In 45 years from 1944 to 1989, game theory became a cross-disciplinary study of great importance for the mathematical social sciences. It also became a compound field - not one study of interdependent decisions, but largely separate studies of noncooperative and cooperative game theory.
What game theory offers is a kit of tools applicable to decision problems in which the consequences of one decision may depend on the decisions of others, previous decisions creating the conditions for current decisions, simultaneous and subsequent decisions, with or without mutual knowledge, with or without some degree of honest mutual commitment to a common strategy. If we choose our tools to fit the job and disregard the dogmas and dichotomies of cooperative and noncooperative, superadditive valuations and rationality, we will find that the tools contribute to the solution of problems of real-world public policy.
- 1. Where two dates are given, the first is the original date of publication, and the second the date of the edition or translation used.
- 2. Kyu Uck Lee, personal communication by e-mail, June 22, 2007.
- 3. “A Chronology of Game Theory,” by Paul Walker, Economics Department, University of Canterbury, Canterbury, New Zealand, http://www.econ.canterbury. ac.nz/personal_pages/paul_walker/gt/hist.htm, accessed 9/9/2014, last modified Sept. 2012.
- 4. In what follows page citations indicated by TGEB will refer to von Neumann and Morgenstern (2004).
- 5. This paper seems to have been available only in German prior to the publication of the translation in Tucker and Luce (1959).
- 6. In what follows citations to CGT will refer to Kuhn, Classics in Game Theory, 1997.
- 7. In what follows page references indicated by CTG4 will refer to volume 4 of Contributions to the Theory of Games, edited by Tucker and Luce.
- 8. In what follows references denoted GD will refer to Luce and Raiffa (1957).
- 9. Von Neumann and Morgenstern had alluded to this at TGEB, p. 224.
- 10. In what follows page references to SC refer to Schelling, Strategy of Conflict, 1960.
- 11. This paragraph relies on an address given by Schelling at Trinity University, San Antonio, Texas on April 18, 2007, and is from memory.
- 12. One evidence of this is that it is not mentioned in some recent advanced texts with coverage of cooperative game theory. See, for example, Peleg and Sudholter, Introduction to the Theory of Cooperative Games, 2003, and Forgo et al., Introduction to the Theory of Games, 1999.
- 13. According to the Oxford English Dictionary, the phrase tit-for-tat is traceable to the 16th-century phrase “tip for tap,” meaning, roughly, push for shove.
- 14. For example, Guth et al. (1982), Henrich et al. (2005), and note also Roth et al. (1991), Roth and Erev (1995), Stanley and Tran (1998), Oosterbeek et al. (2004), Andreoni and Blanchard (2006).