Sequential pairwise trading: convergence and welfare implications

Abstract

This paper characterises the out-of-equilibrium dynamics of a symmetric, pure-exchange economy with two goods and N agents with uniformly distributed preferences and identical endowments. Relaxing the auctioneer assumption, but maintaining a global price rule, sequential random pairwise trading at out-of-equilibrium prices is allowed. Initial mispricing implies rationing, determining excess demand (supply) fading away only at convergence, when the price of the initially cheaper (more expensive) good becomes more expensive (cheaper) than the Walrasian one. The system converges when the sequential price reaches the Walrasian price evaluated at current updated endowments. A perfectly symmetric setting, by initial mispricing and consequent rationed trading, creates asymmetric allocations even at convergence, where welfare is just slightly lower than auctioneer Pareto one. This model sketches a basis for price over-reaction micro-foundations and captures endogenous 'wealth divide' among the population, induced by whether trading is dominated by preferences over goods or by speculation around their prices.