Beschreibung:
<jats:title>Summary</jats:title><jats:p>Consider the domain of economic environments <jats:italic>E</jats:italic> whose typical element is ξ = (<jats:italic>U</jats:italic><jats:sub>1</jats:sub>, <jats:italic>U</jats:italic><jats:sub>2</jats:sub>, Ω, <jats:italic>ω</jats:italic>*), where <jats:italic>u<jats:sub>i</jats:sub></jats:italic> are Neumann-Morgenstern utility functions, Ω is a set of lotteries on a fixed finite set of alternatives, and <jats:italic>ω</jats:italic>* ∈ Ω. A mechanism <jats:italic>f</jats:italic> associates to each ξ a lottery <jats:italic>f</jats:italic>(ξ) in Ω. Formulate the natural version of Nash’s axioms, from his bargaining solution, for mechanisms on this domain. (<jats:italic>e.g</jats:italic>., IIA says that if ξ′ = (<jats:italic>U</jats:italic><jats:sub>1</jats:sub>, <jats:italic>U</jats:italic><jats:sub>2</jats:sub>, Δ, <jats:italic>ω</jats:italic>′), Δ ⊂ Ω, and <jats:italic>f</jats:italic> ∈ Δ then <jats:italic>f</jats:italic>(ξ′) = <jats:italic>f</jats:italic>(ξ).) It is shown that the Nash axioms (Pareto, symmetry, IIA, invariance w.r.t. cardinal transformations of the utility functions) hardly restrict the behavior of the mechanism at all. In particular, for any integer <jats:italic>M</jats:italic>, choose <jats:italic>M</jats:italic> environments <jats:italic>ξ<jats:sub>i</jats:sub>, i</jats:italic> = 1, … , <jats:italic>M</jats:italic>, and choose a Pareto optimal lottery <jats:italic>ω<jats:sub>i</jats:sub></jats:italic> ∈ Ω<jats:sub><jats:italic>i</jats:italic></jats:sub>, restricted only so that no axiom is directly contradicted by these choices. Then there is a mechanism <jats:italic>f</jats:italic> for which <jats:italic>f</jats:italic>(<jats:italic>ξ<jats:sub>i</jats:sub></jats:italic>) = <jats:italic>ω<jats:sub>i</jats:sub></jats:italic>, which satisfies all the axioms, and is continuous on <jats:italic>E</jats:italic>.</jats:p>