A local interaction game is a game where agents play an identical stage game against their neighbors over time. This paper obtains a general result on the long-run equilibrium distribution of the local interaction game whose stage game is the 2 x 2 coordination game. It is established that starting from a random initial configuration with a positive probability of playing the risk dominant strategy, a sufficiently large population coordinates on the risk dominant equilibrium with probability 1 for the nearest neighbor interaction Our result improves previous ones including Blume (1995), Ellison (1993,1995), and Morris (1997) in a non-trivial way. It proves that there is an interactive contagion mechanism through which the risk dominant equilibrium may spread, in addition to the autonomous mechanism considered by others. Taking advantage of the mechanism we prove that for the nearest neighbor interaction, half dominance is sufficient for the degenerate long-run equilibrium distribution concentrated on the risk dominant strategy.
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- Groves, Theodore & Ledyard, John O, 1977.
"Optimal Allocation of Public Goods: A Solution to the "Free Rider" Problem,"
Econometric Society, vol. 45(4), pages 783-809, May.
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- Guoqiang Tian, 1989. "Implementation of the Lindahl Correspondence by a Single-Valued, Feasible, and Continuous Mechanism," Review of Economic Studies, Oxford University Press, vol. 56(4), pages 613-621.
- Andrew Postlewaite & David Wettstein, 1989. "Feasible and Continuous Implementation," Review of Economic Studies, Oxford University Press, vol. 56(4), pages 603-611. Full references (including those not matched with items on IDEAS)
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