Compactness And Convexity of Static Contractual Sets

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Compactness And Convexity of Static Contractual Sets
Murat R Sertel
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= Ac, + X'c', 5 since f. Is linear. Hence, denoting p. = Ap. + A 'pi 2 2 2 2 2 2 2 V. (?!) = V (Z. * I^(c^)) >. U. (p. * I^(e^)), (p. E P. ), J Jl J J J J J Thus, y = (c„, ... , c ) c Y(c), implying c e 2(Y(c)) = S(c). Hence, c e C.
3 A. REM . Without following them through very far, we may briefly indicate some implications of the last two results. Apart from giving some motiv- ation for these results, the remarks below are hoped to be suggestive and inviting to other researchers.
As a result
...of 32. COR. , every continuous functional defined on C will attain a maxiraura (mininiu-m) on that set. As a result of 33. COR. , C allows us to define concave or convex functionals on itself. Thus, one may now go ahead and consider continuous objective functionals on C, specify the risk aversion reflected by their curvatures, and speak of maximizing (minimizing) then-i on C, The relevance of all this is clearer when one begins to consider "social leaders" or "controllers" who may be willing and able to influence the equilibrium outcomes, i.

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