Tham khảo tài liệu 'the free information society bargaining and markets_1', tài chính - ngân hàng, đầu tư chứng khoán phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Preferences 35 Figure The functions V1 - 1 and V2 1 . The origin for the graph of V1 - 1 is the lower left corner of the box the origin for the graph of V2G 1 is the upper right corner. Under assumption A3 any given amount is worth less the later it is received. The final condition we impose on preferences is that the loss to delay associated with any given amount is an increasing function of the amount. A6 Increasing loss to delay The difference Xị Vj xj 1 is an increasing function of Xj. Under this assumption the graph of each function Vj - 1 in Figure has a slope relative to its origin of less than 1 everywhere. The assumption also restricts the character of the function uj in any representation ỗ uj xj of j. If uj is differentiable then A6 implies that Juj xj uj vj xj 1 whenever Vj xj 1 0. This condition is weaker than concavity of Uj which implies u xj uli vi xi 1 . This completes our specification of the players preferences. Since there is no uncertainty explicit in the structure of a bargaining game of alternating offers and since we restrict attention to situations in which neither player uses a random device to make his choice there is no need to make assumptions about the players preferences over uncertain outcomes. 36 Chapter 3. The Strategic Approach The Intersection of the Graphs of vi - 1 and V2 - 1 In our subsequent analysis the intersection of the graphs of i - 1 and v2 - 1 has special significance. We now show that this intersection is unique . there is only one pair x y e X X X such that yi vi xi 1 and x2 v2 y2 1 . This uniqueness result is clear from Figure . Precisely we have the following. Lemma If the preference ordering j of each Player i satisfies A2 through A6 then there exists a unique pair x y e X X X such that y i vi x 1 and x2 v2 y2 1 . Proof. For every x e X let x be the agreement for which i x V1 x1 1 and define H X R by H x x2 v2 -02 x 1 . The pair of agreements x and y x satisfies also x2 v2 y2 1 if and .
