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Dynamics and stability of evolutionary optimal strategies in duopoly

Abstract

In this paper, we analyse the company behaviour in duopoly taking into account the most common strategies, including dominant, reactive, cooperative and tit-for-tat strategies, since they account for most of the decisions made by companies. Dominant, reactive and cooperative strategies may lead to different outcomes, such as Stackelberg, Cournot, Cartel, Cartel with one cheater and Perfect competition equilibria, while the tit-for-tat strategy may lead to Cartel, Cournot or Perfect competition equilibria due to its retribution nature. However, we argue that these outcomes are mainly valid in the short-run since in the long-run the companies learn and adapt to the behavioural pattern of their peer, which leads them to evolve to a new way of thinking and strategic planning taking into account the long-run effects. Due to the long-term perspective, the outcome of the implementation of various strategies in duopoly may not be efficiently solved using simple game theory analysis. For that purpose, we propose the utilization of more complex analysis, an evolutionary game theory, which is based on the adaption of the company to the behaviour of other players in a duopoly. When the probability of choices is applied, new fitness equations are obtained which show the changing tendencies towards the companies’ strategies that ensure payoffs above the average, in the long run, using a replicator dynamics concept. We analyse several scenarios, in which players choose among two, three or four strategies. Our results indicate that the long-run equilibrium and preferred options are significantly altered depending on the starting set of strategies.

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Correspondence to Ilko Vrankić.

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Vrankić, I., Herceg, T. & Pejić Bach, M. Dynamics and stability of evolutionary optimal strategies in duopoly. Cent Eur J Oper Res 29, 1001–1019 (2021). https://doi.org/10.1007/s10100-020-00713-6

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Keywords

  • Evolutionary game theory
  • Duopoly
  • Cooperative strategy
  • Dominant strategy
  • Reactive strategy
  • The tit-for-tat strategy