State-dependent stochastic stability and the non-existence of conventions
Ille, Sebastian (2015) State-dependent stochastic stability and the non-existence of conventions. Social Science Research Network.
Abstract
Arising from criticism in the literature and focusing on 2x2 coordination games, the concept of stochastic stability is extended to take account of state dependent error and sample sizes. Both, error and sample size are expected to be correlated with the loss that occurred, if a player chooses a non-best response strategy. The state independent and state dependent predictions determine the same Stochastically Stable State (SSS) if the game’s pay-off matrix exhibits a form of symmetry, or if only the relative potential loss from idiosyncratic play defines the state dependent variable. Predictions may differ if neither of these conditions is met. In addition, the paper raises a second crucial point. Even if these conditions are met, the minimum stochastic potential is only a necessary but not a sufficient condition for the evolution of an SSS. The SSS must further be sufficiently risk dominant, otherwise no convention will evolve
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