Strategic Experimentation with Congestion

We consider a model of competition between two players, each of whom faces a multi-armed bandit problem. A player chooses between activating a risky option (modelled as a Poisson process with unknown arrival rate) to which she has exclusive access, and competing for the use of a single safe option that can only be used by one player at a time. When players cannot reverse their decision to switch to the safe option, the equilibrium in the two-player game is inefficient and involves too little experimentation. As the priors of the players become closer, competition intensifies and the inefficiency increases until the players behave completely myopically. When the decision to switch to the safe option is revocable, we show that each player attaches a strategic option value to being able to return to her own risky option after having switched to the safe option. This makes the safe option more attractive and in equilibrium the first player to occupy it does so in a state where even a myopic single decision-maker would prefer experimenting. Here, she occupies the safe option in order to strategically force her opponent to experiment. She eventually returns to her risky option, even if the opponent has not had a success, forgoing her access to the safe option forever.