Chaos in Cooperation: Continuous-Valued Prisoner's Dilemmas in Infinite-Valued
Logic
International Journal of Bifurcation and Chaos, vol.
4, no. 4 (1994), 943-958.
Gary Mar and Paul St. Denis <gmar@ccmail.sunysb.edu>
Group for Logic and Formal Semantics
Department of Philosophy, SUNY at Stony Brook
Stony Brook, NY 11794-3750 USA
The Prisoner's dilemma (PD) has become a paradigm
of the evolution of cooperation. The PD can be generalized to the
continuous-valued cases in whch players are allowed to choose intermediate
levels of cooperation. When continuous-valued PDs are played in the
spatial context of cellular automata, generous strategies are favored.
Continuous-valued PDs are naturally represented
in infinite-valued logic. The infinite-valued logic allows us to
prove that cooperative interactions between continuous-valued strategies
are paradigmatically chaotic. Escape-time diagrams using a given
level of mutual coperation as a threshold produce fractal images.
The sensitive dependence of chaotic dynamical systems models practical
unpredictability with the PD (even though only deterministic nonstochastic
strategies are involved) that is characteristic of many real life choice
situations.
For Prisoner's Dilemma software click Prisoner's Dilemma Software.
Index of Sections: