Rubinstein and Wolinsky [Rev. Econ. Stud. 57 (1990) 63] show that a simple homogeneous
market with exogenous matching has a continuum of (non-competitive) perfect equilibria;
however, the unique Markov-perfect equilibrium of this model is competitive. By contrast, in
the more general case of heterogeneous markets, even the Markov property is not enough
to guarantee the perfectly competitive outcome. We define a market game that allows for
heterogeneous values on both sides of the market and exhibit a number of examples of (non …