Related papers: Absorption Paths and Equilibria in Quitting Games

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 discuss importance sampling of exit problems that involve unbounded stopping times; examples are mean first passage times, transition rates or committor probabilities in molecular dynamics. The naive application of variance minimization…

Subtraction games have a rich literature as normal-play combinatorial games (e.g., Berlekamp, Conway, and Guy, 1982). Recently, the theory has been extended to zero-sum scoring play (Cohensius et al. 2019). Here, we take the approach of…

We study best-response type learning dynamics for zero-sum polymatrix games under two information settings. The two settings are distinguished by the type of information that each player has about the game and their opponents' strategy. The…

We introduce a new approach for computing optimal equilibria via learning in games. It applies to extensive-form settings with any number of players, including mechanism design, information design, and solution concepts such as correlated,…

The notions of symmetry and anonymity in strategic games have been formalized in different ways in the literature. We propose a combinatorial framework to analyze these notions, using group actions. Then, the same framework is used to…

We give an algorithm for solving stochastic parity games with almost-sure winning conditions on lossy channel systems, for the case where the players are restricted to finite-memory strategies. First, we describe a general framework, where…

The stable cooperation ratio of spatial evolutionary games has been widely studied using simulations or approximate analysis methods. However, sometimes such ``stable'' cooperation ratios obtained via approximate methods might not be…

We examine the routing problem for self-interested vehicles using stochastic decision strategies. By approximating the road latency functions and a non-linear variable transformation, we frame the problem as an aggregative game. We…

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…

Technology offers new ways to measure the locations of the players and of the ball in sports. This translates to the trajectories the ball takes on the field as a result of the tactics the team applies. The challenge professionals in soccer…

We propose a general definition of perfect equilibrium which is applicable to a wide class of games. A key feature is the concept of completely mixed nets of strategies, based on a more detailed notion of carrier of a strategy. Under…

We study a patrolling game played on a network $Q$, considered as a metric space. The Attacker chooses a point of $Q$ (not necessarily a node) to attack during a chosen time interval of fixed duration. The Patroller chooses a unit speed…

There is a common belief that humans and many animals follow transitive inference (choosing A over C on the basis of knowing that A is better than B and B is better than C). Transitivity seems to be the essence of rational choice. We…

We investigate optimal decision making under imperfect recall, that is, when an agent forgets information it once held before. An example is the absentminded driver game, as well as team games in which the members have limited communication…

We study the applicability of quantum algorithms in computational game theory and generalize some results related to Subtraction games, which are sometimes referred to as one-heap Nim games. In quantum game theory, a subset of Subtraction…

Partial-monitoring games constitute a mathematical framework for sequential decision making problems with imperfect feedback: The learner repeatedly chooses an action, opponent responds with an outcome, and then the learner suffers a loss…

We consider zero-sum stochastic differential games with possibly path-dependent controlled state. Unlike the previous literature, we allow for weak solutions of the state equation so that the players' controls are automatically of feedback…

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…

In this article, we study the behavior of a broad family of real sequences derived from randomized one-pile subtraction games. For any subtraction set $S$, we allow any valid number of chips $s\in S$ to be removed at equal probability at…