Related papers: A dynamic that evolves toward a Nash equilibrium
Computing approximate Nash equilibria in multi-player general-sum Markov games is a computationally intractable task. However, multi-player Markov games with certain cooperative or competitive structures might circumvent this…
Various social contexts ranging from public goods provision to information collection can be depicted as games of strategic interactions, where a player's well-being depends on her own action as well as on the actions taken by her…
We train two neural networks adversarially to play static games. At each iteration, a row and column network observe a new random bimatrix game and output individual mixed strategies. The parameters of each network are independently updated…
In evolutionary game theory, it is customary to be partial to the dynamical models possessing fixed points so that they may be understood as the attainment of evolutionary stability, and hence, Nash equilibrium. Any show of periodic or…
In an $\epsilon$-Nash equilibrium, a player can gain at most $\epsilon$ by unilaterally changing his behaviour. For two-player (bimatrix) games with payoffs in $[0,1]$, the best-known$\epsilon$ achievable in polynomial time is 0.3393. In…
We analyze, using a dynamical systems approach, the replicator dynamics for the asymmetric Hawk-Dove game in which there is a set of four pure strategies with arbitrary payoffs. We give a full account of the equilibrium points and their…
We study model-based and model-free policy optimization in a class of nonzero-sum stochastic dynamic games called linear quadratic (LQ) deep structured games. In such games, players interact with each other through a set of weighted…
We consider games of strategic substitutes and strategic complements on networks. We introduce two different evolutionary dynamics in order to refine their multiplicity of equilibria, and we analyse the system through a mean field approach.…
This paper considers a class of strategic scenarios in which two networks of agents have opposing objectives with regards to the optimization of a common objective function. In the resulting zero-sum game, individual agents collaborate with…
We suggest a novel stochastic-approximation algorithm to compute a symmetric Nash-equilibrium strategy in a general queueing game with a finite action space. The algorithm involves a single simulation of the queueing process with dynamic…
We consider a class of continuous-time dynamic games involving a large number of players. Each player selects actions from a finite set and evolves through a finite set of states. State transitions occur stochastically and depend on the…
Saddle point with a given Morse index on a potential energy surface is an important object related to energy landscape in physics and chemistry. Efficient numerical methods based on iterative minimization formulation have been proposed in…
We consider multi-agent decision making, where each agent optimizes its cost function subject to constraints. Agents' actions belong to a compact convex Euclidean space and the agents' cost functions are coupled. We propose a distributed…
In the context of large population symmetric games, approximate Nash equilibria are introduced through equilibrium solutions of the corresponding mean field game in the sense that the individual gain from optimal unilateral deviation under…
The framework outlined in [arXiv:2010.13024] provides an approximation algorithm for computing Nash equilibria of normal form games. Since NASH is a well-known PPAD-complete problem, this framework has potential applications to other $PPAD$…
We introduce a stochastic learning process called the dampened gradient approximation process. While learning models have almost exclusively focused on finite games, in this paper we design a learning process for games with continuous…
We study constrained bi-matrix games, with a particular focus on low-rank games. Our main contribution is a framework that reduces low-rank games to smaller, equivalent constrained games, along with a necessary and sufficient condition for…
We consider a dynamical system for computing Nash bargaining solutions on graphs and focus on its rate of convergence. More precisely, we analyze the edge-balanced dynamical system by Azar et al and fully specify its convergence for an…
Multi-time scale techniques, such as singular perturbations and averaging theory, have played an essential role in the development of distributed Nash equilibrium-seeking algorithms for network systems. Such techniques intrinsically rely on…
This work proposes a novel set of techniques for approximating a Nash equilibrium in a finite, normal-form game. It achieves this by constructing a new reformulation as solving a parameterized system of multivariate polynomials with tunable…