Related papers: Set Equality in Combinatorial Game Theory
Arithmetic functions in Number Theory meet the Sprague-Grundy function from Combinatorial Game Theory. We study a variety of 2-player games induced by standard arithmetic functions, such as Euclidian division, divisors, remainders and…
We introduce a set-valued solution concept, M equilibrium, to capture empirical regularities from over half a century of game-theory experiments. We show M equilibrium serves as a meta theory for various models that hitherto were considered…
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…
This work is an application of game theory to quantum information. In a state estimate, we are given observations distributed according to an unknown distribution $P_{\theta}$ (associated with award $Q$), which Nature chooses at random from…
We introduce a zero-sum game problem of mean-field type as an extension of the classical zero-sum Dynkin game problem to the case where the payoff processes might depend on the value of the game and its probability law. We establish…
The explicit construction is presented of two-player game satisfying: (i) symmetry with respect to the permutation of the players; (ii) the existence of upper bound on total payoff following from Bell inequality; (iii) the existence of…
This paper introduces a geometric framework for analyzing power relations in games, independent of their strategic form. We define a canonical preference space where each player's relational stance is a normalized vector. This model…
We consider a finite state, finite action, zero-sum stochastic games with data defining the game lying in the ordered field of algebraic numbers. In both the discounted and the limiting average versions of these games we prove that the…
For an arbitrary category, we consider the least class of functors con- taining the projections and closed under finite products, finite coproducts, parameterized initial algebras and parameterized final coalgebras, i.e. the class of…
This compendium features advances in Game Theory, to include: Classical Game Theory: Cooperative and non-cooperative. Zero-sum and non-zero sum games. Potential and Congestion games. Mean Field games. Nash Equilibrium, Correlated Nash…
We introduce the novel notion of winning cores in parity games and develop a deterministic polynomial-time under-approximation algorithm for solving parity games based on winning core approximation. Underlying this algorithm are a number…
Game theory is used by all behavioral sciences, but its development has long centered around tools for relatively simple games and toy systems, such as the economic interpretation of equilibrium outcomes. Our contribution, compositional…
This paper examines multiplayer symmetric constant-sum games with more than two players in a competitive setting, including examples like Mahjong, Poker, and various board and video games. In contrast to two-player zero-sum games,…
This paper develops and analyses a novel quantum combinatorial game: quantum checkers (codenamed Cheqqers). The concepts of superposition, entanglement, measurements and interference from quantum mechanics are integrated into the game of…
A new approach to play games quantum mechanically is proposed. We consider two players who perform measurements in an EPR-type setting. The payoff relations are defined as functions of *correlations*, i.e. without reference to classical or…
Theory of quantum games is a new area of investigation that has gone through rapid development during the last few years. Initial motivation for playing games, in the quantum world, comes from the possibility of re-formulating quantum…
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…
Game semantics is a trace-like denotational semantics for programming languages where the notion of legal observable behaviour of a term is defined combinatorially, by means of rules of a game between the term (the "Proponent") and its…
We consider the class of "well-tempered" integer-valued scoring games, which have the property that the parity of the length of the game is independent of the line of play. We consider disjunctive sums of these games, and develop a theory…
Coordination and cooperation are among the most important issues of game theory. Recently, the attention turned to game theory on graphs and social networks. Encouraged by interesting results obtained in quantum evolutionary game analysis,…