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Melvin Dresher | |
---|---|

Melvin Dresher, early 1940s | |

Born | Krasnystaw, Poland | March 13, 1911

Died | June 4, 1992 81) Kern, California | (aged

Residence | United States |

Alma mater | Yale University |

Known for | Prisoner's dilemma |

Scientific career | |

Fields | Mathematics |

Institutions | RAND |

**Melvin Dresher (Dreszer)** (March 13, 1911 – June 4, 1992) 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 (Albert W. Tucker gave the game its prison-sentence interpretation, and thus the name by which it is known today).

**Poland**, officially the **Republic of Poland**, is a country located in Central Europe. It is divided into 16 administrative subdivisions, covering an area of 312,696 square kilometres (120,733 sq mi), and has a largely temperate seasonal climate. With a population of approximately 38.5 million people, Poland is the sixth most populous member state of the European Union. Poland's capital and largest metropolis is Warsaw. Other major cities include Kraków, Łódź, Wrocław, Poznań, Gdańsk, and Szczecin.

The **United States of America** (**USA**), commonly known as the **United States** or **America**, is a country comprising 50 states, a federal district, five major self-governing territories, and various possessions. At 3.8 million square miles, the United States is the world's third or fourth largest country by total area and is slightly smaller than the entire continent of Europe's 3.9 million square miles. With a population of over 327 million people, the U.S. is the third most populous country. The capital is Washington, D.C., and the largest city by population is New York City. Forty-eight states and the capital's federal district are contiguous in North America between Canada and Mexico. The State of Alaska is in the northwest corner of North America, bordered by Canada to the east and across the Bering Strait from Russia to the west. The State of Hawaii is an archipelago in the mid-Pacific Ocean. The U.S. territories are scattered about the Pacific Ocean and the Caribbean Sea, stretching across nine official time zones. The extremely diverse geography, climate, and wildlife of the United States make it one of the world's 17 megadiverse countries.

A **mathematician** is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

Dresher came to the United States in 1923. He obtained his B.S. from Lehigh University in 1933 and his Ph.D. from Yale University in 1937; the title of his dissertation was "Multi-Groups: A Generalisation of the Notion of Group." Dresher worked as instructor of mathematics, Michigan State College, 1938-1941; statistician, War Production Board, 1941-1944; mathematical physicist, National Defense Research Committee, 1944-1946; professor of mathematics, Catholic University, 1946-1947; research mathematician, RAND, from 1948.

**Lehigh University** is a private research university in Bethlehem, Pennsylvania. It was established in 1865 by businessman Asa Packer. Its undergraduate programs have been coeducational since the 1971–72 academic year. As of 2019, the university had 5,047 undergraduate students and 1,942 graduate students.

**Yale University** is a private Ivy League research university in New Haven, Connecticut. Founded in 1701, it is the third-oldest institution of higher education in the United States and one of the nine Colonial Colleges chartered before the American Revolution.

The **War Production Board** (WPB) was an agency of the United States government that supervised war production during World War II. President Franklin D. Roosevelt established it in January 1942, with Executive Order 9024. The WPB replaced the Supply Priorities and Allocation Board and the Office of Production Management.

He was the author of several RAND research papers on game theory, and his widely acclaimed *The Mathematics of Games of Strategy: Theory and Applications* (originally published in 1961 as *Games of Strategy: Theory and Applications*) continues to be read today.

Dresher's research has been referred to and discussed in a variety of published books, including *Prisoner's Dilemma* by William Poundstone and * A Beautiful Mind * by Sylvia Nasar.

**William Poundstone** is an American author, columnist, and skeptic. He has written a number of books including the *Big Secrets* series and a biography of Carl Sagan. He is a cousin of comedian Paula Poundstone.

* A Beautiful Mind* (1998) is a biography of Nobel Prize-winning economist and mathematician John Forbes Nash, Jr. by Sylvia Nasar, professor of journalism at Columbia University. An unauthorized work, it won the National Book Critics Circle Award in 1998 and was nominated for the Pulitzer Prize in biography. It inspired the 2001 film by the same name.

