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We provide, to the best of our knowledge, the first computational study of extensive-form adversarial team games. These games are sequential, zero-sum games in which a team of players, sharing the same utility function, faces an adversary.…

We consider the problem of two-player zero-sum games. This problem is formulated as a min-max Markov game in the literature. The solution of this game, which is the min-max payoff, starting from a given state is called the min-max value of…

We consider normal-form games with $n$ players and two strategies for each player, where the payoffs are i.i.d. random variables with some distribution $F$ and we consider issues related to the pure equilibria in the game as the number of…

We consider a two-player game of war of attrition under complete information. It is well-known that this class of games admits equilibria in pure, as well as mixed strategies, and much of the literature has focused on the latter. We show…

Cooperative behavior, where one individual incurs a cost to help another, is a wide spread phenomenon. Here we study direct reciprocity in the context of the alternating Prisoner's Dilemma. We consider all strategies that can be implemented…

In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner of the game. Such games are central in formal methods since they model the interaction between a…

We consider 2-players, 2-values minimization games where the players' costs take on two values, $a,b$, $a<b$. The players play mixed strategies and their costs are evaluated by unimodal valuations. This broad class of valuations includes…

We study tournaments where winning a rank-dependent prize requires passing a minimum performance standard. We show that, for any prize allocation, the optimal standard is always at a mode of performance that is weakly higher than the global…

We consider the general model of zero-sum repeated games (or stochastic games with signals), and assume that one of the players is fully informed and controls the transitions of the state variable. We prove the existence of the uniform…

n infinite two-player zero-sum game with a Borel winning set, in which the opponent's actions are monitored eventually but not necessarily immediately after they are played, is determined. The proof relies on a representation of the game as…

Experiments on the ultimatum game have revealed that humans are remarkably fond of fair play. When asked to share an amount of money, unfair offers are rare and their acceptance rate small. While empathy and spatiality may lead to the…

Parity games are abstract infinite-round games that take an important role in formal verification. In the basic setting, these games are two-player, turn-based, and played under perfect information on directed graphs, whose nodes are…

We study a stopping game of preemption type between two players who both act under uncertain competition. In this framework we introduce, and study the effect of, (i) asymmetry of payoffs, allowing e.g. for different investment costs, and…

We investigate a two-player zero-sum differential game with asymmetric information on the payoff and without Isaacs condition. The dynamics is an ordinary differential equation parametrised by two controls chosen by the players. Each player…

We construct an approximate public-signal correlated equilibrium for a nonzero-sum differential game in the class of stochastic strategies with memory. The construction is based on a solution of an auxiliary nonzero-sum continuous-time…

We investigate multi-round team competitions between two teams, where each team selects one of its players simultaneously in each round and each player can play at most once. The competition defines an extensive-form game with perfect…

When opposing parties compete for a prize, the sunk effort players exert during the conflict can affect the value of the winner's reward. These spillovers can have substantial influence on the equilibrium behavior of participants in…

We consider a stochastic tournament game in which each player is rewarded based on her rank in terms of the completion time of her own task and is subject to cost of effort. When players are homogeneous and the rewards are purely rank…

Secure equilibrium is a refinement of Nash equilibrium, which provides some security to the players against deviations when a player changes his strategy to another best response strategy. The concept of secure equilibrium is specifically…

A game has approximate equilibria if for every $\epsilon >0$ there is an $\epsilon$-equilibrium. We show that there is a stochastic game that lacks approximate equilibria. This game has finitely many players and actions, their payoffs are…