A price model with finitely many agents

Abdulrahman Alharbi, Tigran Bakaryan, Rafael Cabral, Sara Campi, Nicholas Christoffersen, Paolo Colusso, Odylo Costa, Serikbolsyn Duisembay, Rita Ferreira, Diogo A. Gomes, Shibei Guo, Julian Gutierrezpineda, Phebe Havor, Michele Mascherpa, Simone Portaro, Ricardo de Lima Ribeiro, Fernando Rodriguez, Johan Ruiz, Fatimah Saleh, Calum StrangeTeruo Tada, Xianjin Yang, Zofia Wróblewska

Research output: Contribution to journalArticlepeer-review

Abstract

Here, we propose a price-formation model, with a population consisting of a finite number of agents storing and trading a commodity. The supply of this commodity is determined exogenously, and the agents are rational as they seek to minimize their trading costs. We formulate our problem as an N-player dynamic game with a market-clearing condition. The limit of this N-player problem is a mean-field game (MFG). Subsequently, we show how to recast our game as an optimization problem for the overall trading cost. We show the existence of a solution using the direct method in the calculus of variations. Finally, we show that the price is the Lagrange multiplier for the balance condition between supply and demand.
Original languageEnglish (US)
JournalBulletin of the Portuguese Mathematical Society
StatePublished - Dec 2019

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