Open AccessCOMPUTING THE EQUILIBRIA OF DYNAMIC COMMON PROPERTY GAMES
Author(s) -
Ligon Ethan,
Narain Urvashi
Publication year - 1997
Publication title -
natural resource modeling
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.28
H-Index - 32
eISSN - 1939-7445
pISSN - 0890-8575
DOI - 10.1111/j.1939-7445.1997.tb00112.x
Subject(s) - property (philosophy) , class (philosophy) , markov perfect equilibrium , sequential game , mathematical economics , computer science , mathematical optimization , focus (optics) , markov chain , quadratic equation , construct (python library) , resource (disambiguation) , state (computer science) , game theory , mathematics , nash equilibrium , algorithm , artificial intelligence , computer network , philosophy , programming language , machine learning , optics , physics , geometry , epistemology
In this paper we discuss techniques for rapidly computing the equilibria of a class of dynamic linear‐quadratic games involving the extraction of a common property resource. Though this class of games has been much studied, the search for equilibria of these games has only been attempted in special cases, and analysis of the game has tended to focus on its steady‐state properties. We construct a pseudo‐planning problem, the optimal of which correspond to the Markov perfect equilibria of the class of games we explore. We show how the optima (equilibria) of this pseudo‐planning problem (game) can be rapidly computed via a Riccati‐like equation. Finally, we illustrate the use of these techniques with several examples involving the extraction of a common property resource.