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.
Highlights
The game of resource extraction belongs to a class of nonzero-sum stochastic infinite-horizon games
The existence of a non-randomized stationary Nash equilibrium in a deterministic game setting was later established by Sundaram [4]
In this study we extend our view to the unexamined class of non-symmetric resource extraction games
Summary
The game of resource extraction ( known as the capital accumulation game) belongs to a class of nonzero-sum stochastic infinite-horizon games. The result of Sundaram relied on the assumptions that the preferences of the players are identical and bounded in the state space, i.e., the space of all possible resource stocks Both of these assumptions were helpful in reporting the existence of a stationary Nash equilibrium in different stochastic frameworks of the game. Some partial results of the Nash equilibrium existence in non-symmetric resource extraction games with unbounded payoffs were obtained in [17, 18] These extensions were achieved at the cost of additional structural assumptions. We restrict our attention to a specific form of the preferences and a concrete stochastic production function, the choices of which are motivated by economic considerations Such settings, on which we elaborate below, enable us to prove the existence of a non-randomized stationary Markov perfect equilibrium in the game. The preceding lemmata is aimed at finding the value functions which solve the corresponding Bellman equation for every player
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