Unraveling of Cooperation in Dynamic Collaboration

We examine collaboration in a one-arm bandit problem in which the players' actions affect the distribution over future payoffs. The players need to exert costly effort both to enhance the value of a risky technology and to learn about its current state. Both product value and learning are public goods, which gives the players incentives to free-ride on each others' actions. This leads to an inefficiently low aggregate level of effort. When the players' actions affect the distribution over future payoffs, they eventually get trapped in the low action, causing an inefficient unraveling of the game. Moreover, the players' incentives to exert effort depend on the state that in turn depends on the aggregate effort. If the players start restricting effort when the belief decreases in expectation, the two effects play in the same direction. Higher effort encourages higher effort and vice versa. Unraveling leads to multiple symmetric Markov perfect equilibria.