Related papers: Strong Nash equilibria and mixed strategies
Generating payoff matrices of normal-form games at random, we calculate the frequency of games with a unique pure strategy Nash equilibrium in the ensemble of $n$-player, $m$-strategy games. These are perfectly predictable as they must…
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…
Computing equilibria of games is a central task in computer science. A large number of results are known for \emph{Nash equilibrium} (NE). However, these can be adopted only when coalitions are not an issue. When instead agents can form…
An extensive literature in economics and social science addresses contests, in which players compete to outperform each other on some measurable criterion, often referred to as a player's score, or output. Players incur costs that are an…
While Nash equilibria are guaranteed to exist, they may exhibit dense support, making them difficult to understand and execute in some applications. In this paper, we study $k$-sparse commitments in games where one player is restricted to…
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…
We study optimal equilibria in multi-player games. An equilibrium is optimal for a player, if her payoff is maximal. A tempting approach to solving this problem is to seek optimal Nash equilibria, the standard form of equilibria where no…
We study the problem of computing an approximate Nash equilibrium of continuous-action game without access to gradients. Such game access is common in reinforcement learning settings, where the environment is typically treated as a black…
In Feinstein and Rudloff (2023), it was shown that the set of Nash equilibria for any non-cooperative $N$ player game coincides with the set of Pareto optimal points of a certain vector optimization problem with non-convex ordering cone. To…
We study the computational complexity of decision problems about Nash equilibria in $m$-player games. Several such problems have recently been shown to be computationally equivalent to the decision problem for the existential theory of the…
We present a polynomial-time algorithm that always finds an (approximate) Nash equilibrium for repeated two-player stochastic games. The algorithm exploits the folk theorem to derive a strategy profile that forms an equilibrium by…
This paper analyzes the structure of mixed-strategy equilibria for Colonel Blotto games, where the outcome on each battlefield is a polynomial function of the difference between the two players' allocations. This paper severely reduces the…
Computing Nash equilibrium policies is a central problem in multi-agent reinforcement learning that has received extensive attention both in theory and in practice. However, provable guarantees have been thus far either limited to fully…
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…
A quantum Cournot game of which classical form game has multiple Nash equilibria is examined. Although the classical equilibria fail to be Pareto optimal, the quantum equilibrium exhibits the following two properties, (i) if the measurement…
We provide an in-depth study of Nash equilibria in multi-objective normal form games (MONFGs), i.e., normal form games with vectorial payoffs. Taking a utility-based approach, we assume that each player's utility can be modelled with a…
We study rational synthesis problems for concurrent games with omega-regular objectives. Our model of rationality considers only pure strategy Nash equilibria that satisfy either a social welfare or Pareto optimality condition with respect…
This paper tackles the problem of adversarial examples from a game theoretic point of view. We study the open question of the existence of mixed Nash equilibria in the zero-sum game formed by the attacker and the classifier. While previous…
Creating strong agents for games with more than two players is a major open problem in AI. Common approaches are based on approximating game-theoretic solution concepts such as Nash equilibrium, which have strong theoretical guarantees in…
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…