TY  - UNPD
A1  - Hakobyan, Zaruhi
A1  - Koulovatianos, Christos
T1  - Symmetric markovian games of commons with potentially sustainable endogenous growth
T2  - Center for Financial Studies (Frankfurt am Main): CFS working paper series ; No. 638
N2  - 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.
T3  - CFS working paper series - 638 
KW  - differential games
KW  - endogenous growth
KW  - tragedy of the commons
KW  - Lagrange-d'Alembert equation
KW  - analytic functions
Y1  - 2019
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/52543
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-525435
UR  - https://ssrn.com/abstract=3516167
IS  - November 26, 2019
PB  - Center for Financial Studies
CY  - Frankfurt, M.
ER  -