In the 1990s and 2000s, advances continued to be made in the topics of noncooperative and cooperative game theory that had come to be traditional, and some research pursued new directions that will be useful for this book. Returning to the long-neglected topic of coalitions in noncooperative games, Bernheim et al. (1987) proposed a property of coalition-proofness as a refinement of Nash equilibrium. The period was, of course, dominated by the Nobel Memorial Prizes of 1994, 2005, 2007, and 2012, which kept the traditional topics in view. Nevertheless, in his inaugural presidential address to the Game Theory Society, Aumann (2003) expressed regret at the division of game theory between cooperative and noncooperative branches, saying that there ought to be one theory of interactive rationality. Certainly the division weakens game theory by its ambiguity, but more than that, common experience tells us that both noncooperative and cooperative actions are parts of our experience. On the one hand, in Maskin’s (2004) words, “We live our lives in coalitions.” On the other hand, tragedies of the commons and other social dilemmas, involuntary unemployment and price competition are no less parts of our experience.

Some works have addressed this division. In 1990, Greenberg proposed a “theory of social situations” as an alternative both to cooperative and noncooperative game theory. Some progress was made on the incorporation of externalities in games in partition function form. Zhao (1992) proposed a theory of “hybrid solutions.” Chwe (1994) addressed problems that arise for a core-like solution in games in partition function form, and Ray and Vohra (1999) proposed a theory to explain the determinants of the coalition structure.

Brandenburger and Stuart (2001, for example) proposed “Biform Games,” a two-stage analysis in which the first stage is a noncooperative game, but the outcome of the noncooperative game is a cooperative game that determines the payoffs to the participants. The solution to the two-stage game is by backward induction. This sort of approach actually has a long history: von Neumann and Morgenstern (1944/2004) argue along these lines in their simple majority game example (p. 222). Nash (1953) variable threat bargaining theory is a formally similar two-stage game. However, Brandenburger and Stuart, working mainly on issues of corporate strategy, show how this approach permits a reconciliation of cooperation within coalitions with such noncooperative phenomena as inefficient externalities. Applying a different bargaining theory, McCain (2013, Chapter 7) extends these examples, and this discussion will play an important part in Part II of this book.

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