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

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Sylenko, Illia
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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 equilib-rium existence in the non-symmetric game setting with an arbitrary numberof agents. Moreover, we allow that the players have unbounded utilities andrelax the assumption that the stochastic kernels of the transition probabilitymust depend only on the amount of resource before consumption. This classof the game has not been examined beforehand. However, we could provethe Markov perfect equilibrium existence only in the specific case of interest.Namely, when the players have constant relative risk aversion (CRRA) powerutilities and the transition law follows a geometric randomwalk in relationto the joint investment. The setup with the chosen characteristics is moti-vated by economic considerations, which makes it relevant to a certain rangeof real-word problems.
Stochastic games, Resource extraction, Markov perfect equilibrium, Isoelastic utility, Geometric random walk, article
Sylenko I. On a special case of non-symmetric resource extraction games with unbounded payoffs[electronic resource] / Illia Sylenko // An International Journal of Optimization and Control: Theories and Applications. - 2021. - Vol. 12, Issue 1. - P. 1-7.