Generalizing the Proportional Response Dynamic for Exchange Economies

Abstract

We investigate generalizing the proportional response dynamic for exchange economies via two extensions: arbitrary endowments and arbitrary network structures. In a complete graph with arbitrary endowments, we show that a simple strategy of splitting up bids equally between sellers of identical goods is a Nash equilibrium. Further, we argue that this strategy is the natural approach for choosing initial bids, implying this is the ideal approach in general. For an arbitrary network with arbitrary endowments, we propose a method for updating bids based on the individual utility extracted for each version of a good. We also prove that these two strategies are identical in a complete graph under a mild assumption on the initial bids.

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