Adding a \"Non-\" in cooperative game theory: a textbook history - Graciani, Marcos Thiago (2023)
This dissertation offers an extensive documentation of game theory textbooks published since 1944 in order to analyze and contextualize the main titles. The evolution of textbooks towards the ones currently used indicates three distinct generations, each corresponding to the books published in 1950-1959, 1966-1970, and 1972-1978. Two important transformations in game theory lay behind these different generations: first, a switch from two- to n-person games; and second, a large diffusion of game theory to other areas of economics, such as industrial organization, and to other sciences. Besides such an exploratory analysis, the dissertation also tracked more closely how textbooks presented specific solution concepts: the Nash equilibrium and the core, usually attributed to D. B. Gillies and L. S. Shapley. Concerning Nashs equilibrium, textbooks suggest that practitioners confused it and J. von Neumanns Minimax Theorem, especially because they focused on studying two-person games in the post-War era. As their interests moved to n-person games, however, Nashs equilibrium failed to occupy a central place in textbooks because cooperative games offered problems that were mathematically more interesting. Finally, in the early 1970s, textbooks applied non-cooperative games to industrial organization problems, at a time when those games were becoming increasingly popular. With respect to the core, textbooks show how it went from an instrument devised for helping one find a games solution (in von Neumann and Morgensterns sense) to a solution concept in its own right. The history of the core through textbooks also elucidates how this concept ended up being neglected to the final chapters of the modern texts. Seemingly, in models in which it attained most success (in general equilibrium theory), the core became characterized as not belonging to game theory; and in models in which it remained closely tied to game theory, such as of industrial organization, it failed in producing remarkable results.