Inefficiency in a frictionless market

Gale and Sabourian (2006) argue that Markov strategies in dynamic matching and bargaining games accommodate non-competitive behavior: with heterogeneous players, outcomes may be inefficient. In this paper, I show that their corroborating example with four players does not comprise a Markov perfect equilibrium (MPE). In fact, I show that all MPEs must be efficient in their setting with only four players. Nevertheless, I construct a continuum of inefficient equilibria in a balanced market with six players. Key to the construction is the dispersion of reservation prices to render inefficient trades individually rational, yet sufficient dynamics of continuation payoffs can be supported only with at least six players. Consequently, inefficiencies are driven by the interplay of heterogeneous valuations and strategic uncertainty from the number of players in the market.