Related papers: Projected solution for Generalized Nash Games with…
We study Nash equilibrium problems with mixed-integer variables in which each player solves a mixed-integer optimization problem parameterized by the rivals' strategies. We distinguish between standard Nash equilibrium problems (NEPs),…
The set of Nash equilibria of a finite game is the set of nonnegative solutions to a system of polynomial equations. In this survey article we describe how to construct certain special games and explain how to find all the complex roots of…
We address the generalized Nash equilibrium seeking problem for a population of agents playing aggregative games with affine coupling constraints. We focus on semi-decentralized communication architectures, where there is a central…
In this paper, we consider the problem of finding a Nash equilibrium in a multi-player game over generally connected networks. This model differs from a conventional setting in that players have partial information on the actions of their…
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…
A fundamental problem with the Nash equilibrium concept is the existence of certain "structurally deficient" equilibria that (i) lack fundamental robustness properties, and (ii) are difficult to analyze. The notion of a "regular" Nash…
This paper has two central aims: first, to provide simple conditions under which the generalized games in choice form and, consequently, the abstract economies, admit equilibrium; second, to study the solvability of several types of systems…
We propose fully-distributed algorithms for Nash equilibrium seeking in aggregative games over networks. We first consider the case where local constraints are present and we design an algorithm combining, for each agent, (i) the projected…
In this paper, a distributed non-model based seeking algorithm which combines the extremum seeking control (ESC) jointly with learning algorithms is proposed to seek a generalized Nash equilibrium (GNE) for a class of noncooperative games…
This paper investigates a fully distributed adaptive Nash equilibrium (NE) seeking algorithm for constrained noncooperative games with prescribed-time stability. On the one hand, prescribed-time stability for the proposed NE seeking…
In 1953, Kuhn showed that every sequential game has a Nash equilibrium by showing that a procedure, named ``backward induction'' in game theory, yields a Nash equilibrium. It actually yields Nash equilibria that define a proper subclass of…
We consider a game in which the action set of each player is uncountable, and show that, from weak assumptions on the common prior, any mixed strategy has an approximately equivalent pure strategy. The assumption of this result can be…
Ensuring that AI systems make strategic decisions aligned with the specified preferences in adversarial sequential interactions is a critical challenge for developing trustworthy AI systems, especially when the environment is stochastic and…
Generalized Nash equilibrium problems with mixed-integer variables constitute an important class of games in which each player solves a mixed-integer optimization problem, where both the objective and the feasible set is parameterized by…
We consider the problem of finding a Nash equilibrium (NE) in a general-sum game, where player $i$'s objective is $f_i(x)=f_i(x_1,...,x_n)$, with $x_j\in\mathbb{R}^{d_j}$ denoting the strategy variables of player $j$. Our focus is on…
Computational aspects of solution notions such as Nash equilibrium have been extensively studied, including settings where the ultimate goal is to find an equilibrium that possesses some additional properties. Furthermore, in order to…
The betweenness property of preference relations states that a probability mixture of two lotteries should lie between them in preference. It is a weakened form of the independence property and hence satisfied in expected utility theory…
We study the computational complexity of Nash equilibria in concurrent games with limit-average objectives. In particular, we prove that the existence of a Nash equilibrium in randomised strategies is undecidable, while the existence of a…
This paper introduces risk-revising players to a class of games with incomplete information. These players enter the game with ex ante risk preferences represented by coherent risk measures and develop time-consistent interim revisions of…
We consider the basic problem of approximating Nash equilibria in noncooperative games. For monotone games, we design continuous time flows which converge in an averaged sense to Nash equilibria. We also study mean field equilibria, which…