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In this paper we unify, simplify, and extend previous work on the evolutionary dynamics of symmetric $N$-player matrix games with two pure strategies. In such games, gains from switching strategies depend, in general, on how many other…

Symmetry arguments are frequently used -- often implicitly -- in mathematical modeling of natural selection. Symmetry simplifies the analysis of models and reduces the number of distinct population states to be considered. Here, I introduce…

We define a general framework of partition games for formulating two-player pebble games over finite structures. We show that one particular such game, which we call the invertible-map game, yields a family of polynomial-time approximations…

Evolutionary Prisoner's Dilemma games with quenched inhomogeneities in the spatial dynamical rules are considered. The players following one of the two pure strategies (cooperation or defection) are distributed on a two-dimensional lattice.…

A bidimensional representation of the space of 2x2 Symmetric Games in the strategic representation is proposed. This representation provides a tool for the classification of 2x2 symmetric games, quantification of the fraction of them having…

We study the population genetics of Evolution in the important special case of weak selection, in which all fitness values are assumed to be close to one another. We show that in this regime natural selection is tantamount to the…

We introduce new theoretical insights into two-population asymmetric games allowing for an elegant symmetric decomposition into two single population symmetric games. Specifically, we show how an asymmetric bimatrix game (A,B) can be…

Richman games are zero-sum games, where in each turn players bid in order to determine who will play next [Lazarus et al.'99]. We extend the theory to impartial general-sum two player games called \emph{bidding games}, showing the existence…

By resorting to the vector space structure of finite games, skew-symmetric games (SSGs) are proposed and investigated as a natural subspace of finite games. First of all, for two player games, it is shown that the skew-symmetric games form…

This paper introduces two fundamentally new concepts to game theory: multilateral Nash equilibria and families of games. Starting with non-cooperative games, we show how these notions together seamlessly integrate into and naturally extend…

Synchronous linear constraint system games are nonlocal games that verify whether or not two players share a solution to a given system of equations. Two algebraic objects associated to these games encode information about the existence of…

Strategic interactions often take place in an environment rife with uncertainty. As a result, the equilibrium of a game is intimately related to the information available to its players. The \emph{signaling problem} abstracts the task faced…

This paper has a twofold scope. The first one is to clarify and put in evidence the isomorphic character of two theories developed in quite different fields: on one side, threshold logic, on the other side, simple games. One of the main…

Parikh's game logic is a PDL-like fixpoint logic interpreted on monotone neighbourhood frames that represent the strategic power of players in determined two-player games. Game logic translates into a fragment of the monotone…

Nearly all simulation-based games have environment parameters that affect incentives in the interaction but are not explicitly incorporated into the game model. To understand the impact of these parameters on strategic incentives, typical…

In previous work on Clebsch-Gordan coefficients, certain remarkable hexagonal arrays of integers are constructed that display behaviors found in Pascal's Triangle. We explain these behaviors further using the binomial transform and discrete…

We compare four different `game-spaces' in terms of their usefulness in characterising multi-player tabletop games, with a particular interest in any underlying change to a game's characteristics as the number of players changes. In each…

I consider a family of games with corresponding payoff matrices, parametrized by the parameter The informal question of interest is: what game is the best? Instead of attempting to suggest a more or less arbitrary definition of the best…

We consider the natural extension of two-player nonlocal games to an arbitrary number of players. An important question for such nonlocal games is their behavior under parallel repetition. For two-player nonlocal games, it is known that…

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…