Spatialization and Greater Generosity in the Stochastic Prisoner's Dilemma

Biosystems 37:3-17 (1996)
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Abstract

The iterated Prisoner’s Dilemma has become the standard model for the evolution of cooperative behavior within a community of egoistic agents, frequently cited for implications in both sociology and biology. Due primarily to the work of Axelrod (1980a, 198Ob, 1984, 1985), a strategy of tit for tat (TFT) has established a reputation as being particularly robust. Nowak and Sigmund (1992) have shown, however, that in a world of stochastic error or imperfect communication, it is not TFT that finally triumphs in an ecological model based on population percentages (Axelrod and Hamilton 1981), but ‘generous tit for tat’ (GTFT), which repays cooperation with a probability of cooperation approaching 1 but forgives defection with a probability of l/3. In this paper, we consider a spatialized instantiation of the stochastic Prisoner’s Dilemma, using two-dimensional cellular automata (Wolfram, 1984, 1986; Gutowitz, 1990) to model the spatial dynamics of populations of competing strategies. The surprising result is that in the spatial model it is not GIFT but still more generous strategies that are favored. The optimal strategy within this spatial ecology appears to be a form of ‘bending over backwards’, which returns cooperation for defection with a probability of 2/3 - a rate twice as generous as GTFT.

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Citations of this work

Making Meaning Happen.Patrick Grim - 2004 - Journal for Experimental and Theoretical Artificial Intelligence 16:209-244.
Simulating Grice: Emergent Pragmatics in Spatialized Game Theory.Patrick Grim - 2011 - In Anton Benz, Christian Ebert & Robert van Rooij, Language, Games, and Evolution. Springer-Verlag.

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References found in this work

The Evolution of Human Altruism.Philip Kitcher - 1993 - Journal of Philosophy 90 (10):497.
The Greater Generosity of the Spatialized Prisoner's Dilemma.Patrick Grim - 1995 - Journal of Theoretical Biology 173:353-359.
Chaos in game dynamics.Brian Skyrms - 1992 - Journal of Logic, Language and Information 1 (2):111-130.

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