The game of resource extraction / capital accumulation is a stochastic nonzero-sum infinite horizon game, obtained as an extension of the well-known optimal growth model to m strategically competing players, who jointly posses a renewable resource. The existence of a Nash equilibrium in different, often symmetric, frameworks of the game received a significant attention in the scientific literature on the topic. The focus of this paper is to introduce the coalitional component to the symmetric problem. Specifically, we examine whether the game with a fixed coalitional structure admits stability against profitable coalitional deviations.It is assumed that the set of all players is partitioned into coalitions which do not intersect and remain consistent throughout the game. The members of each coalition are able to coordinate their actions and perform joint deviations in a cooperative manner. Such setting incorporates a natural concept of established social ties, which may reflect a potential context appearing in practical applications. The corresponding notion of equilibrium in the paper is expressed as a position, from which none of the set coalitions can deviate in a manner to increase a total reward of its members. Its existence is studied in the context of a certain symmetric resource extraction game model with unbounded utilities of the players. This model was studied in [12; 13], concluding a Stationary Markov Perfect Equilibrium existence in both symmetric and non-symmetric game structure. The first feature of the model is that the preferences of the players are considered to be isoelastic in the form of strictly concave power functions. Furthermore, the law of motion between states is set to follow a geometric random walk in relation to players' joint investments. We prove that the game within the formulated settings admits stability against profitable coalitional deviations for any partition on the set of agents. The method provides an algorithm for building the corresponding stationary strategies, which can be useful for practical purposes. Finally, we use two examples with different numerical configurations to illustrate possible patterns of how the individual rewards of the players vary depending on a coalitional structure, which is set at the beginning of the game.

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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