288 research outputs found
Operator approach to values of stochastic games with varying stage duration
We study the links between the values of stochastic games with varying stage
duration , the corresponding Shapley operators and and
the solution of . Considering general non
expansive maps we establish two kinds of results, under both the discounted or
the finite length framework, that apply to the class of "exact" stochastic
games. First, for a fixed length or discount factor, the value converges as the
stage duration go to 0. Second, the asymptotic behavior of the value as the
length goes to infinity, or as the discount factor goes to 0, does not depend
on the stage duration. In addition, these properties imply the existence of the
value of the finite length or discounted continuous time game (associated to a
continuous time jointly controlled Markov process), as the limit of the value
of any time discretization with vanishing mesh.Comment: 22 pages, International Journal of Game Theory, Springer Verlag, 201
Asymptotic Properties of Optimal Trajectories in Dynamic Programming
We prove in a dynamic programming framework that uniform convergence of the
finite horizon values implies that asymptotically the average accumulated
payoff is constant on optimal trajectories. We analyze and discuss several
possible extensions to two-person games.Comment: 9 page
Stochastic Approximations and Differential Inclusions
L'approche en termes de systèmes dynamiques de l'approximation stochastique est étendue au cas ou l'équation différentielle moyenne est remplacée par une inclusion différentielle. Le théorème de Benaim et Hirsch sur l'ensemble limite est étendu a ce cas. On étudie en détail les ensembles ICT et les attracteurs. On donne des applications a des questions de théorie des jeux, en particulier concernant le théorème d'approchabilite de Blackwell et la convergence de "fictitious play".Approximation stochastique;Système dynamique multivalue
Time Average Replicator and Best Reply Dynamics
Using an explicit representation in terms of the logit map we show, in a unilateral framework, that the time average of the replicator dynamics is a perturbed solution of the best reply dynamics.replicator dynamics; best reply dynamics; logit map; perturbed differential inclusion; internally chain transitive set; attractor
On values of repeated games with signals
We study the existence of different notions of value in two-person zero-sum
repeated games where the state evolves and players receive signals. We provide
some examples showing that the limsup value (and the uniform value) may not
exist in general. Then we show the existence of the value for any Borel payoff
function if the players observe a public signal including the actions played.
We also prove two other positive results without assumptions on the signaling
structure: the existence of the value in any game and the existence of
the uniform value in recursive games with nonnegative payoffs.Comment: Published at http://dx.doi.org/10.1214/14-AAP1095 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
e-Consistent Equilibrium
We deal with the concept of e-consistent equilibrium which corresponds to strategies inducing an e-equilbrium in any subgame reached along the play path. Examples and existence conditions are given.
- …