When the asset market is incomplete, competitive equilibria are constrained suboptimal, which provides a scope for pareto improving interventions. Price regulation can be such a pareto improving policy, even when the welfare effects of rationing are taken into account. An appealing aspect of price regulation is that it that it operates anonymously on market variables.
Fix-price equilibria exist under weak assumptions. Such equilibria permit a competitive analysis of an economy with an incomplete asset market that is out of equilibrium. Arbitrage opportunities may arise: with three or more assets actively traded, an individual may hold an arbitrage portfolio at equilibrium.
The local existence of fix-price equilibrium for prices that are almost competitive may fail for robust examples. Under necessary and sufficient conditions for the local existence of fix-price equilibria, Pareto improving price regulation is generically possible.
Two approaches have been proposed in the literature to refine the rationalizability solution concept: either assuming that players make small errors when playing their strategies, or assuming that their is a small amount of payoff uncertainty. We show that both approaches lead to the same refinement if errors are made according to the concept of weakly perfect rationalizability, and there is payoff uncertainty as in Dekel and Fudenberg [Journal of Economic Theory (1990), 52: 243–267]. For both cases, the strategies that survive are obtained by starting with one round of elimination of weakly dominated strategies followed by many rounds of elimination of strictly dominated strategies.