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Asymmetric evolutionary games
Evolutionary game theory is a powerful framework for studying evolution in
populations of interacting individuals. A common assumption in evolutionary
game theory is that interactions are symmetric, which means that the players
are distinguished by only their strategies. In nature, however, the microscopic
interactions between players are nearly always asymmetric due to environmental
effects, differing baseline characteristics, and other possible sources of
heterogeneity. To model these phenomena, we introduce into evolutionary game
theory two broad classes of asymmetric interactions: ecological and genotypic.
Ecological asymmetry results from variation in the environments of the players,
while genotypic asymmetry is a consequence of the players having differing
baseline genotypes. We develop a theory of these forms of asymmetry for games
in structured populations and use the classical social dilemmas, the Prisoner's
Dilemma and the Snowdrift Game, for illustrations. Interestingly, asymmetric
games reveal essential differences between models of genetic evolution based on
reproduction and models of cultural evolution based on imitation that are not
apparent in symmetric games.Comment: accepted for publication in PLOS Comp. Bio
A Graph Theoretical Approach to the Dollar Game Problem
In this thesis we consider a problem in Graph Theory known as the Dollar Game. The Dollar game was first introduced by Matthew Baker of the Georgia Institute of Technology in 2010. It is a game of solitaire, played on a graph, and is a variation of chip firing, or sand-piling games. Baker approached the problem within the context of Algebraic Geometry. It is the goal of this paper to provide an overview of the necessary graph theory to understand the problem presented in this game, as well as background on chip firing games, their history and evolution. Finally we will present a variety of results about the Dollar Game from a graph theoretical standpoint
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