**Sylvia Nasar** is an Uzbek German-born American journalist, best known for her biography of John Forbes Nash, Jr., *A Beautiful Mind*. She received the National Book Critics Circle Award for biography.

**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.

**Recreational mathematics** is mathematics carried out for recreation (entertainment) rather than as a strictly research and application-based professional activity. Although it is not necessarily limited to being an endeavor for amateurs, many topics in this field require no knowledge of advanced mathematics. Recreational mathematics involves mathematical puzzles and games, often appealing to children and untrained adults, inspiring their further study of the subject.

The **evolution of cooperation** can refer to:

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:

**Félix Édouard Justin Émile Borel** was a French mathematician and politician. As a mathematician, he was known for his founding work in the areas of measure theory and probability.

**Evolutionary game theory** (**EGT**) is the application of game theory to evolving populations in biology. It defines a framework of contests, strategies, and analytics into which Darwinian competition can be modelled. It originated in 1973 with John Maynard Smith and George R. Price's formalisation of contests, analysed as strategies, and the mathematical criteria that can be used to predict the results of competing strategies.

**Oskar Morgenstern** was a German-born economist. In collaboration with mathematician John von Neumann, he founded the mathematical field of game theory and its application to economics.

**Albert William Tucker** was a Canadian mathematician who made important contributions in topology, game theory, and non-linear programming.

**Anatol Rapoport** was a Ukrainian-born American mathematical psychologist. He contributed to general systems theory, to mathematical biology and to the mathematical modeling of social interaction and stochastic models of contagion.

**David Harold Blackwell** was an American statistician and mathematician who made significant contributions to game theory, probability theory, information theory, and Bayesian statistics. He is one of the eponyms of the Rao–Blackwell theorem. He was the first African American inducted into the National Academy of Sciences, the first black tenured faculty member at UC Berkeley, and the seventh African American to receive a Ph.D. in Mathematics.

**Robert John Aumann** is an Israeli-American mathematician, and a member of the United States National Academy of Sciences. He is a professor at the Center for the Study of Rationality in the Hebrew University of Jerusalem in Israel. He also holds a visiting position at Stony Brook University, and is one of the founding members of the Stony Brook Center for Game Theory.

**Merrill Meeks Flood** 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.

**Rufus Philip Isaacs** was a game theorist especially prominent in the 1950s and 1960s with his work on differential games.

**Ryszard Syski** was a Polish-American mathematician whose research was in queueing theory.

**Applied mathematics** is the application of mathematical methods by different fields such as science, engineering, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected with research in pure mathematics.

**Drama theory** is one of the problem structuring methods in operations research. It is based on game theory and adapts the use of games to complex organisational situations, accounting for emotional responses that can provoke irrational reactions and lead the players to redefine the game. In a drama, emotions trigger rationalizations that create changes in the game, and so change follows change until either all conflicts are resolved or action becomes necessary. The game as redefined is then played.

**Philip Starr "Phil" Wolfe** was an American mathematician and one of the founders of convex optimization theory and mathematical programming.

**Abraham Neyman** is an Israeli mathematician and game theorist, Professor of Mathematics at the Federmann Center for the Study of Rationality and the Einstein Institute of Mathematics at the Hebrew University of Jerusalem in Israel. He is currently the president of the Israeli Chapter of the Game Theory Society (2014–2018).

**Joseph Pierre (Joe) LaSalle** was an American mathematician specialising in dynamical systems and responsible for important contributions to stability theory, such as LaSalle's invariance principle which bears his name.

- Obituary, July 2, 1992 issue of the
*Palisadian-Post*newspaper (Pacific Palisades, California). - "In Remembrance", July 9, 1992 issue of
*RAND Items*(a biweekly publication for employees of RAND).

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