On the influence of memory on complex dynamics of evolutionary oligopoly models
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ORIGINAL PAPER
On the influence of memory on complex dynamics of evolutionary oligopoly models Gian Italo Bischi · Fabio Lamantia Bruno Scardamaglia
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Received: 1 February 2020 / Accepted: 17 July 2020 © The Author(s) 2020
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. Keywords Evolutionary oligopolies · Memory · Behavioral rules · Complex dynamics
G. I. Bischi Dipartimento di Economia, Società, Politica, Università di Urbino, Urbino, Italy e-mail: [email protected] F. Lamantia (B)· B. Scardamaglia Dipartimento di Economia, Statistica e Finanza, Università della Calabria, Calabria, Italy e-mail: [email protected] B. Scardamaglia e-mail: [email protected] F. Lamantia Faculty of Economics, VŠB - Technical University of Ostrava, Ostrava, Czech Republic
1 Introduction Dynamic models in physics, engineering, natural sciences and economics have the common feature of involving memory of some past states (or a continuous portions of past states) to determine their future time evolution (see, e.g., [15,26,27]). The inclusion of past history in the time evolution adds nontrivial complexities, thus introducing a trade-off between the advantage of dealing with more realistic models and the drawback of dynamic models which are more difficult to be studied. In social sciences, the inclusion of memory in modeling human decisions may sometimes be considered as a method to represent learning processes or discounted averaging methods (see, e.g., [3,16,17,21]). In order to study the effects of increasing memory in systems driven by repeated decisions of economic agents, we consider an evolutionary dynamic model in discrete time recently proposed in [10] and modify it by introducing a recursive method that adds the presence of memory (or discounted past averaging) in the decision process. The model describes an economic system composed by a population of agents facing a binary choice between two different behavioral strategies; the payoff obtained by each agent as a consequence of the chosen option is affected by the number of agents currently making the same choice and is expressed in the form of an evolutionary game based on replicator dynamics in discrete time. This mechanism
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describes how agents change their choices over time according to the currently observed payoff differences. However, decisions in real systems are not only based on currently observed payoff differences but also on information about past performances, which
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