Symmetric Markovian Games of Commons with Potentially Sustainable Endogenous Growth

Differential games of common resources that are governed by linear accumulation constraints have several applications. Examples include political rent-seeking groups expropriating public infrastructure, oligopolies expropriating common resources, industries using specific common infrastructure or equipment, capital flight problems, pollution, etc. Most of the theoretical literature employs specific parametric examples of utility functions. For symmetric differential games with linear constraints and a general time-separable utility function depending only on the player’s control variable, we provide an exact formula for interior symmetric Markovian strategies. This exact solution (a) serves as a guide for obtaining some new closed-form solutions and for characterizing multiple equilibria and (b) implies that if the utility function is an analytic function, then the Markovian strategies are analytic functions, too. This analyticity property facilitates the numerical computation of interior solutions of such games using polynomial projection methods and gives potential for computing modified game versions with corner solutions by employing a homotopy approach.