Strategic Experimentation with Congestion

We consider a game of strategic experimentation in the presence of competition between two agents. Each agent faces a two-armed bandit problem in which she continually chooses between her private, risky arm and a common, safe arm. An agent has exclusive access to her private arm. However, only one of the agents can activate the common arm at any point in time, imposing a negative payoff externality on her opponent. The quality of the risky arms is independent across agents. We show that an agent attaches a strategic option value to being able to return to her private arm after having used the common arm. As a result, the common arm is more attractive than in the absence of competition. By occupying it an agent increases the likelihood of ending the payoff externality imposed by her opponent. We analyse the interesting and counter-intuitive behaviour that ensues in the unique Markov perfect equilibrium of this game. The first agent to occupy the common arm is the one who is more optimistic about her private arm. She does so in a state where even a myopic single decision-maker would prefer her private arm. She eventually returns to her private arm, even if this means forgoing her access to the common arm forever. We show that the common arm also carries a strategic option value when it is risky.