Related papers: Learnable Mixed Nash Equilibria are Collectively R…
In this paper we consider strong Nash equilibria, in mixed strategies, for finite games. Any strong Nash equilibrium outcome is Pareto efficient for each coalition. First, we analyze the two--player setting. Our main result, in its simplest…
To verify the robustness of a program or protocol, it is common in the computer science community to rely on the theoretical framework of game theory. In particular, if one seeks to enforce a desired property, or specification, despite an…
We study repeated games where players use an exponential learning scheme in order to adapt to an ever-changing environment. If the game's payoffs are subject to random perturbations, this scheme leads to a new stochastic version of the…
We introduce a novel class of Nash equilibrium seeking dynamics for non-cooperative games with a finite number of players, where the convergence to the Nash equilibrium is bounded by a KL function with a settling time that can be upper…
In a society of multiple individuals, if everybody is only interested in maximizing his own payoff, will there exist any equilibrium for the society? John Nash proved more than 50 years ago that an equilibrium always exists such that nobody…
In response to a change, individuals may choose to follow the responses of their friends or, alternatively, to change their friends. To model these decisions, consider a game where players choose their behaviors and friendships. In…
We know that the Nash equilibria of a game cannot be computed efficiently unless $P = PPAD$. But can they be learned? Are there dynamics that (1) can be computed efficiently by the players at each strategy profile and (2) are guaranteed to…
We study the quality of outcomes in repeated games when the population of players is dynamically changing and participants use learning algorithms to adapt to the changing environment. Game theory classically considers Nash equilibria of…
Multi-agent learning algorithms have been shown to display complex, unstable behaviours in a wide array of games. In fact, previous works indicate that convergent behaviours are less likely to occur as the total number of agents increases.…
The standard game-theoretic solution concept, Nash equilibrium, assumes that all players behave rationally. If we follow a Nash equilibrium and opponents are irrational (or follow strategies from a different Nash equilibrium), then we may…
We characterize Nash equilibrium by postulating coherent behavior across varying games. Nash equilibrium is the only solution concept that satisfies the following axioms: (i) strictly dominant actions are played with positive probability,…
This paper develops a novel methodology to study robust stability properties of Nash equilibrium points in dynamic games. Small-gain techniques in modern mathematical control theory are used for the first time to derive conditions…
Learning in games discusses the processes where multiple players learn their optimal strategies through the repetition of game plays. The dynamics of learning between two players in zero-sum games, such as Matching Pennies, where their…
We consider the problem of learning stable matchings with unknown preferences in a decentralized and uncoordinated manner, where "decentralized" means that players make decisions individually without the influence of a central platform, and…
Across many domains of interaction, both natural and artificial, individuals use past experience to shape future behaviors. The results of such learning processes depend on what individuals wish to maximize. A natural objective is one's own…
We investigate whether having a unique equilibrium (or a given number of equilibria) is robust to perturbation of the payoffs, both for Nash equilibrium and correlated equilibrium. We show that the set of n-player finite games with a unique…
In a multi-objective game, each individual's payoff is a \emph{vector-valued} function of everyone's actions. Under such vectorial payoffs, Pareto-efficiency is used to formulate each individual's best-response condition, inducing…
We study a class of non-cooperative aggregative games -- denoted as \emph{social purpose games} -- in which the payoffs depend separately on a player's own strategy (individual benefits) and on a function of the strategy profile which is…
We study learning in complete-information games, allowing the players' models of their environment to be misspecified. We introduce Berk--Nash rationalizability: the largest self-justified set of actions -- meaning each action in the set is…
Games with incomplete preferences are an important model for studying rational decision-making in scenarios where players face incomplete information about their preferences and must contend with incomparable outcomes. We study the problem…