Abstract
We introduce a game setting called a joint process, where the history of actions determine the state, and the state and agent properties determine the payoff. This setting is a special case of stochastic games and is a natural model for situations with alternating control. Joint process games have applications as diverse as aggregate rating sites and wiki page updates. These games are related to Black's median voter theorem and also strongly connected to Moulin's strategy-proof voting schemes. When each agent has a personal goal, we look at how the play converges under a simple myopic action rule, and prove that not only do these simple dynamics converge, but the actions selected also form a Nash equilibrium. The convergence point is not the mean or the median of the set of agent goals; instead we prove the convergence point is the median of the set of agent goals and a set of focal points. This work provides the first theoretical model of wiki-type behavior and opens the door to more questions about the properties of these games.
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