We consider a class of differential games with transition equations that are homogeneous of degree one. For any game G with a discount rate r, consider a Markov perfect equilibrium (MPE) with strategies that are linear in the state variables. We show that the time paths of the control variables...

We show that, if relative wealth appears in the utility function, for example due to status seeking, then under certain conditions on the curvature of the utility function and the production function, the poor will eventually catch up with the rich. We give sufficient conditions for the final...

We consider the class of differential games with transition dynamics and constraints that are homogeneous of degree one. We show that if the integrand of the objective function is homogeneous of degree , then best replies to linear homogeneous Markov strategies are linear homogeneous, and the...

We model the non-cooperative choice of levels of inputs whose current usage results in the future decline in their effectiveness. We show that there are multiple equilibria that are Pareto rankable. Compared with the social optimum, lack of cooperation implies excessive use of input, leading to...

We show that in some leader-follower games, a steady-state equilibrium in quantities may exist only with non-stationary shadow prices. We call this type of equilibrium a semi-stationary steady state. Conclusions that are drawn on the assumption that a steady-state equilibrium has stationary...

We show that the famous neutrality result in the theory of public good contributions (Warr, Kemp, Bergstrom, Blume and Varian) depends crucially on the assumption that agents do not take into account the effect of their public good contribution decisions on the relative price of the private...

We offer a new proof of the maximum principle for optimal control problems with fixed endpoint. We allow for inequality constraints involving state variables and control variables. Our proof relies on an application of the envelope theorem. Nous donnons une preuve nouvelle du principe de maximum...