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.

Game‐theoretic approaches to product introduction strategies for durable products

“…We analyze the company behavior in the duopoly market based on the most common strategies, including Cournot and Stackelberg, that account for the decisions made by both companies (Vranki c et al, 2021). The availability of information about the competitor's decision is the main differential aspect that characterizes the nature of these strategies.…”

Strategic Third-Party Product Entry and Mode Choice under Self-Operating Channels and Marketplace Competition: A Game-Theoretical Analysis

“…Recently, several studies have examined the effects of platform business models with respect to other operational decisions, such as product demand uncertainty [25], supplyside competition [26,27], duopolistic competition [28,29], R&D evaluation [30], and the logistics service provision [31]. Our research diverges from the aforementioned literature in that it explores the interactions among the incumbent supplier's self-operating mode (i.e., reselling or revenue sharing), the openness of the platform, and the entry decisions of a third-party supplier, which have not yet been explored.…”

“…Our work, by contrast, considered cases where two competing products are horizontally differentiated so that, under equal prices, some consumers would inherently prefer the incumbent supplier's product while others would favor the entrant supplier's product. Furthermore, we examined how the logistics service impacts the strategic entry of third-party products and price competition between the incumbent and the entrant, which is an important yet still underexplored area of research [28].…”

“…In contrast, we considered cases where two competing products are horizontally differentiated, resulting in an inherent preference for the incumbent supplier's product among others at equal prices. Moreover, we analyzed the impact of a logistics service on the third-party product's strategic entry and price competition between the incumbent and the entrant, which is an important but underexplored area in previous research [28].…”

A discrete time evolution model for fracture networks

“…However, fracture networks are not static objects; they evolve in various manners. Evolution models are popular mathematical tools, used also in operations research (Vrankic et al 2021). This particular evolution may be modeled by regarding an initial fracture network (to which we will refer as primary network) and then consider a family of discrete, local events under the random sequence of which the primary network evolves.…”