Related papers: Multilinear formulations for computing Nash equili…
Since the seminal PPAD-completeness result for computing a Nash equilibrium even in two-player games, an important line of research has focused on relaxations achievable in polynomial time. In this paper, we consider the notion of…
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…
In this paper, Nash equilibrium seeking among a network of players is considered. Different from many existing works on Nash equilibrium seeking in non-cooperative games, the players considered in this paper cannot directly observe the…
This paper addresses the problem of learning a Nash equilibrium in $\gamma$-discounted multiplayer general-sum Markov Games (MG). A key component of this model is the possibility for the players to either collaborate or team apart to…
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 $PPAD$…
In two player bi-matrix games with partial monitoring, actions played are not observed, only some messages are received. Those games satisfy a crucial property of usual bi-matrix games: there are only a finite number of required (mixed)…
AI in Math deals with mathematics in a constructive manner so that reasoning becomes automated, less laborious, and less error-prone. For algorithms, the question becomes how to automate analyses for specific problems. For the first time,…
We introduce a new algorithm for the numerical computation of Nash equilibria of competitive two-player games. Our method is a natural generalization of gradient descent to the two-player setting where the update is given by the Nash…
We consider strongly monotone games with convex separable coupling constraints, played by dynamical agents, in a partial-decision information scenario. We start by designing continuous-time fully distributed feedback controllers, based on…
We study multi-strategies in multiplayer reachability games played on finite graphs. A multi-strategy prescribes a set of possible actions, instead of a single action as usual strategies: it represents a set of all strategies that are…
We introduce Cut-and-Play, a practically-efficient algorithm for computing Nash equilibria in simultaneous non-cooperative games where players decide via nonconvex and possibly unbounded optimization problems with separable payoff…
Inspired by a paper of R. W. Rosenthal, we investigate generalized Nash-equilibria of integer programming games. We show that generalized Nash-equilibria always exist and are related to an optimal solution of a so-called N-fold integer…
Nash equilibria and Pareto optimality are two distinct concepts when dealing with multiple criteria. It is well known that the two concepts do not coincide. However, in this work we show that it is possible to characterize the set of all…
In many real-world settings agents engage in strategic interactions with multiple opposing agents who can employ a wide variety of strategies. The standard approach for designing agents for such settings is to compute or approximate a…
The number of Nash equilibria of the mixed extension of a generic finite game in normal form is finite and odd. This raises the question how large the number can be, depending on the number of players and the numbers of their pure…
Game theory provides a well-established framework for the analysis of concurrent and multi-agent systems. The basic idea is that concurrent processes (agents) can be understood as corresponding to players in a game; plays represent the…
We consider a variant of the hide-and-seek game in which a seeker inspects multiple hiding locations to find multiple items hidden by a hider. Each hiding location has a maximum hiding capacity and a probability of detecting its hidden…
Environments with multi-agent interactions often result a rich set of modalities of behavior between agents due to the inherent suboptimality of decision making processes when agents settle for satisfactory decisions. However, existing…
In this paper we present a novel generic mapping between Graphical Games and Markov Random Fields so that pure Nash equilibria in the former can be found by statistical inference on the latter. Thus, the problem of deciding whether a…
A version of the Monty Hall problem is presented where the players are permitted to select quantum strategies. If the initial state involves no entanglement the Nash equilibrium in the quantum game offers the players nothing more than can…