| Because sequential auctions have permeated society more than ever, it is desirable for participants to have the optimal strategies beforehand. However, finding closed-form solutions to various sequential auction games is challenging. Current literature provides some answers for specific cases but not for general cases. A decision support system that can automate optimal bids for players in different sequential auction games will be useful in solving these complex economic problems, which requires not only economic but also computational efficiency.This thesis contributes in several directions. First, this dissertation derives results related to the multiplicity of equilibria in first-price, sealed-bid (FPSB) auctions, and sequential FPSB auctions, with discrete bids under complete information. It also provides theoretical results for FPSB auctions with discrete bids under incomplete information. These results are applicable to both two-person and multi-person cases.Second, this thesis develops a technique to compute strategies in sequential auctions. It applies Monte Carlo simulation to approximate perfect Bayesian equilibrium for sequential auctions with discrete bids and incomplete information. It also utilizes the leveraged substructure of the game tree which can dramatically reduce the memory and computation time required to solve the game. This approach is applicable to sequences of a wide variety of auctions.Finally, this thesis analyzes the impact of information in sequential auctions with continuous bids and incomplete information when bids are revealed. It provides theoretical results especially the non-existence of pure-strategy symmetric equilibrium in both the symmetric sequential FPSB and the symmetric sequential Vickrey auctions. |
