On Game Theory (1975-1999)

"A proven theorem of game theory states that every game with complete information possesses a saddle point and therefore a solution." (Richard A Epstein, "The Theory of Gambling and Statistical Logic" [Revised Edition], 1977)

"Game theory is a collection of mathematical models designed to study situations involving conflict and/or cooperation. It allows for a multiplicity of decision makers who may have different preferences and objectives. Such models involve a variety of different solution concepts concerned with strategic optimization, stability, bargaining, compromise, equity and coalition formation." (Notices of the American Mathematical Society Vol. 26 (1), 1979)

"Direct application of the theory of games to the solution of real problems has been rare, and its chief uses have been to offer some insight and understanding into the problems of competition (without actually solving them), and to provide mathematicians with new fields to conquer. Many important real problems involve more than two opponents, are not zero-sum, and exceed the bounds of the most developed versions of game theory." (George R Lindsey, "Looking back over the Development and Progress of Operational Research, 1979)

"There are many difficulties in application of [the games] theory to the real world. [., ..] In general, competitors are not in complete opposition. As a matter of fact often they don't even have the same objectives. This difficulty can often be circumvented by using a different objective, 'games of survival'. Secondly, a decision is seldom made once. This motivated the study of multistage games [...]. Finally, decisions are not usually made simultaneously. Recognition of this fact leads to 'games of protocol' [...]. Games of protocol can also be used to handle processes involving three or more people." (Richard E Bellman, "Eye of the Hurricane: An Autobiography", 1984)

"Cybernetics is concerned with scientific investigation of systemic processes of a highly varied nature, including such phenomena as regulation, information processing, information storage, adaptation, self-organization, self-reproduction, and strategic behavior. Within the general cybernetic approach, the following theoretical fields have developed: systems theory" (system), communication theory, game theory, and decision theory." (Fritz B Simon et al, "Language of Family Therapy: A Systemic Vocabulary and Source Book", 1985)

"But the answers provided by the theory of games are sometimes very puzzling and ambiguous. In many situations, no single course of action dominates all the others; instead, a whole set of possible solutions are all equally consistent with the postulates of rationality." (Herbert A Simon et al, "Decision Making and Problem Solving", Interfaces Vol. 17 (5), 1987)

"Game theory can be defined as the study of mathematical models of conflict and cooperation between intelligent rational decision-makers." (Roger B Myerson, "Game Theory: Analysis of Conflict", 1991) 

"Game theory is a theory of strategic interaction. That is to say, it is a theory of rational behavior in social situations in which each player has to choose his moves on the basis of what he thinks the other players' countermoves are likely to be." (John Harsanyi, "Games with Incomplete Information", 1997)

"Like all of mathematics, game theory is a tautology whose conclusions are true because they are contained in the premises." (Thomas Flanagan, "Game Theory and Canadian Politics", 1998)