Thesis (M.S. in Operations Research)--Naval Postgraduate School, Dec. 2004. / Thesis Advisor(s): James N. Eagle, W. Matthew Carlyle. Includes bibliographical references (p. 35). Also available online.

Tong Kwong-Bun. / Thesis submitted in: December 2002. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 77-[80]). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- An Overview --- p.1 / Chapter 1.2 --- Tree Search --- p.2 / Chapter 1.2.1 --- Minimax Algorithm --- p.2 / Chapter 1.2.2 --- The Alpha-Beta Algorithm --- p.4 / Chapter 1.2.3 --- Alpha-Beta Enhancements --- p.5 / Chapter 1.2.4 --- Selective Search --- p.9 / Chapter 1.3 --- Construction of Evaluation Function --- p.16 / Chapter 1.4 --- Contribution of the Thesis --- p.17 / Chapter 1.5 --- Structure of the Thesis --- p.19 / Chapter 2 --- The Probabilistic Forward Pruning Framework --- p.20 / Chapter 2.1 --- Introduction --- p.20 / Chapter 2.2 --- The Generalized Probabilistic Forward Cuts Heuristic --- p.21 / Chapter 2.3 --- The GPC Framework --- p.24 / Chapter 2.3.1 --- The Alpha-Beta Algorithm --- p.24 / Chapter 2.3.2 --- The NegaScout Algorithm --- p.25 / Chapter 2.3.3 --- The Memory-enhanced Test Algorithm --- p.27 / Chapter 2.4 --- Summary --- p.27 / Chapter 3 --- The Fast Probabilistic Forward Pruning Framework --- p.30 / Chapter 3.1 --- Introduction --- p.30 / Chapter 3.2 --- The Fast GPC Heuristic --- p.30 / Chapter 3.2.1 --- The Alpha-Beta algorithm --- p.32 / Chapter 3.2.2 --- The NegaScout algorithm --- p.32 / Chapter 3.2.3 --- The Memory-enhanced Test algorithm --- p.35 / Chapter 3.3 --- Performance Evaluation --- p.35 / Chapter 3.3.1 --- Determination of the Parameters --- p.35 / Chapter 3.3.2 --- Result of Experiments --- p.38 / Chapter 3.4 --- Summary --- p.42 / Chapter 4 --- The Node-Cutting Heuristic --- p.43 / Chapter 4.1 --- Introduction --- p.43 / Chapter 4.2 --- Move Ordering --- p.43 / Chapter 4.2.1 --- Quality of Move Ordering --- p.44 / Chapter 4.3 --- Node-Cutting Heuristic --- p.46 / Chapter 4.4 --- Performance Evaluation --- p.48 / Chapter 4.4.1 --- Determination of the Parameters --- p.48 / Chapter 4.4.2 --- Result of Experiments --- p.50 / Chapter 4.5 --- Summary --- p.55 / Chapter 5 --- The Integrated Strategy --- p.56 / Chapter 5.1 --- Introduction --- p.56 / Chapter 5.2 --- "Combination of GPC, FGPC and Node-Cutting Heuristic" --- p.56 / Chapter 5.3 --- Performance Evaluation --- p.58 / Chapter 5.4 --- Summary --- p.63 / Chapter 6 --- Conclusions and Future Works --- p.64 / Chapter 6.1 --- Conclusions --- p.64 / Chapter 6.2 --- Future Works --- p.65 / Chapter A --- Examples --- p.67 / Chapter B --- The Rules of Chinese Checkers --- p.73 / Chapter C --- Application to Chinese Checkers --- p.75 / Bibliography --- p.77

Thesis (Ph. D.)--University of California, San Diego, 2006. / Vita. Includes bibliographical references.

Approved for public release; distribution in unlimited. / In this thesis, a new fictitious play (FP) procedure is presented to solve two-person zero-sum (TPZS) Blotto games. The FP solution procedure solves TPZS games by assuming that the two players take turns selecting optimal responses to the opponent's strategy observed so far. It is known that FP converges to an optimal solution, and it may be the only realistic approach to solve large games. The algorithm uses dynamic programming (DP) to solve FP subproblems. Efficiency is obtained by limiting the growth of the DP state space. Blotto games are frequently used to solve simple missile defense problems. While it may be unlikely that the models presented in this paper can be used directly to solve realistic offense and defense problems, it is hoped that they will provide insight into the basic structure of optimal and near-optimal solutions to these important, large games, and provide a foundation for solution of more realistic, and more complex, problems. / Captain, Republic of Korea Air Force