can be viewed as computing optimal paths on a Kripke structure, where each path has a minimum number of transitions. We exploit these similarities in a common generalization of extensive games and Kripke structures that we name “graph games”. By extending...
Analyse mathématique élémentaire d'un jeu sportif
Un jeu sportif bien connu, les quatre coins, est l'objet de cette étude. Les règles de ce jeu déterminent une succession de déplacements qui sont organisés selon une structure de groupe. L'ensemble des graphes de déplacement peut être distribué selon trois partitions qui offrent un précieux support à l'étude expérimentale: on obtient alors des classes d'équivalence de type cyclique, de type spatial et de type métrique. Les règles sont porteuses d'une logique qui accorde une grande importance à l'espace...
Approximations of dynamic Nash games with general state and action spaces and ergodic costs for the players
The purpose of this paper is to prove existence of an ε -equilib- rium point in a dynamic Nash game with Borel state space and long-run time average cost criteria for the players. The idea of the proof is first to convert the initial game with ergodic costs to an ``equivalent" game endowed with discounted costs for some appropriately chosen value of the discount factor, and then to approximate the discounted Nash game obtained in the first step with a countable state space game for which existence...