Toward an Extension of Decision Analysis to Competitive Situations

摘要

The purpose of this thesis is to lay the foundation for the extension of Decision Analysis to enable it (1) to advise a decision maker in a competitive situation and (2) to model the preferences of decision makers who do not accept the axioms of Decision Analysis. The intention is to combine Game Theory with Decision Analysis to accomplish the first goal. The second goal will be achieved through the use of utility models currently under development by several investigators. A unified methodology is presented. It contains three major parts: the model of the game, a typology of possible players and a solution method. The model is the Decision Analysis decision tree, modified to include competitors. The typology of players is a modification of a proposal by Harsanyl, and contains the decision maker's information on his opponents. The solution method itself has three major parts. The first is the use of a modified form of rationalizable solutions as the basic decion method. The second is the use of Bayesian updatig to gain information on the type of an opponent based on his previous moves. The third is the use of Hypergames as an additional method of sensitivity analysis to aid in correctly analyzing the infinite regress of expectation. The proposed methodology is mathematically equivalent to treating the opponents' moves as random events. However, the methods by which we assess these probabilities and conduct sensitivity analysis should make this model much more accurate than direct assessment.