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Except for case 5 this question can be answered easily. Consider an arbitrary case, but not case 5. The necessary constraints on the agreement outcomes do not depend on the steps of agreement expected equilibrium payoffs are either of the form ~j I\j' Since the or %ajj , all integer numbers or halves of integer numbers in the specified range are exactly the expected equilibrium payoffs. In case 5 this is more complicated. 3 THE 51 EXPECTED EQUILBRIUM PAYOFFS relationships between the agreement outcomes contingent on the step of agreement.

3) it follows that both first mover types receive the same (discounted) payoff in a play with the low type of the second mover, although the outcomes ~L and aHL might be different. 1 A set of finite and pure equilibrium HI: 33 NECESSARY AND SUFFICmNT CONDITIONS strate~es (for n HL odd, nLL odd, nLL ::; nmJ Demand and accept 99 before step nHL• demand and accept aHL in step nHL• break off after step nHL LI : Demand and accept 99 before step nw demand and accept au in step nw break off after step nu H 2: Break offin each step ~: Demand and accept 99 before step nu +1, demand and accept 100-au in step nu +1, demand and accept 99 in the steps between nu +1 and nHL +1.

A demand of H2 before his break off would be an incentive for L\ to accept since this is more profitable than a conflict with H2. Therefore, a set of strategies for this vector p which allows H2 to demand before the break off cannot be in eqUilibrium. Constraint (D3) is a feasibility constraint. If the high type first mover is having a conflict with the high type second mover and an agreement with the low type second mover he cannot break off immediately. SET OF THE NECESSARY CONSTRAINTS With the term set of the necessary constraints we shall shortly denote the individual 24 CHAPTER 3.

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A Laplace mixture model for identification of differential expression in microarray experiments (200 by Bhowmick D., Davison A.C.


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