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TITLE: The emergence of cooperation in the evolutionary spatial prisoners' dilemma on a path or cycle
SPEAKER: Prof. Jan van Vuuren, Univ. of Stellenbosch, South Africa
ABSTRACT:
In this talk we consider the Evolutionary Spatial Prisoners' Dilemma (ESPD) in which players are modelled by the vertices of an underlying graph G representing some spatial organisational structure amongst the players. During each round of the ESPD every pair of adjacent players in G play a classical prisoners' dilemma against each other, and they update their strategies from one round to the next based on the perceived success (as measured by pay-off values) achieved by the strategies of their neighbours during the previous round. In this way players are able to adapt and learn good strategies from each other as the game progresses, without understanding why these strategies are good. We characterise all steady states of the ESPD for the two cases where G is a path or a cycle, and we also characterise those initial states that lead to the emergence of persistent substates of cooperation over time. We finally determine analytically (i.e. without using simulation) the probability that the game's states will evolve from a randomly generated initial state towards a steady state which accommodates some form of persistent cooperation.
Joint work with Alewyn Burger & Martijn van der Merwe
