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Incomplete cooperative games generalise the classical model of cooperative games by omitting the values of some of the coalitions. This allows to incorporate uncertainty into the model and study the underlying games as well as possible…
Game theory provides a general mathematical background to study the effect of pair interactions and evolutionary rules on the macroscopic behavior of multi-player games where players with a finite number of strategies may represent a wide…
Using semi-tensor product of matrices, the structures of several kinds of symmetric games are investigated via the linear representation of symmetric group in the structure vector of games as its representation space. First of all, the…
In this work, we present a logic based on first-order CTL, namely Game Analysis Logic (GAL), in order to reason about games. We relate models and solution concepts of Game Theory as models and formulas of GAL, respectively. Precisely, we…
First, we consider the problem of deciding whether a nonlocal game admits a perfect entangled strategy that uses projective measurements on a maximally entangled shared state. Via a polynomial-time Karp reduction, we show that independent…
Behavioural equivalences can be characterized via bisimulations, modal logics and spoiler-defender games. In this paper we review these three perspectives in a coalgebraic setting, which allows us to generalize from the particular branching…
Tropical polyhedra have been recently used to represent disjunctive invariants in static analysis. To handle larger instances, tropical analogues of classical linear programming results need to be developed. This motivation leads us to…
Game theory is the mathematical framework for analyzing strategic interactions in conflict and competition situations. In recent years quantum game theory has earned the attention of physicists, and has emerged as a branch of quantum…
Supermodular games find significant applications in a variety of models, especially in operations research and economic applications of noncooperative game theory, and feature pure strategy Nash equilibria characterized as fixed points of…
Game theory is the study of tractable games which may be used to model more complex systems. Board games, video games and sports, however, are intractable by design, so "ludological" theories about these games as complex phenomena should be…
Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not…
Game Theory concepts have been successfully applied in a wide variety of domains over the past decade. Sports and games are one of the popular areas of game theory application owing to its merits and benefits in solving complex scenarios.…
We investigate the existence of certain types of equilibria (Nash, $\varepsilon$-Nash, subgame perfect, $\varepsilon$-subgame perfect, Pareto-optimal) in multi-player multi-outcome infinite sequential games. We use two fundamental…
There are many combinatorial games in which a move can terminate the game, such as a checkmate in chess. These moves give rise to diverse situations that fall outside the scope of the classical normal play structure. To analyze these games,…
We describe an algorithm for computing best response strategies in a class of two-player infinite games of incomplete information, defined by payoffs piecewise linear in agents' types and actions, conditional on linear comparisons of…
In this invited contribution, we propose a comprehensive introduction to game theory applied in computer aided synthesis. In this context, we give some classical results on two-player zero-sum games and then on multi-player non zero-sum…
In Problem #1542 of Mathematics Magazine, Grossman and Turett define the Cantor game. In his 2007 Mathematics Magazine article about the Cantor game, Matt Baker proves several results and poses three challenging questions about it: Do there…
In a zero-sum stochastic game with signals, at each stage, two adversary players take decisions and receive a stage payoff determined by these decisions and a variable called state. The state follows a Markov chain, that is controlled by…
We study biased Maker-Breaker games on a graph system $\{G_1,\ldots,G_s\}$, in which Maker's goal is to claim certain rainbow structures, i.e., specified subgraphs consisting of at most one edge from each graph $G_i$. We consider the…
The space of finite games can be decomposed into three orthogonal subspaces [5], which are the subspaces of pure potential games, nonstrategic games and pure harmonic games. The orthogonal projections onto these subspaces are represented as…