Sunday, 6 January 2013

Evolutionary Justice and the Price of anarchy

This is a link to a very readable paper on Evolutionary Theories of Justice which raised a possibly naive and foolish question in my mind- we have a notion that correlated equilibria in animals must be genetically canalised because they don't have reflexivity and we also have a notion that something like reflexivity is a general module which does some sort of, collocation method, correlated equilibria computation- but does this mean that talk of Justice is really a sort of arbitrage of anarchy?
One of the main tools in the study of selfish behavior is the price of anarchy [14, 20], a measure that compares the worst case performance Nash equilibrium to that of the optimal allocation. Naturally, the concept of the price of anarchy extends to correlated equilibria.
If we know only that the players play at some equilibrium, the price of anarchy bounds the deterioration of system performance due to selfish behavior. On the other hand, there is the optimistic point of view in which the players are guided to play at the best Nash equilibrium.
Especially with correlated equilibria, the latter makes much more sense: The mediator who selects the probability distribution, the correlated equilibrium, and presents it to the players, can select the correlated equilibrium with minimum system cost. In other words, one can view correlated equilibria as a mechanism for enforcing good behavior on selfish users. The optimistic price of anarchy of the best equilibrium is also called price of stability  (Click here for the whole paper)

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