The Evolution of Exchange

The aim of the paper is to introduce the modern techniques of evolutionary game theory introduced into economics by Young (1993) and others to analyze exchange economies. We define a dynamic matching process on the simple housing problem introduced by Shapley and Scarf (1974) and analyze the stochastic stability of its allocations. Our main findings are: 1. All the efficient allocations are stochastically stable. 2. In three-person economies, all the stochastically stable allocations are efficient. 3. An example of a four-agent economy where an inefficient allocation is stochastically stable.

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

General equilibrium, coordination and multiplicity on spot markets

This is a slightly revised English version of a paper published in the "Revue d'Economie Politique" 112 (5) sept-oct 2002. The text reviews recent work on expectational coordination in general equilibrium models of the Walrasian tradition. It evokes briefly the multiplicity questions associated with infinite horizon models and the issues associated with "eductive learning". It examines in a more systematic way the coordination difficulties that would arise in finite horizon models with spot multiplicity and discusses the relationship between coordination and incompleteness.General equilibrium models ; coordination ; multiplicity

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.

Dynamic recontracting processes with multiple indivisible goods

We consider multiple-type housing markets. To capture the dynamic aspect of trade in such markets, we study a dynamic recontracting process similar to the one introduced by Serrano and Volij (2005). First, we analyze the set of recurrent classes of this process as a (non-empty) solution concept. We show that each core allocation always constitutes a singleton recurrent class and provide examples of non-singleton recurrent classes consisting of blocking-cycles of individually rational allocations. For multiple-type housing markets stochastic stability never serves as a selection device among recurrent classes.Next, we propose a method to compute the limit invariant distribution of the dynamic recontracting process. The limit invariant distribution exploits the interplay of coalitional stability and accessibility that determines a probability distribution over final allocations. We provide various examples to demonstrate how the limit invariant distribution discriminates among stochastically stable allocations: surprisingly, some core allocations are less likely to be final allocations of the dynamic process than cycles composed of non-core allocations.core, indivisible goods, limit invariant distribution, stochastic stability

Dynamic Recontracting processes with Multiple Indivisible Goods

We consider multiple-type housing markets. To capture the dynamic aspect of trade in such markets, we study a dynamic recontracting process similar to the one introduced by Serrano and Volij (2005). First, we analyze the set of recurrent classes of this process as a (non-empty) solution concept. We show that each core allocation always constitutes a singleton recurrent class and provide examples of non-singleton recurrent classes consisting of blocking-cycles of individually rational allocations. For multiple-type housing markets stochastic stability never serves as a selection device among recurrent classes. Next, we propose a method to compute the limit invariant distribution of the dynamic recontracting process. The limit invariant distribution exploits the interplay of coalitional stability and accessibility that determines a probability distribution over final allocations. We provide various examples to demonstrate how the limit invariant distribution discriminates among stochastically stable allocations: surprisingly, some core allocations are less likely to be final allocations of the dynamic process than cycles composed of non-core allocations.microeconomics ;

A Dynamic Recontracting Process for Multiple-Type Housing Markets

We consider multiple-type housing markets. To capture the dynamic aspect of trade in such markets, we study a dynamic recontracting process similar to the one introduced by Serrano and Volij (2008). First, we analyze the set of recurrent classes of this process as a (non-empty) solution concept. We show that each core allocation always constitutes a singleton recurrent class and provide examples of non-singleton recurrent classes consisting of blocking-cycles of individually rational allocations. For multiple-type housing markets stochastic stability never serves as a selection device among recurrent classes. Next, we propose a method to compute the limit invariant distribution of the dynamic recontracting process. Furthermore, we discuss how the limit invariant distribution is inuenced by the relative coalitional stability and accessibility of the different stochastically stable allocations. We illustrate our finndings with several examples. In particular, we demonstrate that some core allocations are less likely to be final allocations of the dynamic process than cycles composed of non-core allocations.core; indivisible goods; limit invariant distribution; stochastic stability

Financial deepening and economic growth

The core of Shapley-Shubik games and general equilibrium models with a Venn diagram is applied for a theory on the role of real finance in economic growth among advanced economies. Then the dynamic computable general equilibrium (DCGE) models for Germany, France, UK, Japan and USA are constructed to assess the validity of the over financing hypothesis that reappeared after the financial crisis of 2008. Actual financial deepening ratios observed in the non-consolidated balance sheet of the OECD exceeded by factors of 3.5, 2.4, 5.1, 11.6 and 4.8 to the optimal financial deepening ratios implied by DCGE models respectively in these countries because of excessive leveraging and bubbles up to 19 times of GDP which were responsible for this great recession. Containing such massive fluctuations for macroeconomic stability and growth in these economies is not possible in conventional fiscal and monetary policy models and requires a DCGE analysis like this along with adoption of separating equilibria strategy in line of Miller-Stiglitz-Roth mechanisms to avoid asymmetric information problems in process of financial intermediation so that the gap between actual and optimal ratios of financial deepening remain as small as possible