để mô hình kết quả của đàm phán. Trong các chương tiếp theo chúng tôi mô hình đàm phán chi tiết hơn, sử dụng các mô hình chiến lược như một trong những Chương 3. Chúng tôi phân biệt hai khả năng Lắc và Sutton (1984a) và nghiên cứu các biến thể Bester (1989a) | 144 Chapter 7. A Steady State Market of the following pair of equations. y qus 1 - q J x y 2 1 - x qub 1 - q S 1 - x 2 - y 2 The payoffs in this equilibrium are x y 2 for the seller and 1 - x y 2 for the buyer. Next we verify that in every market equilibrium ơ r we have Us Ub 1. From we have Vs Ws from it follows that Us Ws. Similarly Ub Wb so that Us Ub Ws Wb. Since Ws Wb is the expectation of a random variable all values of which are at most equal to the unit surplus available we have Ws Wb 1. Thus a market equilibrium strategy pair has to be such that the induced variables Vs Vb Ws Wb Us Ub x and y satisfy the four equations the two equations and with us Us and ub Ub and the following additional two equations. Ws x y 2 Wb 1 - x y 2. It is straightforward to verify that solution to these equations which is unique is that given in and . So far we have restricted agents to use semi-stationary strategies each agent is constrained to behave the same way in every match. We now show that if every buyer uses the semi-stationary equilibrium strategy described above then any given seller cannot do better by using different bargaining tactics in different matches. A symmetric argument applies to sellers. In other words the equilibrium we have found remains an equilibrium if we extend the set of strategies to include behavior that is not semi-stationary. Consider some seller. Suppose that every buyer in the market is using the equilibrium strategy described above in which he always offers y and accepts no price above x whenever he is matched. Suppose that the seller can condition her actions on her entire history in the market. We claim that the strategy of always offering x and accepting no price below y is optimal among all possible strategies. The environment the seller faces after any history can be characterized by the following four states ei the seller has no partner e2 the seller has a partner and she has been
