There exists a unique x1 , where 0 ? x1 ? 1 , given that Vt(q1, q2) is an increasing function in q1 .
Proof. When the strategic RA (RA1) gets a bad project, it will get pay-off if it gives the project a GR, and if it refuses rating. 1 and is increasing in x1 . Given that Vt(q1, q2) is increasing in q1 , it is easy to see that ?(lie) is decreasing in x1 and that ?(honest) is increasing in x1 . Thus, if we define x1 such that
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Proof. Suppose that the strategic RA (RA1) gets a good project and that its strategy is x1 . Let us examine whether RA1 wants to deviate:
•if x1 = 1 , we have ?(lie) ? ?(honest) , or . If the RA1 gives NR to the good project, it will get and otherwise. Since RA1 does not want to deviate.
•if x1 = 0 , , hence reputation becomes irrelevant and the RA does not have an incentive to give NR to the good project. Continue reading “Observe that and you can , that is, is decreasing inside the x”