Oligopoly games with Local Monopolistic Approximation

Evolutionary Competition Between Adjustment Processes in Cournot Oligopoly: Instability and Complex Dynamics

“…9 Aggregate equilibrium production is then given by Q * = nq * . The key question is: how do firms learn to play q * ?…”

“…9 Sufficient conditions for the existence and uniqueness of the Cournot-Nash equilibrium are that P (·) is twice continuously differentiable, nonincreasing and concave on the interval where it is positive and that C (·) is twice continuously differentiable, nondecreasing and convex, see Szidarovszky and Yakowitz [43]. For more general conditions on existence and uniqueness, see, e.g., Novshek [34] and Kolstad and Mathiesen [29], respectively.…”

“…For details, see Tuinstra [48] and Bischi et al [9]. 14 Recall that the local stability properties of the fixed point of a nonlinear dynamical system are qualitatively the same as those of the linearized system, provided that the fixed point is hyperbolic (that is, the Jacobian matrix has no eigenvalues on the unit circle), see, e.g., Kuznetsov [32].…”

“…This literature typically considers Cournot duopolies with non-monotonic reaction functions that are postulated ad hoc (Rand [39]), derived from iso-elastic demand functions together with substantial asymmetries in marginal costs (Puu [37]) or derived from cost externalities (Kopel [30]) and shows that best-reply dynamics might result in periodic cycles and chaotic behavior. For these models with nonmonotonic reaction curves, complicated behavior might also arise for other adjustment processes (see, e.g., [1,9]). Although non-monotonic reaction curves cannot be excluded on economic grounds 5 complicated behavior in our model emerges in a much more natural fashion and perpetual but bounded fluctuations occur even for linear demand and cost curves.…”

A continuous time Cournot duopoly with delays

“…The literature on nonlinear duopolies has developed models to study the behaviour of quantitysetting firms with limited information in a discrete time context (Bischi et al, 1998(Bischi et al, , 2007. The main aim of these works was essentially to question the results of stability of equilibria in dynamic models under the hypotheses of rational expectations (that require strong assumptions, such as, e.g., full information of decision makers and the efficient use of the set of available information) and homogeneous economic agents, showing that models with more realistic assumptions such as "bounded rationality" and heterogeneity may predict instability and more complex long-term dynamics.…”