Related papers: Tame and Wild Scoring Play Games

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…

We introduce the category of optiongraphs and option-preserving maps as a model to study impartial combinatorial games. Outcomes, remoteness, and extended nim-values are preserved under option-preserving maps. We show that the four…

We study mean field games with scalar It{\^o}-type dynamics and costs that are submodular with respect to a suitable order relation on the state and measure space. The submodularity assumption has a number of interesting consequences.…

In Combinatorial Game Theory, short game forms are defined recursively over all the positions the two players are allowed to move to. A form is decomposable if it can be expressed as a disjunctive sum of two forms with smaller birthday. If…

We define a natural equivalence relation on collections of cards from the card game SET, and enumerate some of the equivalence classes, vastly generalizing the standard game. On this basis, we describe several alternative games for the SET…

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…

Many packing, scheduling and covering problems that were previously considered by computer science literature in the context of various transportation and production problems, appear also suitable for describing and modeling various…

We survey recent developments in the theory of impartial combinatorial games in misere play, focusing on how the Sprague-Grundy theory of normal-play impartial games generalizes to misere play via the indistinguishability quotient…

Strategic-form min-max game theory examines the existence, multiplicity, selection of equilibria, and the worst-case computational complexity under perfect rationality. However, in many applications, games are drawn from an ensemble, and…

This paper uses category theory to develop an entirely new approach to approximate game theory. Game theory is the study of how different agents within a multi-agent system take decisions. At its core, game theory asks what an optimal…

In this work we propose a kinetic formulation for evolutionary game theory for zero sum games when the agents use mixed strategies. We start with a simple adaptive rule, where after an encounter each agent increases the probability of play…

The security game is a basic model for resource allocation in adversarial environments. Here there are two players, a defender and an attacker. The defender wants to allocate her limited resources to defend critical targets and the attacker…

Game theory is a powerful analytical tool for modeling decision makers strategies, behaviors and interactions. Act and decisions of a decision maker can benefit or negatively impact other decision makers interests. Game theory has been…

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…

This paper provides effective methods for the polyhedral formulation of impartial finite combinatorial games as lattice games. Given a rational strategy for a lattice game, a polynomial time algorithm is presented to decide (i) whether a…

Game theory is usually considered applied mathematics, but a few game-theoretic results, such as Borel determinacy, were developed by mathematicians for mathematics in a broad sense. These results usually state determinacy, i.e. the…

We study the correlated equilibrium polytope $P_G$ of a game $G$ from a combinatorial point of view. We introduce the region of full-dimensionality for this class of polytopes and prove that it is a semialgebraic set for any game. Using a…

Game-theoretic probability uses the structure of gambles to define a concept like probability, but which is more flexible and robust. We show that results in game-theoretic probability can be thought of as minimax theorems for specific…

It is sometimes the case that one solution concept in game theory is equivalent to applying another solution concept to a modified version of the game. In such cases, does it make sense to study the former separately (as it applies to the…

We provide several tests to determine whether a game is a potential game or whether it is a zero-sum equivalent game---a game which is strategically equivalent to a zero-sum game in the same way that a potential game is strategically…