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 to computing modified game versions with corner solutions by employing a homotopy approach.

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Author:Zaruhi Hakobyan, Christos Koulovatianos
Parent Title (English):Center for Financial Studies (Frankfurt am Main): CFS working paper series ; No. 638
Series (Serial Number):CFS working paper series (638)
Publisher:Center for Financial Studies
Place of publication:Frankfurt, M.
Contributor(s):Georges Zaccour
Document Type:Working Paper
Year of Completion:2019
Year of first Publication:2019
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2020/01/13
Tag:Lagrange-d'Alembert equation; analytic functions; differential games; endogenous growth; tragedy of the commons
Issue:November 26, 2019
Page Number:52
Institutes:Wirtschaftswissenschaften / Wirtschaftswissenschaften
Wissenschaftliche Zentren und koordinierte Programme / Center for Financial Studies (CFS)
Dewey Decimal Classification:3 Sozialwissenschaften / 33 Wirtschaft / 330 Wirtschaft
Licence (German):License LogoDeutsches Urheberrecht