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Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…
We consider imperfect information stochastic games where we require the players to use pure (i.e. non randomised) strategies. We consider reachability, safety, B\"uchi and co-B\"uchi objectives, and investigate the existence of…
Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards.…
We establish the existence of optimal scheduling strategies for time-bounded reachability in continuous-time Markov decision processes, and of co-optimal strategies for continuous-time Markov games. Furthermore, we show that optimal control…
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…
We study the conditions under which the iterated elimination of strictly dominated strategies is order independent and we identify a class of discontinuous games for which order does not matter. In this way, we answer the open problem…
We consider an extension of the classical Total Store Order (TSO) semantics by expanding it to turn-based 2-player safety games. During her turn, a player can select any of the communicating processes and perform its next transition. We…
We study natural strategic games on directed graphs, which capture the idea of coordination in the absence of globally common strategies. We show that these games do not need to have a pure Nash equilibrium and that the problem of…
We give a general method for constructing a deterministic strategy of Reality from a randomized strategy in game-theoretic probability. The construction can be seen as derandomization in game-theoretic probability.
We examine the classical contents of quantum games. It is shown that a quantum strategy can be interpreted as a classical strategies with effective density-dependent game matrices composed of transposed matrix elements. In particular,…
We discuss partial specifications in first-order logic FO and also in a Turing-complete extension of FO. We compare the compositional and game-theoretic approaches to the systems.
Recently, in [K.R. Apt and S. Simon: Well-founded extensive games with perfect information, TARK21], we studied well-founded games, a natural extension of finite extensive games with perfect information in which all plays are finite. We…
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…
This paper proposes a new equilibrium concept "robust perfect equilibrium" for non-cooperative games with a continuum of players, incorporating three types of perturbations. Such an equilibrium is shown to exist (in symmetric mixed…
Zero-determinant (ZD) strategies, a recently found novel class of strategies in repeated games, has attracted much attention in evolutionary game theory. A ZD strategy unilaterally enforces a linear relation between average payoffs of…
We investigate uniformity properties of strategies. These properties involve sets of plays in order to express useful constraints on strategies that are not \mu-calculus definable. Typically, we can state that a strategy is…
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…
In the timeline-based approach to planning, the evolution over time of a set of state variables (the timelines) is governed by a set of temporal constraints. Traditional timeline-based planning systems excel at the integration of planning…
We consider the problem of computing the set of initial states of a dynamical system such that there exists a control strategy to ensure that the trajectories satisfy a temporal logic specification with probability 1 (almost-surely). We…
In this article, we look at a hat-guessing game, in which each player must guess the color of their own hat while only seeing the hats of the other players. We focus on the case of two hat colors and a countably infinite number of players.…