On the influence of memory on complex dynamics of evolutionary oligopoly models

Abstract

In this paper, we propose a unitary formulation for evolutionary oligopoly models with memory. In particular, we consider behavioral rules that are stationary at the Nash equilibria so that we can study the stability of the oligopolistic model with memory with generic strategies for determining quantities. Although the introduction of memory does not affect the local stability properties of equilibria, we show how the presence of memory impacts the global dynamics of the system and how the question about the role of memory does not always provide a clear answer in terms of model complexity.

Hybrid dynamics of multi-species resource exploitation

“…Firstly, the phenomenon of having negative interests has been recently observed in the financial world. Secondly, it can be interpreted as a term of fading memory, which places more weight on more recent profits than on older ones, as described in Bischi et al (2020a) (see also Bischi and Merlone (2017) and Bischi et al (2020b) for evolutionary games with fading memory). In the particular case of δ = 0 we have that π * i in ( 11) is equal to π * i in ( 8), which is the original setup in Bischi et al (2013a).…”

Evolutionary oligopoly games with cooperative and aggressive behaviors

“…We show in particular how these dynamics are influenced by the parameters related to the level of cooperation and by the amount of memory, which is stabilizing in our case. In this regard, it is interesting to note that the role of memory in the literature is not always univocal: sometimes it is locally stabilizing or destabilizing [see Hommes et al (2012)], sometimes irrelevant for local stability properties of equilibria but influencing the global dynamics of the system (see Bischi et al (2015) and Bischi et al (2020)). For instance, Bischi et al (2018) find that a short memory is destabilizing compared to the case without memory but a long memory (at the uniform limit) is highly stabilizing.…”