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Brief Notes On Theory
Most of not all of this will be in the text. However to provide a quick place to jot ideas and respond to comments, I'll place info here too.
After our initial tweets (friendfeed link) and other notices were doing this, we had some great comments and questions about the general theory. Here are general responses. More thoughtful responses with citations will be part of the manuscripts
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First, I should point out I see more heuristic value in the model, and I think keeping the simplest model possible will yield the greatest benefits. Not that it shouldn't be accurate, but I'm not trying to model every nuance of social interaction.
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I am and will be modelling things as 2 person games. N-Person games are modeled as coalitions and what happens is each coalition becomes a subgame of some number of players. If it's more than two, then we get subcoalitions, with the final result being that can always be broken down to a lot of 2 person games.
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For an equilibrium I am using an Evolutionary Stable Strategy (ESS). Briefly this just means that a system is in ESS when no invading other strategy can have higher fitness than the stable strategies. ESS's are a subset of the more general NASH equalibrium which says (from wikipedia)
_In game theory, Nash equilibrium (named after John Forbes Nash, who proposed it) is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally[1]:14. If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium. _
I think an ESS works well here because first ESS specifically incorporates the frequency of strategies. We don't have to assume that actual evolution is happening, at least not genetic evolution. I assume we are modelling something more akin to Cultural Evoltuion as modelled in Cavalli-Sforza, L. L. and M. Feldman. 1981. Cultural Transmission and Evolution. Princeton University Press, Princeton. The model I provide explicitly incorporates changing frequencies of strategies.