We consider preference relations over information that are monotone: more information is preferred to less. We prove that, if a preference relation on information about an uncountable set of states of nature is monotone, then it is not representable by a utility function.

The set of possible outcomes of a strongly ordinal bimatrix game is studied by imbedding each pair of possible payoffs as a point on the standard two-dimensional integral lattice. In particular, we count the number of different Pareto optimal sets of each cardinality; we establish asymptotic...

Previous research has established that the predictions made by game theory about strategic behavior in incomplete information games are quite sensitive to the assumptions made about the players' infinite hierarchies of beliefs. We evaluate the severity of this robustness problem by...

We consider abstract exchange mechanisms wherein individuals submit "diversified" offers in m commodities, which are then redistributed to them. Our first result is that if the mechanism satisfies certain natural conditions embodying "fairness" and "convenience" then it admits unique prices, in...

We consider mechanisms that provide traders the opportunity to exchange commodity i for commodity j, for certain ordered pairs ij. Given any connected graph G of opportunities, we show that there is a unique mechanism M_G that satisfies some natural conditions of "fairness" and "convenience."...

A feasible social state is irreducible if and only if, for any non-trivial partition of individuals with two groups, there exists another feasible social state at which every individual in the first group is equally well-off and someone strictly better-off. Competitive equilibria decentralize...

Consider agents who undertake costly effort to produce stochastic outputs observable by a principal. The principal can award a prize deterministically to the agent with the highest output, or to all of them with probabilities that are proportional to their outputs. We show that, if there is...

An overlapping generations model of an exchange economy is considered, with individuals having a finite expected life-span. Conditions concerning birth, death, inheritance and bequests are fully specified. Under such conditions, the existence of stationary Markov equilibrium is established in...