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I am doing a micro course right now. I came upon this question while studying and I was hoping for help/hints on how to solve it or what resources to consult to better understand the topic.

the general layout was : Mechanisms Binary: yes, produced; no, not produced Decision rule, a(v') specifies the chosen alternative Transfer rule, t(v') specifies transfers p(v')=-t(v') Weakly budget balanced: Sum of payments at least equal to costs

However, now We are given a decision rule represented by the blue triangle. The line represents the combinations of player 1&2's valuation such that v1+v2=< cost but now no longer the 'diagonal of the rectangle'. We are then asked whether 1) the decision rule can be done with a truthful mechanism 2)can a decision rule be done with any mechanism without ending up with a budget deficit 3) can a decision rule be done under the participation constraint that no one ever ends up with a negative utility 4) can a decision rule be done under the participation constraint that no one ever pays more than their valuation.

I really do not know how to approach this question simply based on the graph nor do I understand the "decision rule". If anyone could point me in the right direction I would be really grateful.

Decision rule represented by the blue triangle

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