Beyond Tit-for-Tat: overall profit on spatial evolutionary games
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Beyond Tit-for-Tat: overall profit on spatial evolutionary games
A standard extension for evolutionary game theory is adding space and fixing the players over some well defined structure- most of times a simple grid, but there' s a lot done about games in complex networks, too. Basically, players can interact only with other players that are (at most) k-order neighbors. While in non-spatial evolutionary games the dynamics are given for the fraction of the population that plays a particular strategy, generally in spatial models population is fixed and what changes in time is the probability for a particular player to play a certain strategy. Usually, the dynamical systems for these probabilities depend on the success of that particular strategy: in plain words, you try to play strategies that you know that work well. One nice paper to get familiarized with this is http://www.math.ubc.ca/~doebeli/reprints/killingback_doebeli_1996.pdf. The point is that all the papers that I' ve read so far related with spatial game theory pay attention to the nature of the Nash equilibrium -generally a mixed strategy- and its spatial structure. My idea is to look for another criterion to analyze the optimality of a certain strategy -or a certain history of strategies- in terms of the final accumulated wealth of the player. What I' m trying to say? Well, in spatial game theory context we often think of a strategy like an optimal one if it can do it well against all of its neighbors. But it is reasonable if we consider the accumulated wealth -namely, the sum of all the individual gain/losses of the entire game- like a parameter of how good a whole history of strategies is. What if we find that the optimal history of strategies has well-defined characteristic times that depend on the size of the system? Is there a well-defined function fitting the wealth-rank relation? Is there a correlation between accumulated wealth and the fraction of time that a player played a certain strategy? A reasonable first step would be to run a classical hawk-dove or something like it in a grid. If the results are promising, further extension to other games and network topologies would be great.
If you' ve reached this line I can guess that you may have some interest, so let' s talk about it today at afternoon. I' ll be pleased to give more mathematical precision if it is needed, and of course I'm waiting for improves/advices for this project.
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