Games and nets literature review

Literature

Eguilez, V. et al. Cooperation and emergence of role differentiation in the dynamics of social networks. arXiv: physics (2006) pdf

I found this paper describing a very similar model and I believe this is more or less what we intend to do.

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.

Goyal, S. Learning in Networks: a Survey. Forthcoming in, Group formation in economics: networks, clubs, and coalitions (2003) pdf

A broad overview of learning on both static and adaptive networks. The paper examines a variety of games including those involving information aquisition, information sharing, cooperation, conflict and others.

Jin, E., Girvin, M. and Newman, M. Structure of Growing Social Networks Physical Review E (2001) pdf

Some interesting ideas in general, but specifically useful for thinking about how to model the growth and decay of social networks. Also, since this is co-authored by Mark Newman it would be convenient to ask him about the ideas put forth in the paper.

Not yet read:

Nowak, M. and Sigmund, K. Evolutionary dynamics of biological games. Science 303 (2004) pdf

Lieberman, E. Hauert, C. Nowak, M. Evolutionary dynamics on graphs. Nature 433 (2005) pdf

Albert, R. and Barabási, A. Topology of Evolving Networks: Local Events and Universality Physical Review Letters (2000) pdf

Jackson, M. and Wolinski, A. A Strategic Model of Social and Economic Networks Journal of Economic Theory (1996) pdf

Bala, V. and Goyal, S. A Noncooperative Model of Network Formation Econometrica (2000) 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 d, 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 .

Dall, S. et al. Information and its use by animals in evolutionary ecology. TREE 20 4 (2005) pdf

This paper includes a section on 'inadvertant social information' - ie cues. The authors mention that use of social cues can lead to informational cascades - there's a literature in economics on this that I know exists but haven't read much of. This can be valuable, but can also lead to important errors. An examples among animals is the take-off behaviour of large flocks of birds. Many of the birds in a departing flock will take off on the basis of only social cues from the birds around them - this may be valuable if it usually signifies approaching danger, but a waste of energy if it does not. The sharing of information through social cues has useful emergent group level results such as 1. the synchronisation of patch departure 2. the rapid learning of local habitat depletion 3. the estimation of habitat or bredding colony quality (eg from observation of the number of offspring fledged in various colonies). There are likely to be costs involved in both types of information collection (social and individual) and as a result it may pay to specialise in one or the other. Information pooling among social insects is heavily studied, often in haplodiploid species such as ants or bees.

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