On a special case of non-symmetric resource extraction games with unbounded payoffs

Authors

DOI:

https://doi.org/10.11121/ijocta.01.2022.001070

Keywords:

stochastic games, resource extraction, Markov perfect equilibrium, isoelastic utility, geometric random walk

Abstract

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.

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Author Biography

Illia Sylenko, National University of Kyiv-Mohyla Academy

is a Ph.D. student at the National University of Kyiv-Mohyla Academy, Ukraine. Previously obtained a Bachelor degree in Applied Mathematics (National University of Kyiv-Mohyla Academy), a Master's degree in Scientific Computing (Université Lille 1) and a Master's degree in Optimization (Université Paris-Sud).

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Published

2021-11-16

How to Cite

Sylenko, I. (2021). On a special case of non-symmetric resource extraction games with unbounded payoffs. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 12(1), 1–7. https://doi.org/10.11121/ijocta.01.2022.001070

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Research Articles