Games and nets literature review

Ohtsuki, H., Hauert, C., Lieberman, E. & Nowak, M.A. A simple rule for the evolution of cooperation on graphs and social networks. Nature 441: 502-505 (2006). pdf

This is a simple exploration of how network structure -- in particular, connectedness -- affects the evolution of cooperation. They find that a good predictor for whether cooperation can invade and spread in a network is whether the benefit-cost ratio is greater than the (average) degree of the graph. They derive the result exactly for a cycle, approximately for a random graph where every node has the same degree, and use simulation to show that the fit is good for true random graphs and scale-free networks.

Santos, F.C., Pacheco, J.M. & Lenaerts T. Evolutionary dynamics of social dilemmas in structured heterogeneous populations. Proc Nat Acad Sci USA 103: 3490-3494 (2006). pdf

The authors show that heterogeneity in the degree of the graph (e.g. scale-free networks as opposed to single-scale networks) can encourage the evolution of cooperation. They simulate using what amounts to an imitation rule on a fixed network structure, and parameterize the game that is played so that it can represent three popular games: Stag Hunt, Hawk-Dove, and Prisoner's Dilemma.

Page, K. Nowak, M. Sigmund, K. The spatial ultimatum game. Proc. R. Soc. Lond. B 267, 2177-2182 (2000) pdf

In an ultimatum game played between members of a population with random mixing offer strategies evolve towards zero, provided the mutation rate per generation is small. On a 1D lattice they approximate a fair split, and on a 2D grid they are around 0.35.

Not yet read: Nowak, M. and Sigmund, K. Evolutionary dynamics of biological games. Science 303 (2004) pdf

Social Foraging

Rogers A. Does biology constrain culture? American Anthropologist 90(4): 819–831 (1988). pdf

Rogers shows that in a population with both individual learning strategies and social learning strategies, for certain probabilites of environmental change in any given generation, the mixed evolutionarily stable strategy will be at a point at which the payoff from social learning exactly matches that of individual learning. Individual learning is assumed to have a constant, frequency independent payoff. He assumes individual learning to have a cost associated with it and social learning to be costless. The model has no space or other structure across which animals communicate. If the environment changes with too great a probability per generation social learners will be eliminated.

Wakano, J. Aoki, K. and Feldman, M. A mathematical analysis of social learning Theoretical Population Biology 66 249–258 (2004) pdf

The authors present a model in which social learning, individual learning and fixed (genetic) strategies are in competition. Social learning has cost s, individual learning has cost c and making a mistake about the state of the environment has cost s. d < c < s. The fitnesses of the different strategies vary as a function of the number of generations between environmental changes l. Individual learners win when the environment changes every generation (l = 1), decreasing in frequency as the number of generations between changes increases. Social learners are at zero frequency when l = 1, rising in frequency while l < 684. When l > 684 innate strategies suddenly rise from zero frequency to take over the whole population. This critical value of l* = 683 is for a given set of parameters .

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