Lattice Games with Strategic Takeover

Feldman, Barry and Nagel, Kai (1993) Lattice Games with Strategic Takeover.
Published in: Lectures in complex systems : the proceedings of the 1992 Complex Systems Summer School, Santa Fé, New Mexico, June 1992., Santa Fe Institute studies in the sciences of complexity : Lectures. 5 Addison-Wesley 1993, pp. 603-614.


This contribution explores a topic of interest in a surprising number of physical and social sciences, the iterated prisoner's dilemma game. We use this game to construct a simple model of strategic interaction on a lattice. The basic game describes two prisoners, accused of having committed a crime together, who are unable to communicate. Each is told that, if he confesses (defection), he will get a lighter sentence, but that he will receive a very heavy sentence if he does not confess and the other prisoner does. However, if neither confesses (cooperation), each receives a medium sentence. Both prisoners defecting is the only equilibrium in the game because they cannot make a binding agreement to cooperate. In the basic game theoretic analysis, cooperation can be sustained only by the indefinite repetition (iteration) of the game. The expected future benefits of cooperation must be greater than defection, and cooperation is difficult to sustain. The principal variation in our work is that we arrange agents on a lattice and have them play the same strategy simultaneously, but only against their immediate neighbors. The secondary variation in our work is that in most of our runs we allow payoffs to accumulate and, if an agent goes bankrupt, he is ''taken over'' by his most successful neighbor and adopts her strategy. Thus successful strategies propagate spatially, in a simple representation of diffusion through economic and social networks. In our study there are four important factors to consider: (1) how many iterations an agent can remember and what he can remember; (2) the relative advantage to noncooperation; (3) the degree of ''selection pressure''; and (4) the geometry of the lattice. In some of our runs we introduce a low rate of mutation in strategies which gives our work some of the quality of genetic algorithm methods. The work reported here focuses primarily on the effects of selection pressure and variations in the incentive to defect. It is rare that two players would play only against each other or that all agents would play all other agents in realistic economic situations. Typically, we expect a network of connections between agents. One approach to studying such networks is to model them as spatial behavior on a d-dimensional lattice. Axelrod already reports on experiments similar to ours on a lattice, but, in his work, agents play their neighbors separately. Most studies of evolutionary processes assume random or uniform matching. Here we allow the diffusion of strategies to take place, but do not make prior assumptions as to how complete ''mixing'' will be.

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