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Is there a classifier that ensures optimal robustness against all adversarial attacks? This paper answers this question by adopting a game-theoretic point of view. We show that adversarial attacks and defenses form an infinite zero-sum game…

We explore the twin questions of when and why the strategy method creates behavioral distortions in the elicitation of choices in laboratory studies of sequential games. While such distortions have been widely documented, the theoretical…

Recently, Press and Dyson have proposed a new class of probabilistic and conditional strategies for the two-player iterated Prisoner's Dilemma, so-called zero-determinant strategies. A player adopting zero-determinant strategies is able to…

A strictly strategy-proof mechanism is one that asks agents to use strictly dominant strategies. In the canonical one-dimensional mechanism design setting with private values, we show that strict strategy-proofness is equivalent to strict…

At a mixed Nash equilibrium, the payoff of a player does not depend on her own action, as long as her opponent sticks to his. In a periodic strategy, a concept developed in a previous paper (arXiv:1307.2035v4), in contrast, the own payoff…

We introduce a new model involving TU-games and exogenous structures. Specifically, we consider that each player in a population can choose an element in a strategy set and that, for every possible strategy profile, a TU-game is associated…

Game Theory concepts have been successfully applied in a wide variety of domains over the past decade. Sports and games are one of the popular areas of game theory application owing to its merits and benefits in solving complex scenarios.…

A game-theoretic framework for time-inconsistent stopping problems where the time-inconsistency is due to the consideration of a non-linear function of an expected reward is developed. A class of mixed strategy stopping times that allows…

We study stochastic zero-sum games on graphs, which are prevalent tools to model decision-making in presence of an antagonistic opponent in a random environment. In this setting, an important question is the one of strategy complexity: what…

An unknown positive number of items arrive at independent uniformly distributed times in the interval [0,1] to a selector, whose task is to pick online the last one. We show that under the assumption of an adversary determining the number…

The paper is devoted to dynamic games. We consider a general enough framework, which is not limited to e.g. differential games and could accommodate both discrete and continuous time. Assuming common dynamics, we study two game families…

We introduce and investigate a range of general notions of a game. Our principal notion is based on a set of agents modifying a relational structure in a discrete evolution sequence. We also introduce and study a variety of ways to model…

Real-life agents seldom have unlimited reasoning power. In this paper, we propose and study a new formal notion of computationally bounded strategic ability in multi-agent systems. The notion characterizes the ability of a set of agents to…

We show the existence and effective computability of optimal winning strategies for request-response games in case the quality of a play is measured by the limit superior of the mean accumulated waiting times between requests and their…

Tit-for-Tat strategy is a strategy in repeated two-player symmetric games which imitates the previous action of the opponent. We show that the Tit-for-Tat strategy is a zero-determinant strategy, which unilaterally equalizes the expected…

We introduce the concept of deformed zero-determinant strategies in repeated games. We then show that the Tit-for-Tat strategy in the repeated prisoner's dilemma game is a deformed zero-determinant strategy, which unilaterally equalizes the…

At the beginning of a dynamic game, players may have exogenous theories about how the opponents are going to play. Suppose that these theories are commonly known. Then, players will refine their first-order beliefs, and challenge their own…

The transitivity of preferences is one of the basic assumptions used in the theory of games and decisions. It is often equated with rationality of choice and is considered useful in building rankings. Intransitive preferences are considered…

What payoffs are positionally determined for deterministic two-player antagonistic games on finite directed graphs? In this paper we study this question for payoffs that are continuous. The main reason why continuous positionally determined…

Using methods from the statistical mechanics of disordered systems we analyze the properties of bimatrix games with random payoffs in the limit where the number of pure strategies of each player tends to infinity. We analytically calculate…