A Computational Analysis of the Core of a Trading Economy with Three Competitive Equilibria and a Finite Number of Traders

Alok Kumar and Martin Shubik

Yale School of Management Working Papers from Yale School of Management

Abstract: In this paper we examine the structure of the core of a trading economy with three competitive equilibria as the number of traders (N) is varied. We also examine the sensitivity of the multiplicity of equilibria and of the core to variations in individual initial endowments. Computational results show that the core first splits into two pieces at N = 5 and then splits a second time into three pieces at N = 12. Both of these splits occur not at a point but as a contiguous gap. As N is increased further, the core shrinks by N = 600 with essentially only the 3 competitive equilibria remaining. We find that the speed of convergence of the core toward the three competitive equilibria is not uniform. Initially, for small N, it is not of the order 1/N but when N is large, the convergence rate is approximately of the order 1/N. Small variations in the initial individual endowments along the price rays to the competitive equilibria make the respective competitive equilibrium (CE) unique and once a CE becomes unique, it remains so for all allocations on the price ray. Sensitivity analysis of the core reveals that in the large part of the endowment space where the competitive equilibrium is unique, the core either converges to the single CE or it splits into two segments, one of which converges to the CE and the other disappears.

Keywords: Core; Multiple competitive equilibria; Speed of convergence; Sensitivity Analysis. (search for similar items in EconPapers)
Date: 2001-09-01, Revised 2003-11-01
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Related works:
Working Paper: A Computational Analysis of the Core of a Trading Economy with Three Competitive Equilibria and a Finite Number of Traders (2003)
Working Paper: A Computational Analysis of the Core of a Trading Economy with Three Competitive Equilibria and a Finite Number of Traders (2001)
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