Inevitability of Collusion in a Coopetitive Bounded Rational Cournot Model with Increasing Demand - CAMPBELL, Michael (Journal of Mathematical Economics and Finance, 2016)
A coopetitive model, using the structure formulated by D. Carf`ı, is constructed for a bounded rational Cournot model with increasing demand (as with Veblen goods) and any number of agents. This model has a cooperative strategy parameter that interpolates be- tween perfect competition and collusion. For this model, H. Dixon’s result of the “inevitability of collusion” is demonstrated using a cluster expansion idea from percolation models in sta- tistical mechanics to prove positivity of correlation functions. Specifically, it is shown that every agent’s expected payoff increases as the cooperatively chosen interpolation parameter approaches the value that gives collusion. Therefore agents will cooperatively agree to collude. When the behavior is perfectly rational (zero temperature), collusion does not result in an in- crease in payoffs since agents produce at maximum output in competition or collusion: agents gain no benefit for putting in the extra effort to collude. So we see that neoclassical analysis (i.e., Nash equilibrium analysis) can not explain collusion in this case. However when we consider the full bounded rational model (positive temperatures), we recover Dixon’s result to see that agents will cooperatively decide to collude to maximize payoffs. We point out that the neoclassical model is the zero-temperature limit of the general bounded rational model utilized here in accordance with the Bohr correspondence principle.