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Game theory is the standard tool used to model strategic interactions in evolutionary biology and social science. Traditional game theory studies the equilibria of simple games. But is traditional game theory applicable if the game is…

Infinite chess is chess played on an infinite edgeless chessboard. The familiar chess pieces move about according to their usual chess rules, and each player strives to place the opposing king into checkmate. The mate-in-n problem of…

Evolutionary game dynamics of two players with two strategies has been studied in great detail. These games have been used to model many biologically relevant scenarios, ranging from social dilemmas in mammals to microbial diversity. Some…

Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent's moves. We consider delay games with winning conditions expressed in weak monadic second order logic with…

This paper provides effective methods for the polyhedral formulation of impartial finite combinatorial games as lattice games. Given a rational strategy for a lattice game, a polynomial time algorithm is presented to decide (i) whether a…

This paper is concerned with continuous-time pursuit and evasion games. Typically, we have a lion and a man in a metric space: they have the same speed, and the lion wishes to catch the man while the man tries to evade capture. We are…

In numerous positional games the identity of the winner is easily determined. In this case one of the more interesting questions is not {\em who} wins but rather {\em how fast} can one win. These type of problems were studied earlier for…

For zero-sum two-player continuous-time games with integral payoff and incomplete information on one side, one shows that the optimal strategy of the informed player can be computed through an auxiliary optimization problem over some…

We investigate a game played between two players, Maker and Breaker, on a countably infinite complete graph where the vertices are the rational numbers. The players alternately claim unclaimed edges. It is Maker's goal to have after…

In timeline-based planning, domains are described as sets of independent, but interacting, components, whose behaviour over time (the set of timelines) is governed by a set of temporal constraints. A distinguishing feature of timeline-based…

In this paper, we study the notion of admissibility for randomised strategies in concurrent games. Intuitively, an admissible strategy is one where the player plays `as well as possible', because there is no other strategy that dominates…

Selective versions of screenability and of strong screenability coincide in a large class of spaces. We show that the corresponding games are not equivalent in even such standard metric spaces as the closed unit interval. We identify…

In this note we discuss a theory of combinatorial games that involve transmitting the moves through a noisy channel that can introduce errors during the transmission. Players are aware of this interference and incorporate this variable into…

Infinite draughts, or checkers, is played just like the finite game, but on an infinite checkerboard extending without bound in all four directions. We prove that every countable ordinal arises as the game value of a position in infinite…

The game theoretic concepts of rationalizability and iterated dominance are closely related and provide characterizations of each other. Indeed, the equivalence between them implies that in a two player finite game, the remaining set of…

A large body of research is currently investigating on the connection between machine learning and game theory. In this work, game theory notions are injected into a preference learning framework. Specifically, a preference learning problem…

In many multiagent environments, a designer has some, but limited control over the game being played. In this paper, we formalize this by considering incompletely specified games, in which some entries of the payoff matrices can be chosen…

Consider a two-player game repeated N times. Player 1 can choose between two styles (for interpretability, offensive and defensive), whereas Player 2 uses a single fixed style. Let X N\,:= \#wins -\#losses for Player 1 after N games, and…

We examine a two-person game we call Will-Testing in which the strategy space for both players is a real number. It has no equilibrium. When an infinitely large set of players plays this in all possible pairings, there is an equilibrium for…

In many combinatorial games, one can prove that the first player wins under best play using a simple but non-constructive argument called strategy-stealing. This work is about the complexity behind these proofs: how hard is it to actually…