Walrasian Tatonnement by Sequential Pairwise Trading: Convergence and Welfare Implications

This paper characterizes the out-of-equilibrium dynamics of a symmetric, pure exchange economywith two goods and N agents with uniformly distributed preferences and identical endowments.Relaxing the auctioneer assumption, but maintaining a global price rule, sequentially 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 resource allocations even at convergence, where welfare is less than a standardized 1% lower than the auctioneer Pareto one. This model sketches a possible basis for price over-reaction microfoundation and captures endogenous ""wealth divide"" among the population, induced by whether agent trading is dominatedby good preferences or just by speculation around their prices.