SFB 303 Discussion Paper No. B - 193

Author: Binmore, Ken, and Larry Samuelson
Title: Evolutionary Stability in Repeated Games Played by Finite Automata
Abstract: Using a modified definition of evolutionary stability we show that a population consisting of entirely of TAT-FOR-TIT machines is evolutionarily viable. However, the new definition makes it impossible to ignore the case of polymorphous populations in which different machines may co-exist in a symbiotic relationship. Extending our analysis to include such populations, we show in general that only utilitarian outcomes are evolutionarily viable. The paper is organized in the following way. Sections 2 and 3 provide a discussion of the issues that motivate our work. Section 4 considers some of the modeling problems that our approach entails and explains how we deal with some of these problems and evade others. Sections 5 and 6 introduce the necessary formalities, and introduce our modified definition of an evolutionary stable strategy. Section 7 establishes that a population consisting of only one type of machine must be utilitarian if it is to be evolutionarily stable according to our modified definition. Section 8 seeks to explain why such a result needs to be generalized to the case of polymorphous populations of machines. Section 9 provides such a generalization.
Creation-Date: July 1991
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