This paper extends the model developed in “Complexity and Competition” (Gale and Sabourian, Econometrica 2005). In that paper, decentralized finite markets are treated as extensive-form matching and bargaining games. In these games there are many inefficient outcomes supported by subgame perfect equilibria. GS introduce an equilibrium refinement in which players maintain an aversion to complexity and show that such a refinement eliminates non-competitive outcomes. We admit more general environments and show that whether an aversion to complexity eliminates inefficient equilibria in this class of market games depends on supply and how valuations are distributed. There are many markets whose complexity averse equilibria preclude efficiency and there are many finite markets that have no simple subgame perfect equilibria. These results hold when the definition of complexity developed in GS is generalized to include a richer class of Markov partitions of the strategy space.
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