On Feb 24, 2006, PED Seminar Series Presents

Spatial snowdrift games and the tragedy of the commune: some new perspectives on the problem of cooperation

by Professor Michael Doebeli

The Snowdrift game, in which cooperators have an advantage when rare, is a useful alternative to the Prisoner’s Dilemma for studying the problem of cooperation. I first briefly discuss spatial Snowdrift games, which reveal that, in contrast to the Prisoner’s Dilemma, spatial structure is generally not beneficial for cooperation in Snowdrift games. This is essentially due to the fact that in the Snowdrift game, cooperative acts yield benefits not only to others, but also to the cooperator itself. It is natural to assume that such cooperative acts can vary continuously, which naturally leads to the definition of continuous Snowdrift games. For such games, the naïve expectation is that cooperative investments evolve to some intermediate value, representing a cooperative state in which all individuals contribute equally. However, an analysis combining evolutionary game theory and adaptive dynamics shows that natural selection often results in evolutionary diversification from initially uniform populations into a stable state in which cooperators making large investments coexist with defectors who invest very little. Other scenarios are also possible, but in population in which initially all individuals make similar cooperative investments, the tragedy of the commune is that when individuals benefit from their own actions, highly asymmetric cooperative investments often evolve.

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