Hierarchical Game under Uncertainty: a Case of Different Social Behavior

In the paper, a two-level hierarchical game with one upper-level player and N lower-level players is considered. The game models the heterogeneous social behavior of the bottom-level players. Unlike classical game-theoretic models, where all agents are strictly selfish, it is assumed that the bottom-level players are divided into two groups: committed altruists acting within the Berge equilibrium (the desire to maximize the payoff of others) and selfish agents adhering to the traditional Nash equilibrium and maximizing their own payoff. Furthermore, the payoff functions of each player are affected by interval uncertainty. The concept of a Pareto-guaranteed hybrid equilibrium is formalized for the proposed game. A linear-quadratic hierarchical game under uncertainty with one top-level player and three bottom-level players, two of whom are altruists and one of whom adheres to a selfish behavior model, is given as a model example. A Pareto-guaranteed hybrid equilibrium is constructed analytically for this game. The approach developed in this article allows for more accurate modeling of real-world socioeconomic processes characterized by information asymmetry and the presence of different behavioral incentives among individuals, for example, in macroeconomic governance systems or in models of state-society interactions.

Keywords

Berge equilibrium; Nash equilibrium; hybrid equilibrium; uncertainty; hierarchical game.

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