Existence and properties of equilibria for a dynamic game on productive assets

We consider a model in which two agents share access to the same stock of a productive asset and study the implications of non-cooperative consumption behavior over time. Under standard assumptions on the production function we construct infinitely many Nash equilibria, all of which consist of stationary Markovian strategies. These equilibria result in overconsumption so that the uniquely determined long-run asset stock is too low as compared to the cooperative solution. However, in the limit as the discount rate becomes sufficiently small the stead states generated by the Markovian Nash equilibria converge to the efficient steady state. (C) 1996 Academic Press, Inc.