相关论文: Infinite asymptotic games

We study the problem of computing all Nash equilibria of a subclass of finite normal form games. With algebraic characterization of the games, we present a method for computing all its Nash equilibria. Further, we present a method for…

We introduce quantitative reductions, a novel technique for structuring the space of quantitative games and solving them that does not rely on a reduction to qualitative games. We show that such reductions exhibit the same desirable…

The objective of this book is to give a comprehensive presentation of the research field concerned with infinite duration games on graphs. Historically, these game models appeared in the study of automata and logic, and they later became…

Let X_i, i\in N, be i.i.d. B-valued random variables, where B is a real separable Banach space. Let \Phi be a smooth enough mapping from B into R. An asymptotic evaluation of Z_n=E(\exp (n\Phi (\sum_{i=1}^nX_i/n))), up to a factor (1+o(1)),…

We construct numerical approximations for Mean Field Games with fractional or nonlocal diffusions. The schemes are based on semi-Lagrangian approximations of the underlying control problems/games along with dual approximations of the…

We study mean field games and corresponding $N$-player games in continuous time over a finite time horizon where the position of each agent belongs to a finite state space. As opposed to previous works on finite state mean field games, we…

This paper investigates the discrete-time asynchronous games in which noncooperative agents seek to minimize their individual cost functions. Building on the assumption of partial asynchronism, i.e., each agent updates at least once within…

By resorting to the vector space structure of finite games, skew-symmetric games (SSGs) are proposed and investigated as a natural subspace of finite games. First of all, for two player games, it is shown that the skew-symmetric games form…

We develop a flexible stochastic approximation framework for analyzing the long-run behavior of learning in games (both continuous and finite). The proposed analysis template incorporates a wide array of popular learning algorithms,…

We consider turn-based game arenas for which we investigate uniformity properties of strategies. These properties involve bundles of plays, that arise from some semantical motive. Typically, we can represent constraints on allowed…

Graph games of infinite length are a natural model for open reactive processes: one player represents the controller, trying to ensure a given specification, and the other represents a hostile environment. The evolution of the system…

For a class of finite horizon first order mean field games and associated N-player games, we give a simple proof of convergence of symmetric N-player Nash equilibria in distributed open-loop strategies to solutions of the mean field game in…

Multi-dimensional mean-payoff and energy games provide the mathematical foundation for the quantitative study of reactive systems, and play a central role in the emerging quantitative theory of verification and synthesis. In this work, we…

We prove an optimal result of stability under $\ell_p$-sums of some concentration properties for Lipschitz maps defined on Hamming graphs into Banach spaces. As an application, we give examples of spaces with Szlenk index arbitrarily high…

The theory of mean field games aims at studying deterministic or stochastic differential games (Nash equilibria) as the number of agents tends to infinity. Since very few mean field games have explicit or semi-explicit solutions, numerical…

We consider an n-player symmetric stochastic game with weak interaction between the players. Time is continuous and the horizon and the number of states are finite. We show that the value function of each of the players can be approximated…

We introduce a simple class of mean field games with absorbing boundary over a finite time horizon. In the corresponding $N$-player games, the evolution of players' states is described by a system of weakly interacting It\^o equations with…

Infinitesimal contraction analysis, wherein global asymptotic convergence results are obtained from local dynamical properties, has proven to be a powerful tool for applications in biological, mechanical, and transportation systems. The…

This paper aims to solve two fundamental problems on finite or infinite horizon dynamic games with perfect or almost perfect information. Under some mild conditions, we prove (1) the existence of subgame-perfect equilibria in general…

We study infinite two-player games where one of the players is unsure about the set of moves available to the other player. In particular, the set of moves of the other player is a strict superset of what she assumes it to be. We explore…