Defensive alliances in spatial models of cyclical population interactions

As a generalization of the 3-strategy Rock-Scissors-Paper game dynamics in space, cyclical interaction models of six mutating species are studied on a square lattice, in which each species is supposed to have two dominant, two subordinated and a neutral interacting partner. Depending on their interaction topologies, these systems can be classified into four (isomorphic) groups exhibiting significantly different behaviors as a function of mutation rate. On three out of four cases three (or four) species form defensive alliances which maintain themselves in a self-organizing polydomain structure via cyclic invasions. Varying the mutation rate this mechanism results in an ordering phenomenon analogous to that of magnetic Ising model.Comment: 4 pages, 3 figure

Motion of influential players can support cooperation in Prisoner's Dilemma

We study a spatial Prisoner's dilemma game with two types (A and B) of players located on a square lattice. Players following either cooperator or defector strategies play Prisoner's Dilemma games with their 24 nearest neighbors. The players are allowed to adopt one of their neighbor's strategy with a probability dependent on the payoff difference and type of the given neighbor. Players A and B have different efficiency in the transfer of their own strategy therefore the strategy adoption probability is reduced by a multiplicative factor (w < 1) from the players of type B. We report that the motion of the influential payers (type A) can improve remarkably the maintenance of cooperation even for their low densities.Comment: 7 pages, 7 figure

A Game Theoretic Approach To Learning Shape Categories and Contextual Similarities

Abstract. The search of a model for representing and evaluating the similarities between shapes in a perceptually coherent way is still an open issue. One reason for this is that our perception of similarities is strongly influenced by the underlying category structure. In this paper we aim at jointly learning the categories from examples and the similar-ity measures related to them. There is a chicken and egg dilemma here: class knowledge is required to determine perceived similarities, while the similarities are needed to extract class knowledge in an unsuper-vised way. The problem is addressed through a game theoretic approach which allows us to compute 2D shape categories based on a skeletal rep-resentation. The approach provides us with both the cluster information needed to extract the categories, and the relevance information needed to compute the category model and, thus, the similarities. Experiments on a database of 1000 shapes showed that the approach outperform other clustering approaches that do not make use of the underlying contextual information and provides similarities comparable with a state-of-the-art label-propagation approach which, however, cannot extract categories.

Analytical Results for Individual and Group Selection of Any Intensity

The idea of evolutionary game theory is to relate the payoff of a game to reproductive success (= fitness). An underlying assumption in most models is that fitness is a linear function of the payoff. For stochastic evolutionary dynamics in finite populations, this leads to analytical results in the limit of weak selection, where the game has a small effect on overall fitness. But this linear function makes the analysis of strong selection difficult. Here, we show that analytical results can be obtained for any intensity of selection, if fitness is defined as an exponential function of payoff. This approach also works for group selection (= multi-level selection). We discuss the difference between our approach and that of inclusive fitness theory