Homework number 3
1.
Strategy Proof
We have a tree
T. Each player is located in a node in the tree T, which is its private
information. We like to select one node X. The cost of a player is the distance
(in edges) from his location to X. Build a strategy proof algorithm (without
money) to select X, which is not a dictatorship.
2.
Sequential Mechanism: Assume that we
have two Strategy Proof mechanisms, A and B over the same set of players. Would
running sequentially, first mechanism A and then mechanism B maintain the
strategy proof property?
HINT : Consider selling two identical products by
running sequentially two second price auctions.
CORRECTION:
The question should be: Is the joint action, where every agent bids its true
value in both mechanisms a Nash Equilibrium.
3.
Market Clearing Price: Assume
that we have n products and n buyers in a matching market. Each
buyer has a non-negative valuation for each product, and each buyer will buy
exactly one product. Assume that every buyer has a higher valuation for product
a then product b. Does this implies that in ANY market clearing
prices the price of product a is higher than
the price of product b.
The
homework is due June 7, 2010