Related papers: Games with finitely generated structures

Coordination games have been of interest to game theorists, economists, and ecologists for many years to study such problems as the emergence of local conventions and the evolution of cooperative behavior. Approaches for understanding the…

We present a new variant of the potential game and show that certain compact subsets of $\R^n$, including a large class of self-affine sets, are winning in our game. We prove that sets with sufficiently strong winning conditions are…

We consider the degrees of non-computability (Weihrauch degrees) of finding winning strategies (or more generally, Nash equilibria) in infinite sequential games with certain winning sets (or more generally, outcome sets). In particular, we…

We study first-order as well as infinitary logics extended with quantifiers closed upwards under embeddings. In particular, we show that if a chain of quasi-homogeneous structures is sufficiently long then a given formula of such a logic is…

In this paper, we study finite-agent linear-quadratic games on graphs. Specifically, we propose a comprehensive framework that extends the existing literature by incorporating heterogeneous and interpretable player interactions. Compared to…

In this paper we first define a new kind of potential games, called coset weighted potential game, which is a generalized form of weighted potential game. Using semi-tensor product of matrices, an algebraic method is provided to verify…

Here, we establish the existence of weak solutions to a wide class of time-dependent monotone mean-field games (MFGs). These MFGs are given as a system of degenerate parabolic equations with initial and terminal conditions. To construct…

Traditionally social sciences are interested in structuring people in multiple groups based on their individual preferences. This pa- per suggests an approach to this problem in the framework of a non- cooperative game theory. Definition of…

We initiate the study of the phantom version of Maker-Breaker positional games. In a phantom game, the moves of one of the players are hidden from the other player, who still has the complete information. We look at the biased $(a:b)$…

The notion of Aronszajn-null sets generalizes the notion of Lebesgue measure zero on the real line and the Euclidean space to infinite dimensional Banach spaces. We present a game-theoretic approach to Aronszajn-null sets, establish its…

Many forcing notions obtained using the creature technology are naturally connected with certain integer games.

We present a new model of incomplete information games without private information in which the players use a distributionally robust optimization approach to cope with the payoff uncertainty. With some specific restrictions, we show that…

A real-valued game has the finite improvement property (FIP), if starting from an arbitrary strategy profile and letting the players change strategies to increase their individual payoffs in a sequential but non-deterministic order always…

In this paper, some new criteria for detecting whether a finite game is potential are proposed by solving potential equations. The verification equations with the minimal number for checking a potential game are obtained for the first time.…

We study multi-structural games, played on two sets $\mathcal{A}$ and $\mathcal{B}$ of structures. These games generalize Ehrenfeucht-Fra\"{i}ss\'{e} games. Whereas Ehrenfeucht-Fra\"{i}ss\'{e} games capture the quantifier rank of a…

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 study the structural complexity of bimatrix games, formalized via rank, from an empirical perspective. We consider a setting where we have data on player behavior in diverse strategic situations, but where we do not observe the relevant…

We analyze grand-canonical minority games with infinite and finite score memory and different updating timescales (from `on-line' games to `batch' games) in detail with various complementary methods, both analytical and numerical. We focus…

We encode arbitrary finite impartial combinatorial games in terms of lattice points in rational convex polyhedra. Encodings provided by these \emph{lattice games} can be made particularly efficient for octal games, which we generalize to…

We detail the rules and mathematical structure of Al-Jabar, a game invented by the authors based on intuitive concepts of color-mixing and ideas from abstract algebra. Game-play consists of manipulating colored game pieces; we discuss how…