Melvin Dresher

Short description: Polish-American mathematician (1911-1992)

Melvin Dresher

Melvin Dresher, early 1940s

Born| (1911-03-13)March 13, 1911

Krasnystaw, Poland

Died| June 4, 1992(1992-06-04) (aged 81)

Kern, California, US

Education| Lehigh University
Yale University
Known for| Prisoner's dilemma
Scientific career
Fields| Mathematics
Institutions| Michigan State College
War Production Board
National Defense Research Committee
Catholic University of America
RAND
Doctoral advisor| Øystein Ore

Melvin Dresher (born Dreszer; March 13, 1911 – June 4, 1992) was a Poland -born United States 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).[1][2]

## Contents

* 1 Education and career
* 2 Family
* 3 Bibliography
* 4 References

## Education and career

The Mathematics of Games of Strategy: Theory and Applications by Melvin Dresher

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 under the supervision of Øystein Ore; 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 of America, 1946–1947; research mathematician, RAND, from 1948.

Dresher 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.[3]

## Family

Dresher married Martha Whitaker (m. 1937) and is survived by his daughter Olivia Dresher (b. 1945)[4] and son Paul Dresher (b. 1951).

## Bibliography

* Bohnenblust, H.; Dresher, Melvin; Girshick, M.; Harris, Theodore; Helmer-Hirschberg, Olaf; McKinsey, J.; Shapley, Lloyd; Snow, R. (1948) (in en). Mathematical Theory of Zero-Sum Two-Person Games with a Finite Number or a Continuum of Strategies. RAND Corporation. doi:10.7249/r115. https://www.rand.org/pubs/reports/R115.html.
* Berge, Claude, ed (1970). Contributions to the theory of games. 3: C. Berge ... Ed. by M. Dresher. Annals of mathematics studies (4. print ed.). Princeton, NJ: Princeton Univ. Pr. ISBN 978-0-691-07936-3.
* Dresher, Melvin (1981). The mathematics of games of strategy: theory and applications (unabridged republ. of the [ed.] ... Englewood Cliffs, N.J., 1961 ed.). New York: Dover. ISBN 978-0-486-64216-1.
* Dresher, M., ed (1985). Advances in game theory. Annals of mathematics studies (Repr. from the hardcover ed.). Princeton, NJ: Princeton Univ. Press. ISBN 978-0-691-07902-8.
* Dresher, Melvin (2007). Games of strategy: theory and applications (New RAND ed.). Santa Monica, Calif: RAND Corp. ISBN 978-0-8330-4225-5.

## References

* 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).

1. ↑ Taylor, Timothy (2020-01-17). "CONVERSABLE ECONOMIST: The Prisoner's Dilemma: Celebrating its 70th Anniversary". https://conversableeconomist.blogspot.com/2020/01/the-prisoners-dilemma-celebrating-its.html.
2. ↑ Kuhn, Steven (2019), Zalta, Edward N., ed., "Prisoner’s Dilemma", The Stanford Encyclopedia of Philosophy (Metaphysics Research Lab, Stanford University), https://plato.stanford.edu/archives/win2019/entries/prisoner-dilemma/, retrieved 2023-12-23
3. ↑ Hounshell, David (1997). "The Cold War, RAND, and the Generation of Knowledge, 1946-1962". Historical Studies in the Physical and Biological Sciences 27 (2): 237–267. doi:10.2307/27757779. ISSN 0890-9997. https://www.jstor.org/stable/27757779.
4. ↑ Dresher, Olivia (2020-01-17). "OliviaDresher.com: BIO". http://fraglit.com/od/bio/.

* v
* t
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Topics in game theory

Definitions|

* Cooperative game
* Determinacy
* Escalation of commitment
* Extensive-form game
* First-player and second-player win
* Game complexity
* Graphical game
* Hierarchy of beliefs
* Information set
* Normal-form game
* Preference
* Sequential game
* Simultaneous game
* Simultaneous action selection
* Solved game
* Succinct game

Equilibrium
concepts|

* Nash equilibrium
* Subgame perfection
* Mertens-stable equilibrium
* Bayesian Nash equilibrium
* Perfect Bayesian equilibrium
* Trembling hand
* Proper equilibrium
* Epsilon-equilibrium
* Correlated equilibrium
* Sequential equilibrium
* Quasi-perfect equilibrium
* Evolutionarily stable strategy
* Risk dominance
* Core
* Shapley value
* Pareto efficiency
* Gibbs equilibrium
* Quantal response equilibrium
* Self-confirming equilibrium
* Strong Nash equilibrium
* Markov perfect equilibrium

Strategies|

* Dominant strategies
* Pure strategy
* Mixed strategy
* Strategy-stealing argument
* Tit for tat
* Grim trigger
* Collusion
* Backward induction
* Forward induction
* Markov strategy

Classes
of games|

* Symmetric game
* Perfect information
* Repeated game
* Signaling game
* Screening game
* Cheap talk
* Zero-sum game
* Mechanism design
* Bargaining problem
* Stochastic game
* n-player game
* Large Poisson game
* Nontransitive game
* Global game
* Strictly determined game
* Potential game

Games|

* Go
* Chess
* Infinite chess
* Checkers
* Tic-tac-toe
* Prisoner's dilemma
* Optional prisoner's dilemma
* Traveler's dilemma
* Coordination game
* Chicken
* Centipede game
* Volunteer's dilemma
* Dollar auction
* Battle of the sexes
* Stag hunt
* Matching pennies
* Ultimatum game
* Rock paper scissors
* Pirate game
* Dictator game
* Public goods game
* Blotto game
* War of attrition
* El Farol Bar problem
* Fair division
* Fair cake-cutting
* Cournot game
* Deadlock
* Diner's dilemma
* Guess 2/3 of the average
* Kuhn poker
* Nash bargaining game
* Prisoners and hats puzzle
* Trust game
* Princess and Monster game
* Rendezvous problem

Theorems|

* Arrow's impossibility theorem
* Aumann's agreement theorem
* Folk theorem
* Minimax theorem
* Nash's theorem
* Purification theorem
* Revelation principle
* Zermelo's theorem

Key
figures|

* Albert W. Tucker
* Amos Tversky
* Ariel Rubinstein
* Claude Shannon
* Daniel Kahneman
* David K. Levine
* David M. Kreps
* Donald B. Gillies
* Drew Fudenberg
* Eric Maskin
* Harold W. Kuhn
* Herbert Simon
* Hervé Moulin
* Jean Tirole
* Jean-François Mertens
* Jennifer Tour Chayes
* John Harsanyi
* John Maynard Smith
* Antoine Augustin Cournot
* John Nash
* John von Neumann
* Kenneth Arrow
* Kenneth Binmore
* Leonid Hurwicz
* Lloyd Shapley
* Melvin Dresher
* Merrill M. Flood
* Olga Bondareva
* Oskar Morgenstern
* Paul Milgrom
* Peyton Young
* Reinhard Selten
* Robert Axelrod
* Robert Aumann
* Robert B. Wilson
* Roger Myerson
* Samuel Bowles
* Suzanne Scotchmer
* Thomas Schelling
* William Vickrey

See also|

* All-pay auction
* Alpha–beta pruning
* Bertrand paradox
* Bounded rationality
* Combinatorial game theory
* Confrontation analysis
* Coopetition
* First-move advantage in chess
* Game mechanics
* Glossary of game theory
* List of game theorists
* List of games in game theory
* No-win situation
* Solving chess
* Topological game
* Tragedy of the commons
* Tyranny of small decisions

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