Albert W. Tucker

The citation reads as follows:

• Presentation of the 1980 von Neumann Prize for Theory jointly to David Gale, Harold W. Kuhn, and Albert W. Tucker will come as no surprise to those familiar with their contributions to the theory of optimization. Their research played a seminal role in laying the foundations of game theory, linear and non-linear programming — work that continues to be of fundamental importance to modern operations research and management science.

The early research of the founders of the 'Princeton School,' concerned the mathematical theory of linear inequalities as applied to linear programs, matrix games, the now-classical formulations of symmetric games, games in extensive form, n-person games, games of perfect recall, and the value of information. The list of their accomplishments, not to mention distinguished students and collaborators, is too long to present in detail. Pure mathematics played a strong role in their research. Topological notions such as homotopic and fixed point methods, first introduced by Tucker, now find among their many and wide applications the recent work of Kuhn for computing optima and equilibria; they are used by Gale in his studies of games of connectivity. The surprising association between combinatorics and continuous variable optimization was exhibited by Kuhn in his well-known Hungarian method for solving the assignment problem. The idea of duality, while properly credited to von Neumann, was developed independently by them. The famous Kuhn-Tucker Conditions play a fundamental role in non-linear programming. Gale's research is known for its mathematical elegance. His contributions range from optimal assignment problems in a general setting to major contributions to mathematical economics such as his solution of the n-dimensional 'Ramsey Problem' and his important theory of optimal economic growth. Finally a special thanks to Albert Tucker for his leadership role — not only did he involve the mathematical community from the very beginning, but he organized the research efforts, and set standards for rigor and clarity of exposition that have been a source of inspiration to all.