Modelling Cournot Games as Multi-agent Multi-armed Bandits

TL;DR

This paper models repeated Cournot oligopoly games using multi-agent multi-armed bandits, proposing novel algorithms that improve learning efficiency and analyzing equilibrium outcomes through simulations.

Contribution

It introduces two new MA-MAB algorithms leveraging ordered action spaces and demonstrates their effectiveness in modeling Cournot competition.

Findings

$oldsymbol{ ext{epsilon-greedy+HL}}$ and $oldsymbol{ ext{epsilon-greedy+EL}}$ outperform traditional methods.

The algorithms facilitate convergence to various market equilibria.

Simulations show improved cumulative regret performance.

Abstract

We investigate the use of a multi-agent multi-armed bandit (MA-MAB) setting for modeling repeated Cournot oligopoly games, where the firms acting as agents choose from the set of arms representing production quantity (a discrete value). Agents interact with separate and independent bandit problems. In this formulation, each agent makes sequential choices among arms to maximize its own reward. Agents do not have any information about the environment; they can only see their own rewards after taking an action. However, the market demand is a stationary function of total industry output, and random entry or exit from the market is not allowed. Given these assumptions, we found that an $\epsilon$-greedy approach offers a more viable learning mechanism than other traditional MAB approaches, as it does not require any additional knowledge of the system to operate. We also propose two novel approaches that take advantage of the ordered action space: $\epsilon$-greedy+HL and $\epsilon$-greedy+EL. These new approaches help firms to focus on more profitable actions by eliminating less profitable choices and hence are designed to optimize the exploration. We use computer simulations to study the emergence of various equilibria in the outcomes and do the empirical analysis of joint cumulative regrets.