Equilibrium in a Symmetric Game of Resource Extraction with Coalitional Structure

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