Mechanism Design and Social Choice Part II:
Problem Set 2
Problem 1 For each of the following situations:
(a) model the situations as a quasi-linear environment.
(b) derive the general VCG mechanism and the Pivot Mechanism
1. There is a public project that can either be implemented or not. A finite number of agents is affected by the project. Some agents gain from the project others suffer.
2. A seller has several identical units of an indivisible good. He faces a finite number of potential buyers that demand one or several units. Assume that the marginal utility of a unit is non-increasing.
3. Bilateral Trade: A seller has a single indivisible object that he could either use himself or sell to a (single) buyer.
4. Partnership Dissolution: Two entrepreneurs jointly own a firm (each of them has an ownership share of 50%). Because of a management deadlock, the partnership has to be dissolved. There are three possible outcomes: One of the partners buys the ownership share of the other partner or the firm is shut down and the assets are sold.
Problem 2 Show that the is no VCG-mechanism with balanced budget in the bilateral- trade environment considered in problem one. Give an intuition for this negative result.
Problem 3 Apply the expected externality mechanism to the bilateral trade problem and the partnership dissolution problem. In both settings, check for each agent whether he participates voluntarily if he knows his own type but not the type of the other agent.
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