Related papers: Universal Nash Equilibrium Strategies for Differen…
Zero-sum games arise in a wide variety of problems, including robust optimization and adversarial learning. However, algorithms deployed for finding a local Nash equilibrium in these games often converge to non-Nash stationary points. This…
In this paper, we study a distributed continuous-time design for aggregative games with coupled constraints in order to seek the generalized Nash equilibrium by a group of agents via simple local information exchange. To solve the problem,…
We consider two classes of constrained finite state-action stochastic games. First, we consider a two player nonzero sum single controller constrained stochastic game with both average and discounted cost criterion. We consider the same…
We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…
Many efficient algorithms have been designed to recover Nash equilibria of various classes of finite games. Special classes of continuous games with infinite strategy spaces, such as polynomial games, can be solved by semidefinite…
This paper analyses two-player nonzero-sum games of optimal stopping on a class of linear regular diffusions with not non-singular boundary behaviour (in the sense of It\^o and McKean (1974), p.\ 108). We provide sufficient conditions under…
This paper considers a class of noncooperative games in which the feasible decision sets of all players are coupled together by a coupled inequality constraint. Adopting the variational inequality formulation of the game, we first introduce…
In game theory, the concept of Nash equilibrium reflects the collective stability of some individual strategies chosen by selfish agents. The concept pertains to different classes of games, e.g. the sequential games, where the agents play…
The preferences of players in non-cooperative games represent their choice in the set of available options, which meet the completeness property if players are able to compare any pair of available options. In the existing literature, the…
Secure equilibrium is a refinement of Nash equilibrium, which provides some security to the players against deviations when a player changes his strategy to another best response strategy. The concept of secure equilibrium is specifically…
Successful algorithms have been developed for computing Nash equilibrium in a variety of finite game classes. However, solving continuous games -- in which the pure strategy space is (potentially uncountably) infinite -- is far more…
In this paper we investigate two-player zero-sum stochastic differential games with an ergodic payoff, in which the diffusion coefficient does not need to be non-degenerate. We first establish the existence of a viscosity solution to the…
We study a discrete-time finite-horizon two-players nonzero-sum stopping game where the filtration of Player 1 is richer than the filtration of Player 2. A major difficulty which is caused by the information asymmetry is that Player 2 may…
The value of a zero-sum differential games is known to exist, under Isaacs' condition, as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation. In this note we provide a self-contained proof based on the construction of…
This paper develops an algorithm for upper- and lower-bounding the value function for a class of linear time-varying games subject to convex control sets. In particular, a two-player zero-sum differential game is considered where the…
This paper focuses on a kind of linear quadratic non-zero sum differential game driven by backward stochastic differential equation with asymmetric information, which is a natural continuation of Wang and Yu [IEEE TAC (2010) 55: 1742-1747,…
This paper explores distributed Nash equilibrium seeking problems for games in which the players have limited knowledge on other players' actions. In particular, the involved players are considered to be high-order integrators with their…
Towards characterizing the optimization landscape of games, this paper analyzes the stability of gradient-based dynamics near fixed points of two-player continuous games. We introduce the quadratic numerical range as a method to…
We study $n$-agent Bayesian Games with $m$-dimensional vector types and linear payoffs, also called Linear Multidimensional Bayesian Games. This class of games is equivalent with $n$-agent, $m$-game Uniform Multigames. We distinguish…
This paper investigates a class of general linear-quadratic mean field games with common noise, where the diffusion terms of the system contain the state variables, control variables, and the average state terms. We solve the problem using…