Endogenous Equilibria in Liquid Markets with Frictions and Boundedly Rational Agents

37 Pages Posted: 10 Apr 2012

See all articles by Paolo Dai Pra

Paolo Dai Pra

University of Padua - Department of Pure and Applied Mathematics

Fulvio Fontini

University of Padova - Department of Economics and Management "Marco Fanno"

Elena Sartori

Ca Foscari University of Venice - Department of Management

Marco Tolotti

Ca Foscari University of Venice - Department of Management

Date Written: August 5, 2011

Abstract

In this paper we propose a simple binary mean field game, where N agents may decide whether to trade or not a share of a risky asset in a liquid market. The asset's returns are endogenously determined taking into account demand and transaction costs. Agents' utility depends on the aggregate demand, which is determined by all agents' observed and forecasted actions. Agents are boundedly rational in the sense that they can go wrong choosing their optimal strategy. The explicit dependence on past actions generates endogenous dynamics of the system. We, firstly, study under a rather general setting (risk attitudes, pricing rules and noises) the aggregate demand for the asset, the emerging returns and the structure of the equilibria of the asymptotic game. It is shown that multiple Nash equilibria may arise. Stability conditions are characterized, in particular boom and crash cycles are detected. Then we precisely analyze properties of equilibria under significant examples, performing comparative statics exercises and showing the stabilizing property of exogenous transaction costs.

Keywords: Endogenous dynamics, Nash equilibria, Bounded rationality, Transaction costs, Mean field games, Random utility

JEL Classification: D81, C62, C72

Suggested Citation

Dai Pra, Paolo and Fontini, Fulvio and Sartori, Elena and Tolotti, Marco, Endogenous Equilibria in Liquid Markets with Frictions and Boundedly Rational Agents (August 5, 2011). Department of Management, Università Ca' Foscari Venezia Working Paper No. 7/2011, Available at SSRN: https://ssrn.com/abstract=2037854 or http://dx.doi.org/10.2139/ssrn.2037854

Paolo Dai Pra

University of Padua - Department of Pure and Applied Mathematics ( email )

Via Belzoni 7
Padova, 35100
ITALY

Fulvio Fontini

University of Padova - Department of Economics and Management "Marco Fanno" ( email )

Via del Santo, 33
Padova, 35123
Italy

Elena Sartori

Ca Foscari University of Venice - Department of Management ( email )

San Giobbe, Cannaregio 873
Venice, 30121
Italy

Marco Tolotti (Contact Author)

Ca Foscari University of Venice - Department of Management ( email )

San Giobbe, Cannaregio 873
Venice, 30121
Italy

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