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The Free Information Society Bargaining and Markets_4

Tham khảo tài liệu 'the free information society bargaining and markets_4', tài chính - ngân hàng, đầu tư chứng khoán phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 104 Chapter 5. Bargaining between Incompletely Informed Players she obtains x Cl the same payoff that she obtains if she accepts the offer. If Player 2L rejects an offer x in which X1 x then the state changes to H so that Player 2L obtains Cl CL. The condition X 1 Cl CL ensures that this payoff is no more than x2. The fact that no player can benefit from any other deviation can be checked similarly. Finally the postulated beliefs are consistent with the strategies. This completes the proof of Part 2 of the proposition. 5.4 Delay in Reaching Agreement In Chapter 3 we found that in the unique subgame perfect equilibrium of a bargaining game of alternating offers in which the players preferences are common knowledge agreement is reached immediately. In the previous section we constructed sequential equilibria for the game r nH in which when Player 1 faces a strong opponent agreement is reached with delay but in these equilibria this delay never exceeds one period. Are there any equilibria in which the negotiation lasts for more than two periods If so can the bargaining time remain bounded away from zero when the length of a period of negotiation is arbitrarily small In the case that nH 2ci ci CH we now construct a sequential equilibrium in which negotiation continues for several periods. Choose three numbers n z from the interval ci 1 Cl Cl such that z n Cl CL this is possible if the bargaining costs are small and let t be an even integer. Recall that for each a G ci 1 Cl Cl there is a sequential equilibrium in which immediate agreement is reached on a 1 a by Part 2 of Proposition 5.3 . The players strategies in the equilibrium we construct are as follows. Through period t Player 1 proposes the agreement 1 0 and rejects every other agreement and Players 2h and 2L each propose the agreement 0 1 and reject every other agreement Player 1 retains her original belief that the probability with which she faces Player 2H is nH. If period t is reached without any of the .