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Conjectural variations in the oligopoly game with different types of reflexive behavior and successive number of players

A game-theoretic model of oligopoly with reflexive player behavior and quantity conjectural variations is proposed. The model generalizes two types of player reflexion –symmetric and asymmetric. It allows to describe the forecasts regarding competitors’ actions more flexibly and to study a wider range of market equilibrium options. For symmetric reflexions, the model is examined in terms of the influence of reflexivity rank and the number of players, revealing the dependence of equilibria on the depth of players’ strategic thinking. For asymmetric reflexions, the model is analyzed depending on the type of representation and the number of players. The goal of the study is to develop a method for calculating conjectural variations for both symmetric and asymmetric player representations. Unlike existing methods for calculating conjectural variations, which ignore the interactions between the number of players and the depth and type of reflexivity, this study yields new results for linear demand and cost functions. These results have significant practical implications and allow for the calculation of game equilibria with arbitrary reflexivity ranks and an arbitrary number of players, while also taking into account the type of reflexion of the analyzed player. This expands the toolkit for modeling real-world market situations. Thus, this study makes a significant contribution to the development of reflexive game theory by offering an adequate mathematical framework for analyzing strategic interactions in oligopoly settings, taking into account the heterogeneous expectations of players, which is necessary for forecasting market dynamics. To visualize the analytical results, graphical interpretations of the patterns of change in hypothetical variations are presented, which are used to formulate conclusions. Read more...