It is well known that the set of correlated equilibrium distributions of an n-player noncooperative game is a convex polytope that includes all the Nash equilibrium distributions. We demonstrate an elementary yet surprising result: the Nash equilibria all lie on the boundary of the polytope....

Game-theoretic solution concepts such as Nash and Bayesian equilibrium start from an assumption that the players’ sets of possible payoffs, measured in units of von Neumann–Morgenstern utility, are common knowledge, and they go on to define rational behavior in terms of equilibrium strategy...

De Finetti's treatise on the theory of probability begins with the provocative statement PROBABILITY DOES NOT EXIST, meaning that probability does not exist in an objective sense. Rather, probability exists only subjectively within the minds of individuals. De Finetti defined subjective...

We model a situation in which two retailers consider launching an "Advance Booking Discount" (ABD) program. In this program, customers are enticed to precommit their orders at a discount price prior to the regular selling season. However, these precommitted orders are filled during the selling...

In the academic literature and professional practice, there are a number of alternative and apparently competing methods for valuing risky projects. In this paper, we compare and contrast three different approaches: risk-adjusted discount-rate analysis, option pricing analysis, and decision...

Decisions are often made under conditions of uncertainty about the actions of supposedly-rational competitors. The modeling of optimal behavior under such conditions is the subject of noncooperative game theory, of which a cornerstone is Harsanyi's formulation of games of incomplete information....