48 citations · 155 across the 10 of their papers we have counts for
11 papers
Percolation Markov Decision Processes
Melissa González García, Guillaume Vigeral
We study Percolation Markov Decision Processes (PMDPs), in which the decision maker repeatedly moves a token through the d-dimensional integer lattice with deterministic transition…
Absorbing games with irrational values
Miquel Oliu-Barton
Can an absorbing game with rational data have an irrational limit value? Yes: In this note we provide the simplest examples where this phenomenon arises. That is, the following $3\…
Zero-sum Stochastic Games: Limit Optimal Trajectories
Sylvain Sorin, Guillaume Vigeral
We consider zero sum stochastic games. For every discount factor , a time normalization allows to represent the game as being played on the interval [0, 1]. We introduce the tra…
Semi-algebraic sets and equilibria of binary games
Guillaume Vigeral, Yannick Viossat
Any nonempty, compact, semi-algebraic set in [0, 1] n is the projection of the set of mixed equilibria of a finite game with 2 actions per player on its first n coordinates. A simi…
Operator approach to values of stochastic games with varying stage duration
Sylvain Sorin, Guillaume Vigeral
We study the links between the values of stochastic games with varying stage duration , the corresponding Shapley operators and and the solution of $\dot f…
A Zero-Sum Stochastic Game with Compact Action Sets and no Asymptotic Value
Guillaume Vigeral
We give an example of a zero-sum stochastic game with four states, compact action sets for each player, and continuous payoff and transition functions, such that the discounted val…