L2-preferences-Part1

L2-preferences-Part1 - Preferences Preferences Preferences...

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Preferences. Preferences Primitives: X : “set of alternatives” Closed and convex set ± : “at least as good as” (weakly preferred) Binary relation: x ± y ² : (strictly preferred) x ² y means x ± y and y x (indifference) x y means x ± y and y ± x Do not confuse “ ± ” with “ ”: the latter is a statement about real numbers. Preference Theory Preferences Rationality Assumptions 1 Completeness : x , y X , we have either x ± y and/or y ± x . 2 Transitivity : x , y , z X , we have: x ± y and y ± z = x ± z . Rationality = completeness and transitivity. Note, completeness implies Reflexivity : x X , we have x x . Preference Theory Preferences Continuity Assumptions (don’t worry about too much) Definition ± is continuous if it is preserved under limits. That is, suppose: lim n →∞ ( x n , y n ) = ( x , y ) and x n ² y n for all n. then x ² y . Intuitively (and all you need to know) is that preferences are continuous if x ² y means that the agent prefers alternatives
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This note was uploaded on 10/22/2009 for the course ECG 700 taught by Professor Morrill during the Fall '09 term at N.C. State.

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L2-preferences-Part1 - Preferences Preferences Preferences...

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