Know-how sharing with stochastic innovations

We provide a model of know-how sharing between competing firms in which each of two firms gets a stochastic innovation in its stock of know-how in every period. Separately considering the cases when innovations are indivisible and divisible, we examine the nature of the subgame perfect sharing agreements that can obtain. We discover that both stochasticity and indivisibility undermine the ability to support sharing. Furthermore, we find that there are equilibria in which know-how sharing can be intermittent and that small innovations are more likely to be shared than large ones, when innovations are divisible but not necessarily when they are indivisible.