2016/09/28 by Daniel Hernández–Hernández, Hernández-Hernández, Daniel, Mihai Ŝırbu +1
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Game Theory and Voting Systems #Markov Chains and Monte Carlo Methods #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1609.09173
openalex publication_date 2016/09/28 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
For a zero-sum stochastic game which does not satisfy the Isaacs condition,\nwe provide a value function representation for an Isaacs-type equation whose\nHamiltonian lies in between the lower and upper Hamiltonians, as a convex\ncombination of the two. For the general case (i.e. the convex combination is\ntime and state dependent) our representation amounts to a random change of the\nrules of the game, to allow each player at any moment to see the other player's\naction or not, according to a coin toss with probabilities of heads and tails\ngiven by the convex combination appearing in the PDE. If the combination is\nstate independent, then the rules can be set all in advance, in a deterministic\nway. This means that tossing the coin along the game, or tossing it repeatedly\nright at the beginning leads to the same value. The representations are\nasymptotic, over time discretizations. Space discretization is possible as\nwell, leading to similar results.\n