An Existence Result for Hierarchical Stackelberg v/s Stackelberg Games


In an exceedingly hierarchical Stackelberg v/s Stackelberg game, a collection of players called leaders play a Nash game constrained by the equilibrium conditions of a definite Nash game played amongst another set of players, known as followers. Generically, follower equilibria are non-distinctive as a function of leader methods and the decision problems of leaders are highly nonconvex and lacking in standard regularity conditions. Consequently, the provision of sufficient conditions for the existence of worldwide or even native equilibria remains a largely open question. In this paper, we present what is possibly the primary general existence result for equilibria for this category of games. Importantly, we impose no single-valuedness assumption on the equilibrium of the follower-level game. Specifically, underneath the idea that the objectives of the leaders admit a quasi-potential operate, a notion introduced in this paper, the global and local minimizers of a suitably defined optimization problem are shown to be the worldwide and local equilibria of the sport. In result, existence of equilibria can be guaranteed by the solvability of an optimization problem which holds beneath gentle conditions. We have a tendency to inspire quasi-potential games through an application in Communication networks.

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