Heterogeneity and the (de)stabilizing role of rationality

Abstract

a r t i c l e i n f o Article history: Available online xxx a b s t r a c tIn this paper we study oligopolies of generic size consisting of heterogeneous firms, which adopt best response adjustment mechanisms with either perfect foresight (rational firms) or static expectations (naive firms). Assuming an isoelastic demand function and possibly different marginal costs for the two groups of firms, we focus on the local stability of the Nash equilibrium. We show that, with respect to the oligopoly composition, described in terms of the fraction of rational firms, different scenarios are possible. We find that a high rationality degree may not always guarantee stability, in particular when rational firms have sufficiently larger marginal costs. In fact, in this situation, increasing the fraction of rational firms can even introduce instability. Besides the usual scenarios in which replacing some naive firms with rational ones leads to a stabilization of (or at least keeps unchanged) the dynamics, we provide a family of situations, characterized by costs ratio favorable to naive firms, in which equilibrium loses its stability when naive firms are replaced by rational ones. The results we present are both analytical and simulative.

Effects of Size, Composition, and Evolutionary Pressure in Heterogeneous Cournot Oligopolies with Best Response Decisional Mechanisms

“…On the other hand, in nonlinear contexts this may not be true anymore. For instance, in the working paper [18], where we deal with an isoelastic demand function, we find that increasing the number of rational firms may destabilize the system, under suitable conditions on marginal costs. It would be also interesting to analyze nonlinear frameworks with multiple Nash equilibria, in order to investigate the role of in such a different context, as well.…”

“…In particular, such works, in view of giving a foundation to the concept of Nash equilibrium, investigate under which conditions the dynamics converge towards the Nash equilibrium or towards a different attractor. To that research strand belong, for instance, the contributions by Agiza and Elsadany [8,9], by Agiza et al [10,11], by Ahmed and Agiza [12], by Angelini et al [13], by Bischi and Naimzada [14], by Canovas et al [15], by Cavalli and Naimzada [16,17], by Cavalli et al [18,19], by Elabbasy et al [20], by Ji [21], by Li and Ma [22], by Matsumoto [23], by Naimzada and Sbragia [24], by Pu and Ma [25], by Tramontana [26], and by Tuinstra [27].…”

“…Finally, we allow each group of firms to have different marginal costs. The approach of considering the market split into two groups of firms, identical within each group, is common in the oligopoly literature, as shown, for instance, by the works of Anufriev et al [28], Bischi et al [29], Cavalli et al [18], Droste et al [30], and Matsumoto and Szidarovszky [5]. The theoretical rationale for such an approach is that although it concerns one of the simplest possible forms of heterogeneity among firms, besides keeping the study analytically tractable, it allows obtaining interesting results, for example, with respect to equilibrium stability and chaotic dynamics, which can be straightforwardly interpreted and linked to the heterogeneity in rationality.…”

Monopoly models with time-varying demand function

“…In real situations, firms are usually constrained in arbitrarily increasing or decreasing their production levels (see [32]). The use of similar bounding techniques is quite common in the modelling of analogous economic contexts, see for example [33,34]. We stress that, since the bounding mechanism is linear on [β 1 , β 2 ], both the analytical results of Section 3 and the simulations reported in Section 4 do not change as long as q…”

A note on symmetry breaking in a non linear marketing model

“…Recently, part of the literature has focused on understanding how the interaction among groups of agents adopting heterogeneous strategies (Cavalli et al 2015) and the possibility of switching between groups (Bischi et al 2015) can generate non-trivial dynamic phenomena. The present work is directly connected to the articles of Bischi et al ( , 1999 and investigates whether the perfect knowledge of the economic mechanisms characterizing the market and the adoption of the best reply are capable of determining the loss (or achievement) of synchronization (in the short and long run) among the behaviors adopted by players, when applied to strategic contexts other than Puu (1991).…”