Constrained gaming approaches to decisionmaking under uncertainty

It is shown that various types of models, including those used by Fishburn to examine the consistency or otherwise of individual preference and probability rankings, and by McInerney to determine optimal crop planting strategies under conditions of uncertainty, can be both represented and generalized by means of a class of constrained games. The duality properties of these games not only serve to evaluate particular strategy choices, but to indicate ways in which decisionmakers might choose whether or not to modify prior probability judgements or contingent payoff evaluations. The form of these duality properties also suggests further extensions and generalizations to other classes of problems, including problems with explicitly nonlinear structures.