Student Q&A for Homework 3
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| Question No. 1 |
| Question: CORRECTION FOR INVERSE SHAPLEY |
| Abswer: In question 5b, change the values to (1/6, 2/3, 1/6). |
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| Question No. 2 |
| Question: For question #5 on shapley value, to prove that a set of Shapley values is impossible, the hint says to write down a set of linear constraints. Could you give us an example of such a linear constraint? |
| Abswer: Think about all possible orderings. A particular assignment to Shapley values corresponds to a certain "structure" in them, and a corresponding set of constraints for agents' weights. |
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| Question No. 3 |
| Question: For question 5) parts a-c, are you looking for a possible weight assignment that would result in the required Shapley values or are you looking for a range of all possible values? There are multiple weight assignments possible for the required Shapley values in some parts, and depending on which assignment one picks it seems that the answer in part d) will be affected (since we will need to use the assigned weights to write down equations for the core). |
| Abswer: In case where the Shapley values calculated in the inverse problem correspond to a range, pick just one assignment from within this product range and work with that. |
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| Question No. 4 |
| Question: For P4(b), what does 'reasonable way' means? do we have to prove how asymmetry can improve revenue analytically? |
| Abswer: I think the question seeks out some economic intuition, not a proof. |
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| Question No. 5 |
| Question: For 6(c), are you asking an equilibrium in strictly dominant strategy? or in weakly dominant strategy? I think the answer will be changed according to what it is. |
| Abswer: In general dominant usually is understood as weakly dominant. The Vickrey auction for example is not strictly dominant incentive compatible, neither is Groves. |
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