This book deals with the important economic problem of uncertainty. The first attempt was to simplify and unify some results usually taught in courses in mathematical economics. The economic interpretation of the results was representations of preferences as sums or integrals and the decomposition of preferences into utilities and probabilities. The book contains all the classical results, but the main justification of the book is that the approach taken in the earlier versions was also the proper approach in generalizing from preferences, which were total preorders to preferences, which were not total or transitive. The same mathematics gives representations which are additive. It also gives decompositions where concepts of utility, probability, and uncertainty appeared. These results are new and give a solution to how uncertainty can be formalized.

Competition and efficiency is at the core of economic theory. This volume collects papers of leading scholars, which extend the conventional general equilibrium model in important ways: Efficiency and price regulation are studied when markets are incomplete and existence of equilibria in such settings is proven under very general preference assumptions. The model is extended to include geographical location choice, a commodity space incorporating manufacturing imprecision and preferences for club-membership, schools and firms. Inefficiencies arising from household externalities or group membership are evaluated. Core equivalence is shown for bargaining economies. The theory of risk aversion is extended and the relation between risk taking and wealth is experimentally investigated. Other topics include determinacy in OLG with cash-in-advance constraints, income distribution and democracy in OLG, learning in OLG and in games, optimal pricing of derivative securities, the impact of heterogeneity at the individual level for aggregate consumption, and adaptive contracting in view of uncertainty.

Competition and efficiency is at the core of economic theory. This volume collects papers of leading scholars, which extend the conventional general equilibrium model in important ways: Efficiency and price regulation are studied when markets are incomplete and existence of equilibria in such settings is proven under very general preference assumptions. The model is extended to include geographical location choice, a commodity space incorporating manufacturing imprecision and preferences for club-membership, schools and firms. Inefficiencies arising from household externalities or group membership are evaluated. Core equivalence is shown for bargaining economies. The theory of risk aversion is extended and the relation between risk taking and wealth is experimentally investigated. Other topics include determinacy in OLG with cash-in-advance constraints, income distribution and democracy in OLG, learning in OLG and in games, optimal pricing of derivative securities, the impact of heterogeneity at the individual level for aggregate consumption, and adaptive contracting in view of uncertainty.