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 Strange; Teruo Tada; Xianjin Yang; Zofia Wróblewska

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 journal › Article › peer-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 language	English (US)
Journal	Bulletin of the Portuguese Mathematical Society
State	Published - Dec 2019

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Alharbi, A., Bakaryan, T., Cabral, R., Campi, S., Christoffersen, N., Colusso, P., Costa, O., Duisembay, S., Ferreira, R., Gomes, D. A., Guo, S., Gutierrezpineda, J., Havor, P., Mascherpa, M., Portaro, S., Ribeiro, R. D. L., Rodriguez, F., Ruiz, J., Saleh, F., ... Wróblewska, Z. (2019). A price model with finitely many agents. Bulletin of the Portuguese Mathematical Society. https://repository.kaust.edu.sa/bitstream/10754/662310/1/Template_BSPM_Especial.pdf

@article{3e6f0d2690f048798f71f70a4cb0b6dc,

title = "A price model with finitely many agents",

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.",

author = "Abdulrahman Alharbi and Tigran Bakaryan and Rafael Cabral and Sara Campi and Nicholas Christoffersen and Paolo Colusso and Odylo Costa and Serikbolsyn Duisembay and Rita Ferreira and Gomes, {Diogo A.} and Shibei Guo and Julian Gutierrezpineda and Phebe Havor and Michele Mascherpa and Simone Portaro and Ribeiro, {Ricardo de Lima} and Fernando Rodriguez and Johan Ruiz and Fatimah Saleh and Calum Strange and Teruo Tada and Xianjin Yang and Zofia Wr{\'o}blewska",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: Applied Mathematics Summer School",

year = "2019",

month = dec,

language = "English (US)",

journal = "Bulletin of the Portuguese Mathematical Society",

}

Alharbi, A, Bakaryan, T, Cabral, R, Campi, S, Christoffersen, N, Colusso, P, Costa, O, Duisembay, S, Ferreira, R, Gomes, DA, Guo, S, Gutierrezpineda, J, Havor, P, Mascherpa, M, Portaro, S, Ribeiro, RDL, Rodriguez, F, Ruiz, J, Saleh, F, Strange, C, Tada, T, Yang, X & Wróblewska, Z 2019, 'A price model with finitely many agents', Bulletin of the Portuguese Mathematical Society. <https://repository.kaust.edu.sa/bitstream/10754/662310/1/Template_BSPM_Especial.pdf>

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 -

A price model with finitely many agents

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