TY - JOUR

T1 - A price model with finitely many agents

AU - Alharbi, Abdulrahman

AU - Bakaryan, Tigran

AU - Cabral, Rafael

AU - Campi, Sara

AU - Christoffersen, Nicholas

AU - Colusso, Paolo

AU - Costa, Odylo

AU - Duisembay, Serikbolsyn

AU - Ferreira, Rita

AU - Gomes, Diogo A.

AU - Guo, Shibei

AU - Gutierrezpineda, Julian

AU - Havor, Phebe

AU - Mascherpa, Michele

AU - Portaro, Simone

AU - Ribeiro, Ricardo de Lima

AU - Rodriguez, Fernando

AU - Ruiz, Johan

AU - Saleh, Fatimah

AU - Strange, Calum

AU - Tada, Teruo

AU - Yang, Xianjin

AU - Wróblewska, Zofia

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Applied Mathematics Summer School

PY - 2019/12

Y1 - 2019/12

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/662310

M3 - Article

JO - Bulletin of the Portuguese Mathematical Society

JF - Bulletin of the Portuguese Mathematical Society

ER -