Section 3: Exchanges

Key Learning Points

• Discuss an important category of auctions, exchanges, in which agents can act as both buyers and sellers.
• Discuss two varieties, those designed to allocate goods and those designed to aggregate information.

Activities

1. Read Section 11.4 of the text.

2. Do the following exercises:

   Consider the following lobbying problem. There are n different companies, each of which wants the government to pass legislation that will benefit that company and will have no direct effect on the other companies. If the legislation that favours company i is passed, i’s profit will be v_i; otherwise it will be 0. To try to influence government policy, each company, i, considers donating some amount, d_i, to the government. Let’s consider the case where all v_i are independent random variables distributed uniformly [0, 1]. Somewhat cynically, the government will pass the single piece of legislation that benefits its biggest donor; of course, it will keep all the donations it receives.

   1. Model this problem as an auction. State all the relevant assumptions that you make in building this model and explain why they are reasonable.
   2. Find a symmetric Bayes-Nash equilibrium of this game. You may assume that for this game there exists a symmetric, pure-strategy equilibrium for which the bid amount is a monotonically increasing function of the agent’s valuation.