Related papers: Periodic Strategies II: Generalizations and Extens…

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…

Contrary to the customary view that the celebrated Nash-equilibrium theorem in Game Theory is paradigmatic for non-cooperative games, it is shown that, in fact, it is essentially based on a particularly strong cooperation assumption.…

This paper investigates mixed strategies in dynamic games with perfect information. We present an example to show that a player may obtain higher payoff by playing mixed strategy. By contrast, the main result of the paper shows that every…

It is well-known that for infinitely repeated games, there are computable strategies that have best responses, but no computable best responses. These results were originally proved for either specific games (e.g., Prisoner's dilemma), or…

For the iterated Prisoner's Dilemma, there exist Markov strategies which solve the problem when we restrict attention to the long term average payoff. When used by both players these assure the cooperative payoff for each of them. Neither…

We consider a tournament among four equally strong semifinalists. The players have to decide how much stamina to use in the semifinals, provided that the rest is available in the final and the third-place playoff. We investigate optimal…

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 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…

We study the existence of mixed-strategy equilibria in concurrent games played on graphs. While existence is guaranteed with safety objectives for each player, Nash equilibria need not exist when players are given arbitrary terminal-reward…

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…

Nash equilibrium is a key concept in game theory fundamental for elucidating the equilibrium state of strategic interactions, finding applications in diverse fields such as economics, political science, and biology. However, the Nash…

We consider a nonzero-sum N-player Markov game on an abstract measurable state space with compact metric action spaces. The payoff functions are bounded Carath\'eodory functions and the transitions of the system are assumed to have a…

This paper studies the existence of pure Nash equilibria in resource graph games, which are a general class of strategic games used to succinctly represent the players' private costs. There is a finite set of resources and the strategy set…

In evolutionary game theory, it is customary to be partial to the dynamical models possessing fixed points so that they may be understood as the attainment of evolutionary stability, and hence, Nash equilibrium. Any show of periodic or…

Game theory is a very profound study on distributed decision-making behavior and has been extensively developed by many scholars. However, many existing works rely on certain strict assumptions such as knowing the opponent's private…

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…

Individuals, or organizations, cooperate with or compete against one another in a wide range of practical situations. Such strategic interactions are often modeled as games played on networks, where an individual's payoff depends not only…

Motivated by the scarcity of accurate payoff feedback in practical applications of game theory, we examine a class of learning dynamics where players adjust their choices based on past payoff observations that are subject to noise and…

We study pure Nash equilibria in infinite-duration games on graphs, with partial visibility of actions but communication (based on a graph) among the players. We show that a simple communication mechanism consisting in reporting the…

We present a novel variant of fictitious play dynamics combining classical fictitious play with Q-learning for stochastic games and analyze its convergence properties in two-player zero-sum stochastic games. Our dynamics involves players…