Symmetric Markovian Games of Commons with Potentially Sustainable Endogenous Growth

52 Pages Posted: 30 Jan 2020

See all articles by Zaruhi Hakobyan

Zaruhi Hakobyan

National Research University Higher School of Economics; Universite du Luxembourg - Luxembourg School of Finance

Christos Koulovatianos

Department of Finance, University of Luxembourg

Date Written: November 26, 2019

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.

Keywords: differential games, endogenous growth, tragedy of the commons, Lagrange-d’Alembert equation, analytic functions

JEL Classification: C73, C61, D74, E0, O40, O44

Suggested Citation

Hakobyan, Zaruhi and Koulovatianos, Christos, Symmetric Markovian Games of Commons with Potentially Sustainable Endogenous Growth (November 26, 2019). CFS Working Paper, No. 638, 2019, Available at SSRN: https://ssrn.com/abstract=3516167 or http://dx.doi.org/10.2139/ssrn.3516167

Zaruhi Hakobyan

National Research University Higher School of Economics ( email )

Myasnitskaya street, 20
Moscow, Moscow 119017
Russia

Universite du Luxembourg - Luxembourg School of Finance ( email )

162a, avenue de la Faïencerie
Luxembourg-Limpertsberg, L-1511
Luxembourg

Christos Koulovatianos (Contact Author)

Department of Finance, University of Luxembourg ( email )

4 Rue Albert Borschette
Luxembourg, L-1246
Luxembourg

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