  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.
