Merrill M. Flood

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Merrill Meeks Flood (1908 – 1991 [1] ) was an American mathematician, notable for developing, with Melvin Dresher, the basis of the game theoretical Prisoner's dilemma model of cooperation and conflict while being at RAND in 1950 (Albert W. Tucker gave the game its prison-sentence interpretation, and thus the name by which it is known today). [2]

Melvin Dresher (Dreszer) was a Polish-born American mathematician, notable for developing, with Merrill Flood, the game theoretical model of cooperation and conflict known as the Prisoner's dilemma while at RAND in 1950.

Game theory is the study of mathematical models of strategic interaction between rational decision-makers. It has applications in all fields of social science, as well as in logic and computer science. Originally, it addressed zero-sum games, in which one person's gains result in losses for the other participants. Today, game theory applies to a wide range of behavioral relations, and is now an umbrella term for the science of logical decision making in humans, animals, and computers.

The prisoner's dilemma is a standard example of a game analyzed in game theory that shows why two completely rational individuals might not cooperate, even if it appears that it is in their best interests to do so. It was originally framed by Merrill Flood and Melvin Dresher while working at RAND in 1950. Albert W. Tucker formalized the game with prison sentence rewards and named it "prisoner's dilemma", presenting it as follows:

Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The offer is:

Biography

Flood received an MA in mathematics at the University of Nebraska, and a PhD at Princeton University in 1935 under the supervision of Joseph Wedderburn, for the dissertation Division by Non-singular Matric Polynomials.

Princeton University is a private Ivy League research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the nine colonial colleges chartered before the American Revolution. The institution moved to Newark in 1747, then to the current site nine years later, and renamed itself Princeton University in 1896.

Joseph Henry Maclagan Wedderburn FRSE FRS was a Scottish mathematician, who taught at Princeton University for most of his career. A significant algebraist, he proved that a finite division algebra is a field, and part of the Artin–Wedderburn theorem on simple algebras. He also worked on group theory and matrix algebra.

In the 1930s he started working at Princeton University, and after the War he worked at the Rand Corporation, Columbia University, the University of Michigan [3] and the University of California.

Columbia University is a private Ivy League research university in Upper Manhattan, New York City. Established in 1754, Columbia is the oldest institution of higher education in New York and the fifth-oldest institution of higher learning in the United States. It is one of nine colonial colleges founded prior to the Declaration of Independence, seven of which belong to the Ivy League. It has been ranked by numerous major education publications as among the top ten universities in the world.

The University of Michigan, often simply referred to as Michigan, is a public research university in Ann Arbor, Michigan. The university is Michigan's oldest; it was founded in 1817 in Detroit, as the Catholepistemiad, or University of Michigania, 20 years before the territory became a state. The school was moved to Ann Arbor in 1837 onto 40 acres (16 ha) of what is now known as Central Campus. Since its establishment in Ann Arbor, the university campus has expanded to include more than 584 major buildings with a combined area of more than 34 million gross square feet spread out over a Central Campus and North Campus, two regional campuses in Flint and Dearborn, and a Center in Detroit. The university is a founding member of the Association of American Universities.

The University of California (UC) is a public university system in the U.S. state of California. Under the California Master Plan for Higher Education, the University of California is a part of the state's three-system public higher education plan, which also includes the California State University system and the California Community Colleges System.

In the 1950s Flood was one of the founding members of TIMS and its second President in 1955. End 1950s he was among the first members of the Society for General Systems Research. In 1961, he was elected President of the Operations Research Society of America (ORSA), and from 1962 to 1965 he served as Vice President of the Institute of Industrial Engineers. In 1983 he was awarded ORSA's George E. Kimball Medal.

Work

Flood is considered a pioneer in the field of management science and operations research, who has been able to apply their techniques to problems on many levels of society. According to Xu (2001) "as early as 1936–1946, he applied innovative systems analysis to public problems and developed cost-benefit analysis in the civilian sector and cost effectiveness analysis in the military sector". [3]

Management science (MS) is the broad interdisciplinary study of problem solving and decision making in human organizations, with strong links to management, economics, business, engineering, management consulting, and other sciences. It uses various scientific research-based principles, strategies, and analytical methods including mathematical modeling, statistics and numerical algorithms to improve an organization's ability to enact rational and accurate management decisions by arriving at optimal or near optimal solutions to complex decision problems. Management science helps businesses to achieve goals using various scientific methods.

Operations research, or operational research (OR) in British usage, is a discipline that deals with the application of advanced analytical methods to help make better decisions. Further, the term operational analysis is used in the British military as an intrinsic part of capability development, management and assurance. In particular, operational analysis forms part of the Combined Operational Effectiveness and Investment Appraisals, which support British defense capability acquisition decision-making.

The Merriam-Webster dictionary defines system analysis as "the process of studying a procedure or business in order to identify its goals and purposes and create systems and procedures that will achieve them in an efficient way". Another view sees system analysis as a problem-solving technique that breaks down a system into its component pieces for the purpose of the studying how well those component parts work and interact to accomplish their purpose.

Traveling salesman problem

In the 1940s Flood publicized the name Traveling salesman problem (TSP) within the mathematical community at mass. Flood publicized the traveling salesman problem in 1948 by presenting it at the RAND Corporation. According to Flood "when I was struggling with the problem in connecting with a school-bus routing study in New Jersey". [4]

Even more important, as far as common usage goes, Dr. Flood himself claimed to have coined the term "software" in the late 1940s. [5]

Hitchcock transportation problem

Equally at home in his original field of the mathematics of matrices and in the pragmatic trenches of the industrial engineer, his research addressed an impressive array of operations research problems. His 1953 paper on the Hitchcock transportation problem is often cited, but he also published work on the traveling salesman problem, and an algorithm for solving the von Neumann hide and seek problem. [3]

Publications

• 1948, A Game Theoretic Study of the Tactics of Area Defense, RAND Research Memorandum
• 1949, Illustrative example of application of Koopmans' transportation theory to scheduling military tanker fleet, RAND Research Memorandum.
• 1951, A Preference Experiment. RAND Research Paper
• 1951, A Preference Experiment (Series 2, Trial 1).RAND Research Paper
• 1952, A Preference Experiment (Series 2, Trials 2, 3, 4). RAND Research Paper
• 1952, Aerial Bombing Tactics : General Considerations (A World War II Study), RAND Research Memorandum.
• 1952, On Game-Learning Theory and Some Decision-Making Experiments. RAND Research Paper
• 1952, Preference Experiment. RAND Research Memorandum
• 1952, Some Group Interaction Models. RAND Research Memorandum

Related Research Articles

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References

1. Saul I. Gass (2005). An annotated timeline of operations research: an informal history. p.49.
2. Huixian Xu et al. (2001). "Merrill M. Flood: 2nd President of TIMS (1955) and 10th President of ORSA, 1961–62" Archived September 28, 2006, at the Wayback Machine .. Accessed April 15, 2008
3. Leonardo Zambito, The Traveling Salesman Problem: A Comprehensive Survey fall 2006. Retrieved April 15, 2008.
4. Flood, Merrill (1 December 1984). "Letter to the editor". Datamation. pp. 15–16.