Algorithms for hierarchical power
A flexible concept of hierarchical power is developed within the framework of noncooperative game theory to extend the systems-theory approach to the analysis of strategic interactions among decision makers having asymmetric roles. The definition focuses on the rules of play, rather than the structure of the model, to capture the asymmetry of the decision makers' positions. Hierarchical power involves the ability of a decision maker to choose a strategy in the knowledge of the opponent's choice. The effects of incorporating hierarchical power in a game are studied, a procedure for computing the hierarchical-power outcome when there are two decision makers is developed, and a computational method for assessing the stability of outcomes based on the rules of hierarchical power is also given. Computer programs have been developed to ease the computations involved in both these applications. The use of these stability concepts indicates that hierarchical power tends to stabilize cooperative behavior in many noncooperative situations. An exploratory study of two well known classes of games involving two decision makers shows that hierarchical power can provide a new technique for analyzing conflicts within hierarchical systems of decision makers.