Open AccessOn a special case of non-symmetric resource extraction games with unbounded payoffs
Author(s) -
Illia Sylenko
Publication year - 2022
Publication title -
an international journal of optimization and control: theories and applications/e-an international journal of optimization and control: theories and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.287
H-Index - 6
eISSN - 2146-5703
pISSN - 2146-0957
DOI - 10.11121/ijocta.01.2022.001070
Subject(s) - markov perfect equilibrium , mathematical economics , class (philosophy) , asset (computer security) , markov process , stochastic game , constant (computer programming) , resource (disambiguation) , markov chain , computer science , investment (military) , mathematics , range (aeronautics) , mathematical optimization , nash equilibrium , computer network , statistics , materials science , computer security , artificial intelligence , composite material , programming language , machine learning , politics , political science , law
The game of resource extraction/capital accumulation is a stochastic infinite-horizon game, which models a joint utilization of a productive asset over time. The paper complements the available results on pure Markov perfect equilibrium existence in the non-symmetric game setting with an arbitrary number of agents. Moreover, we allow that the players have unbounded utilities and relax the assumption that the stochastic kernels of the transition probability must depend only on the amount of resource before consumption. This class of the game has not been examined beforehand. However, we could prove the Markov perfect equilibrium existence only in the specific case of interest. Namely, when the players have constant relative risk aversion (CRRA) power utilities and the transition law follows a geometric random walk in relation to the joint investment. The setup with the chosen characteristics is motivated by economic considerations, which makes it relevant to a certain range of real-word problems.