Related papers: Impartial games on two finite Groups
Estimating discrete games of complete information is often computationally difficult due to partial identification and the absence of closed-form moment characterizations. This paper proposes computationally tractable approaches to…
The game of i-Mark is an impartial combinatorial game introduced by Sopena (2016). The game is parametrized by two sets of positive integers $S$, $D$, where $\min D\ge 2$. From position $n\ge 0$ one can move to any position $n-s$, $s\in S$,…
Combinatorial Game Theory is a branch of mathematics and theoretical computer science that studies sequential 2-player games with perfect information. Normal play is the convention where a player who cannot move loses. Here, we generalize…
We consider extensive games with perfect information with well-founded game trees and study the problems of existence and of characterization of the sets of subgame perfect equilibria in these games. We also provide such characterizations…
Playing impartial games under the normal and misere conventions may differ a lot. However, there are also many "exceptions" for which the normal and misere plays are very similar. As early as in 1901 Bouton noticed that this is the case…
Getting a group to adopt cooperative norms is an enduring challenge. But in real-world settings, individuals don't just passively accept static environments, they act both within and upon the social systems that structure their…
In this paper we study elimination of imaginaries in some classes of pure ordered abelian groups. For the class of ordered abelian groups with bounded regular rank (equivalently with finite spines) we obtain weak elimination of imaginaries…
Entropy games and matrix multiplication games have been recently introduced by Asarin et al. They model the situation in which one player (Despot) wishes to minimize the growth rate of a matrix product, whereas the other player (Tribune)…
We present a causality-based algorithm for solving two-player reachability games represented by logical constraints. These games are a useful formalism to model a wide array of problems arising, e.g., in program synthesis. Our technique for…
We introduce perfect half space games, in which the goal of Player 2 is to make the sums of encountered multi-dimensional weights diverge in a direction which is consistent with a chosen sequence of perfect half spaces (chosen dynamically…
We characterize three interrelated concepts in epistemic game theory: permissibility, proper rationalizability, and iterated admissibility. We define the lexicographic epistemic model for a game with incomplete information. Based on it, we…
Subtraction games are a class of impartial combinatorial games whose positions correspond to nonnegative integers and whose moves correspond to subtracting one of a fixed set of numbers from the current position. Though they are easy to…
We study multi-player games with perfect information and general payoff function, where the set of stages is the set of non-positive integers $\{\ldots,-2,-1,0\}$. We define two related equilibrium concepts: one considering only deviations…
We study variations of classical combinatorial games on two finite heaps of tokens, a.k.a. \emph{subtraction games}. Given non-negative integers $p_1,q_1, p_2,q_2$, where $p_1q_2 > q_1p_2$, $p_1>0$ and $q_2>0$, two players alternate in…
We examine the long-run behavior of a wide range of dynamics for learning in nonatomic games, in both discrete and continuous time. The class of dynamics under consideration includes fictitious play and its regularized variants, the…
Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms…
The mean field games system is a coupled pair of nonlinear partial differential equations arising in differential game theory, as a limit as the number of agents tends to infinity. We prove existence and uniqueness of classical solutions…
The notions of entanglement and nonlocality are among the most striking ingredients found in quantum information theory. One tool to better understand these notions is the model of nonlocal games; a mathematical framework that abstractly…
We study the emergence of altruistic behaviour in collective games. In particular, we take into account Toral's version of collective Parrondo's paradoxical games, in which the redistribution of capital between agents, who can play…
Pursuit-Evasion Games (in discrete time) are stochastic games with nonnegative daily payoffs, with the final payoff being the cumulative sum of payoffs during the game. We show that such games admit a value even in the presence of…