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

Melvin Dresher, early 1940s | |

Born | |

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

Alma mater | Yale University |

Known for | Prisoner's dilemma |

Scientific career | |

Fields | Mathematics |

Institutions | RAND |

**Melvin Dresher** (born **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).

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.

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.

**Game theory** is the study of mathematical models of strategic interaction among rational decision-makers. It has applications in all fields of social science, as well as in logic, systems science and computer science. Originally, it addressed zero-sum games, in which each participant's gains or losses are exactly balanced by those of 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 or as a part of a student's formal education. 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* is a 1984 book by political scientist Robert Axelrod that expanded a highly influential paper of the same name, and popularized the study upon which the original paper had been based. Since 2006, reprints of the book have included a foreword by Richard Dawkins and been marketed as a revised edition.

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 possible outcomes are:

In game theory, the **Nash equilibrium**, named after the mathematician John Forbes Nash Jr., is a proposed solution of a non-cooperative game involving two or more players in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy.

**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 an 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 an 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.

**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.

**Leonid** "**Leo**" **Hurwicz** was a Polish-American economist and mathematician, known for his work in game theory and mechanism design. He originated the concept of incentive compatibility, and showed how desired outcomes can be achieved by using incentive compatible mechanism design. Hurwicz shared the 2007 Nobel Memorial Prize in Economic Sciences for his seminal work on mechanism design. Hurwicz was one of the oldest Nobel Laureates, having received the prize at the age of 90.

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

**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 served as 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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