Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/213007 
Year of Publication: 
2019
Series/Report no.: 
CFS Working Paper Series No. 638
Publisher: 
Goethe University Frankfurt, Center for Financial Studies (CFS), Frankfurt a. M.
Abstract: 
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 to computing modified game versions with corner solutions by employing a homotopy approach.
Subjects: 
differential games
endogenous growth
tragedy of the commons
Lagrange-d'Alembert equation
analytic functions
JEL: 
C73
C61
D74
E0
O40
O44
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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