Generalized Divide the Dollar
Evolutionary Computation (CEC), 2016 IEEE Congress on
Divide the dollar is a two-player simultaneous derived from a game invented by John Nash because its strategy space has an entire subspace of Nash equilibria. This study describes and explores a family of generalizations of divide the dollar with easily controlled properties. If we view divide the dollar as modeling the process of making a bargain, then the generalized game makes it easy to model the impact of external subsidies on bargaining. Classical divide the dollar is compared to four generalizations representing a simple subsidy in three different amounts and a more complex type of subsidy. The distribution of simple strategies that arise under replicator dynamics is compared to the bids that arise in populations of evolving, adaptive agents. Agents are encoded using a finite state representation that conditions its transitions on the result of bargains. These results fall into three categories, the first player obtains a higher amount, the second one does, or the agents fail to make a deal. The replicator dynamic results are compared to obtain the naive degree of distortion caused by the subsidies. The results for evolving agents are then examined to figure out the degree to which adaption compensated for or amplifies this distortion.
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D. Ashlock and G. Greenwood, "Generalized divide the dollar," 2016 IEEE Congress on Evolutionary Computation (CEC), Vancouver, BC, 2016, pp. 343-350.