Mistakes in Cooperation: The Stochastic Stability of Edgeworth's Recontracting

Abstract

In an exchange economyw ith a finite number of indivisible goods, we analyze a dynamic trading process of coalitional recontracting where agents may make mistakes with small probability. We show first that the recurrent classes of the unperturbed (mistakefree) process consist of (i) all core allocations as absorbing states, and (ii) cycles of non-core allocations. Next, we introduce a perturbed process, where the resistance of each transition is a function of the number of agents that make mistakes - do not improve - in the transition and of the seriousness of each mistake. If preferences are always strict, we show that the unique stochasticallystable state of the perturbed process is the Walrasian allocation. In economies with indifferences, non-core cycles are sometimes stochastically stable, while some core allocations are not.

Keywords: stochastic stability, exchange economies, assignment problems, core, Walrasian equilibrium

JEL Classification: C7, D51, D61, D63.