Extensions on "Sequentially Optimal Mechanisms"
نویسنده
چکیده
This document establishes that the result in "Sequentially Optimal Mechanisms" is robust to a number of extensions. 1. Robustness: Longer Horizon & Alternative Degrees of Transparency We will show that our result is robust in a number of di¤erent directions. The rst extension considers the possibility that the game lasts arbitrarily long, but nitely many periods. The next three extensions are related to the degree of transparency of mechanisms. We have so far assumed that the seller observes the message that the buyer submits to the mediator, ; the action that he chooses s; and whether trade takes place or not. In the rst extension we consider the case where the seller simply observes whether trade took place or not. In the second extension we look at an intermediate case where the seller observes the messages that the buyer submits to the mediator, and whether trade took place or not, but does not observe the action chosen by the buyer. Finally we allow the seller to observe everything, that is the message that the buyer submits to the mediator ; the recommendation that he receives from the mediator n; the action he chooses s and whether trade took place or not. This is the maximal amount of information that the seller can observe. 1.1 Sequentially Optimal Mechanisms for 2 < T <1: We proceed by induction and we obtain the characterization of sequentially optimal mechanisms for the case that T > 2: The overall structure of the proof is as in the two-period case. Of course the execution gets at times more involved and the notation a bit more cumbersome.
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