Exact solution of a modified El Farol's bar problem: Efficiency and the role of market impact

TL;DR

This paper provides an exact analytical solution to a modified El Farol's bar problem, revealing how agents' awareness of their market impact influences collective efficiency and fluctuations.

Contribution

It introduces an exact solution for a model inspired by the El Farol and Minority games, highlighting the importance of agents accounting for market impact.

Findings

Accounting for market impact reduces global fluctuations.

Agents' adaptive behavior improves efficiency and utility.

Market impact awareness leads to more stable collective outcomes.

Abstract

We discuss a model of heterogeneous, inductive rational agents inspired by the El Farol Bar problem and the Minority Game. As in markets, agents interact through a collective aggregate variable -- which plays a role similar to price -- whose value is fixed by all of them. Agents follow a simple reinforcement-learning dynamics where the reinforcement, for each of their available strategies, is related to the payoff delivered by that strategy. We derive the exact solution of the model in the ``thermodynamic'' limit of infinitely many agents using tools of statistical physics of disordered systems. Our results show that the impact of agents on the market price plays a key role: even though price has a weak dependence on the behavior of each individual agent, the collective behavior crucially depends on whether agents account for such dependence or not. Remarkably, if the adaptive behavior of agents accounts even ``infinitesimally'' for this dependence they can, in a whole range of parameters, reduce global fluctuations by a finite amount. Both global efficiency and individual utility improve with respect to a ``price taker'' behavior if agents account for their market impact.