This paper studies the endogenous timing of moves in a game with competition in basic research between a university and a commercial firm. It examines the conditions under which the two entities end up investing in innovation at equilibrium, both under simultaneous and sequential moves. It argues that when the innovation process is not too costly, under any timing, the firm conducts research despite the opportunities for complete free riding. The two sequential move games with either player as leader emerge as equilibrium endogenous timings, with both entities realizing higher profits in either outcome than in a simultaneous move game. Each entity also profits more by following than by leading. Finally, as a proxy for a welfare analysis, we compare the propensities for innovation across the three scenarios and find that university leadership yields a superior performance. This may be used as a selection criterion to choose the latter scenario as the unique outcome of endogenous timing.
A general model for noncooperative extraction of common-property resource is considered. The main result is that this sequential game has a Nash equilibrium in stationary strategies. The proof is based on an infinite dimensional fixed-point theorem, and relies crucially on the topology of epi-convergence. A byproduct of the analysis is that Nash equilibrium strategies may be selected such that marginal propensities of consumption are bounded above by one.
JEL Classification: 026, 632, 213, 721
Keywords: Sequential games, Dynamic programming, Fixed point theorem, Nash equilibrium, Common property, Natural resources, Common property
Existence of equilibrium is proved for an exchange strategic market game with complete markets. An example of equilibrium with inconsistent prices is given.
We show that the monotonicity property of optimal paths (or, equivalently, the uniform boundedness of the marginal propensity of consumption by unity) is a necessary condition for local (as well as for global) optimality, and is also sufficient for local optimality, but not for global optimality. We also show that the well-known properties of the value function — continuity and monotonicity — are sufficient (along with the above conditions) to guarantee global optimality. In other words, if at any stock level, a local non-global maximizer is selected, a discontinuity in the value function will be observed. We suggest that the previous literature on this problem has not distinguished between local and global maxima, and consequently has not attempted to derive conditions that uniquely characterize global optimality. This is the major aim of this paper, and we hope to have provided some insight towards a systematic approach to non-convex dynamic optimization.