Mistakes in cooperation: the stochastic stability of edgeworth's recontracting

In an exchange economy with a finite number of indivisible goods, we analyze a dynamic trading process of coalitional recontracting where agents maymake mistakes with small probability. We show first that the recurrent classes of the unperturbed (mistake-free) process consist of (i) all core allocations as absorbing states, and (ii) non-singleton classes 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 stochastically stable 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. The robustness of these results is confirmed in a weak coalitional recontracting process

MISTAKES IN COOPERATION: THE STOCHASTIC STABILITY OF EDGEWORTH'S RECONTRACTING

In an exchange economy with a finite number of indivisible goods, we analyze a dynamic trading process of coalitional recontracting where agents maymake mistakes with small probability. We show first that the recurrent classes of the unperturbed (mistake-free) process consist of (i) all core allocations as absorbing states, and (ii) non-singleton classes 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 stochastically stable 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. The robustness of these results is confirmed in a weak coalitional recontracting process.

Mistakes in cooperation: the stochastic stability of edgeworth's recontracting.

In an exchange economy with a finite number of indivisible goods, we analyze a dynamic trading process of coalitional recontracting where agents maymake mistakes with small probability. We show first that the recurrent classes of the unperturbed (mistake-free) process consist of (i) all core allocations as absorbing states, and (ii) non-singleton classes 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 stochastically stable 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. The robustness of these results is confirmed in a weak coalitional recontracting process.

Decentralized trade, random utility and the evolution of social welfare

We study decentralized trade processes in general exchange economies and house allocation problems with and without money. The processes are subject to persistent random shocks stemming from agents' maximization of random utility. By imposing structure on the utility noise term -logit distribution-, one is able to calculate exactly the stationary distribution of the perturbed Markov process for any level of noise. We show that the stationary distribution places the largest probability on the maximizers of weighted sums of the agents' (intrinsic) utilities, and this probability tends to 1 as noise vanishe

On the Failure of Core Convergence in Economies with Asymmetric Information

In interim economies with asymmetric information, we show a robust failure of the core convergence theorem. We begin by showing that the coarse core of Wilson (1978) does not converge to any set of price equilibrium allocations considered in the literature. To prove our main point we construct a simple example of a replicated sunspot economy with strictly convex and monotonic preferences. We also show that the coarse core may not satisfy the equal treatment property. Moreover, coarse core allocations satisfying the equal treatment property may not converge to price equilibrium allocations. The result applies to any notion of price equilibrium (including rational expectations equilibria, Radner equilibria, sunspot equilibria) in which fully informed consumers receive a consumption plan maximizing ex-post utility over the ex-post budget set. The non-convergence result holds for several different notions of the interim core proposed in the literature, including the fine core (Wilson (1978)), the private core (Yannelis (1991)), the core in the pooling case (Ichiishi and Idzik (1996), Goenka and Shell (1997)), the incentive compatible core (Vohra (1999)), the coarse+ core (Lee and Volij (forthcoming)), the core with endogenous communication (Volij (forthcoming)). This failure of core convergence is a basic consequence of asymmetric information, which at the interim stage, imposes important restrictions on coalition formation. (Informational constraints may rule out many coalitions of types of consumers that would be present in the standard Debreu and Scarf (1963) complete information framework.) In particular, our negative results do not rely on the lack of `informational smallness' of agents (at least in the sense in which this term has recently been formalized in McLean and Postlewaite (1999)).

Decentralized trade, random utility and the evolution of social welfare.

We study decentralized trade processes in general exchange economies and house allocation problems with and without money. The processes are subject to persistent random shocks stemming from agents' maximization of random utility. By imposing structure on the utility noise term -logit distribution-, one is able to calculate exactly the stationary distribution of the perturbed Markov process for any level of noise. We show that the stationary distribution places the largest probability on the maximizers of weighted sums of the agents' (intrinsic) utilities, and this probability tends to 1 as noise vanishes

On the Failure of Core Convergence in Economies with Asymmetric Information

In interim economies with asymmetric information, we show that the coarse core of Wilson (1978) does not converge to price equilibrium allocations as the economy is replicated. This failure of core convergence is a basic consequence of asymmetric information and extends to any reasonable notion of either (interim) core or price equilibrium.core, price equilibrium, asymmetric information, interim economies, sunspot economies.