On price taking behavior in a nonrenewable resource cartel–fringe game

We consider a nonrenewable resource game with one cartel and a set of fringe members. We show that (i) the outcomes of the closed-loop and the open-loop nonrenewable resource game with the fringe members as price takers (the cartel–fringe game à la Salant, 1976) coincide and (ii) when the number of fringe firms becomes arbitrarily large, the equilibrium outcome of the closed-loop Nash game does not coincide with the equilibrium outcome of the closed-loop cartel–fringe game. Thus, the outcome of the cartel–fringe open-loop equilibrium can be supported as an outcome of a subgame-perfect equilibrium. However the interpretation of the cartel–fringe model, where from the outset the fringe is assumed to be price taker, as a limit case of an asymmetric oligopoly with the agents playing Nash–Cournot, does not extend to the case where firms can use closed-loop strategies.