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Monday, December 19, 2011 • 12:00 • Conference Room, ECLT

“Evolutionary explorations of rationality”

by

Kristian Lindgren

Professor, Chalmers University of Technology, Sweden

Co- Director, European Centre for Living Technology, Italy

ABSTRACT

Backward Induction has become a standard solution concept leading to the Nash equilibrium for finitely repeated games in game theory. While being supported by common knowledge of rationality, this assumption has been questioned. By using replicator-mutation dynamics, we investigate under what circumstances the Nash equilibrium is reached in an evolutionary context. We examine explicitly two types of strategies that could possibly alter the Backward induction procedure or disturb the stability of the equilibrium. The first type, the ”Convincers”, insists with two rounds of initial cooperation, trying to establish a more long-term coop- erative play in the game, while the second type, the ”Follower”, being a first round defector, has the capability to respond to the invite. For these strategies, back- ward induction applies, as there for any round in the game is a representative from each of these types switching to unconditional defect. The evolutionary dynamics can keep the system away from the non-cooperative fixed point, and the system cycles through a sequence with different levels of cooperation. The main result is that this holds also in the limit of zero mutation rate, contrary to what has been observed for simpler sets of strategies. This emphasizes how unstable the Nash equilibrium is if one considers players that include more advanced strategic choices in the game. A detailed analysis on how the evolutionary dynamics depends on payoff parameters, game length, and mutation rate is performed.

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