A General Equilibrium Theorem for the Economy of Giving

TL;DR

This paper proves a general equilibrium theorem for gift economies, showing conditions for unique, exponentially converging equilibria where mutual yields sum to zero, extending previous models of giving transactions.

Contribution

It establishes a rigorous, general equilibrium theorem for gift economies, providing conditions for uniqueness and convergence of the model's equilibrium.

Findings

Unique equilibrium exists under certain conditions.

Convergence to equilibrium is exponential.

Total mutual yields sum to zero at equilibrium.

Abstract

In [1] we presented a model for transactions when goods are given away in the expectation of a later settlement. In settings where people keep track of their social accounts we were able to redefine concepts like account balance, yield curve and the law of diminishing returns. In this paper we establish a general equilibrium theorem, conjectured in [1], by developing sufficient conditions for any instance of the standard model (or Gift Economy Model) to have a unique equilibrium. The convergence to that equilibrium is exponential and for each pair of entities P and Q the total sum of yields from all mutual transactions is equal to zero. [1] W.P. Weijland, Mathematical Foundations for the Economy of Giving, ArXiv Categories: q-fin.GN, Report 1401.4664, 2014.