Modeling undependable subsidies with three-player generalized divide the dollar

Divide the dollar is a two-player simultaneous game derived from a game invented by John Nash because its strategy space contains an entire subspace of Nash equilibria. This study applies a family of generalizations of divide the dollar, called set-based divide the dollar, to the problem of understanding the impact of undependable subsidies. Set based divide the dollar defines a family of games with easily controlled properties making it ideal for this modeling task. These subsidies are intended to encourage deal making but, if abruptly discontinued or funded unreliably, may have different effects from those intended. The study also demonstrates the generalization of the game to three players, something that the set-based formalism makes easy. Agents are encoded using a finite state representation that conditions its transitions on the result of deals. These results fall into three categories, the agent obtains the highest amount, the agent receives a lesser amount, or the agents fail to make a deal. This study compares a situation with no subsidies with dependable and undependable subsidies, using the rate at which deals are made as a assessment statistic. Two sorts of undependability are studied, abrupt cessation of the subsidy and unreliable funding.