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A fundamental shortcoming of the concept of Nash equilibrium is its computational intractability: approximating Nash equilibria in normal-form games is PPAD-hard. In this paper, inspired by the ideas of smoothed analysis, we introduce a…
We consider a gossip approach for finding a Nash equilibrium in a distributed multi-player network game. We extend previous results on Nash equilibrium seeking to the case when the players' cost functions may be affected by the actions of…
Aggregative games have many industrial applications, and computing an equilibrium in those games is challenging when the number of players is large. In the framework of atomic aggregative games with coupling constraints, we show that…
We study the effectiveness of iterated elimination of strictly-dominated actions in random games. We show that dominance solvability of games is vanishingly small as the number of at least one player's actions grows. Furthermore,…
Determining a Nash equilibrium in a $2$-player non-zero sum game is known to be PPAD-hard (Chen and Deng (2006), Chen, Deng and Teng (2009)). The problem, even when restricted to win-lose bimatrix games, remains PPAD-hard (Abbott, Kane and…
A fundamental open problem in monotone game theory is the computation of a specific generalized Nash equilibrium (GNE) among all the available ones, e.g. the optimal equilibrium with respect to a system-level objective. The existing GNE…
This paper studies the distributed generalized Nash equilibrium seeking problem for aggregative games with coupling constraints, where each player optimizes its strategy depending on its local cost function and the estimated strategy…
In this paper, we present a method for finding approximate Nash equilibria in a broad class of reachability games. These games are often used to formulate both collision avoidance and goal satisfaction. Our method is computationally…
In this paper, we study the problem of the distributed Nash equilibrium seeking of N-player games over jointly strongly connected switching networks. The action of each player is governed by a class of uncertain nonlinear systems. Our…
Playing a symmetric bi-matrix game is usually physically implemented by sharing pairs of 'objects' between two players. A new setting is proposed that explicitly shows effects of quantum correlations between the pairs on the structure of…
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,…
Is there an algorithm that takes a game in normal form as input, and outputs a Nash equilibrium? If the payoffs are integers, the answer is yes, and lot of work has been done in its computational complexity. If the payoffs are permitted to…
We consider the problem of learning sparse polymatrix games from observations of strategic interactions. We show that a polynomial time method based on $\ell_{1,2}$-group regularized logistic regression recovers a game, whose Nash…
We compute a parametric description of the totally mixed Nash equilibria of a generic game in normal form with pre-fixed structure. Using this representation, we show conditions under which a game has the maximum possible number of this…
We present a fully-distributed algorithm for Nash equilibrium seeking in aggregative games over networks. The proposed scheme endows each agent with a gradient-based scheme equipped with a tracking mechanism to locally reconstruct the…
Auctions are modeled as Bayesian games with continuous type and action spaces. Determining equilibria in auction games is computationally hard in general and no exact solution theory is known. We introduce an algorithmic framework in which…
Distributed optimization and Nash equilibrium (NE) seeking problems have drawn much attention in the control community recently. This paper studies a class of non-cooperative games, known as N-cluster game, which subsumes both cooperative…
Nash equilibrium is a solution concept in non-strictly competitive, non-cooperative game theory that finds applications in various scientific and engineering disciplines. A non-strictly competitive, non-cooperative game model is presented…
We analyse the computational complexity of finding Nash equilibria in stochastic multiplayer games with $\omega$-regular objectives. While the existence of an equilibrium whose payoff falls into a certain interval may be undecidable, we…
The Nash equilibrium problem is a widely used tool to model non-cooperative games. Many solution methods have been proposed in the literature to compute solutions of Nash equilibrium problems with continuous strategy sets, but, besides some…