Bounded Rational Players in a Symmetric Random Exchange Market

Aliyu Yusuf, Bruno Oliveira, Alberto Pinto () and Athanasios N. Yannacopoulos
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Aliyu Yusuf: Department of Mathematics, Faculty of Computing and Mathematical Sciences, Kano University of Science and Technology, Wudil 064, Nigeria
Bruno Oliveira: Faculty of Science and Nutrition, University of Porto, 4200-465 Porto, Portugal
Alberto Pinto: Faculty of Science, University of Porto, 4200-465 Porto, Portugal
Athanasios N. Yannacopoulos: Department of Statistics, Athens University of Economics and Business, Athens 10434, Greece

Mathematics, 2024, vol. 12, issue 23, 1-15

Abstract: A model of Edgeworthian economies is studied, in which participants are randomly chosen at each period to exchange two goods to increase their utilities, as described by the Cobb–Douglas utility function. Participants can trade deviating from their bilateral equilibrium, provided that the market and the trade follow appropriate symmetry conditions. The article aims to study the convergence to equilibrium in a situation where individuals or small groups of participants trade in a market, and prices are determined by interactions between the participants rather than by demand and supply alone. A dynamic matching and bargaining game is considered, with statistical duality imposed on the market game, ensuring that each participant has a counterpart with opposite preferences. This guaranties that there is sufficient incentive for trade. It is shown that, in each period, the expected logarithm of the trading price in the Edgeworthian economy equals the expected Walrasian price. This demonstrates that, under symmetry conditions, the trading price in the Edgeworthian economy is related to the Walrasian price, indicating convergence of the trading price in the Edgeworthian economy towards the Walrasian price. The study suggests that, under the right conditions, the decentralized trading model leads to price convergence similar to what would be expected in a more classical Walrasian economy, where prices balance demand and supply.

Keywords: game theory; general equilibrium; Walrasian price; random matching market (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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