This bachelor's thesis studies Myerson's lemma, one of the fundamental results in mechanism design theory for single-parameter environments. The lemma provides a complete characterization of dominant-strategy incentive-compatible direct-revelation mechanisms: an allocation rule is implementable if and only if it is monotone, while the corresponding payment rule is uniquely determined by Myerson's payment formula.
The thesis introduces the basic concepts of auction theory and mechanism design, presents a proof of Myerson's lemma, and discusses its most important applications, including threshold payments, the revelation principle, and algorithmic mechanism design. These results are illustrated through knapsack auctions and sponsored search auctions. Finally, the thesis examines the limitations of Myerson's lemma, its connection to optimal auction design and reserve prices, and explains why substantially more complex problems arise in multi-parameter environments.
|
