Aumann's and Schelling's Game Theory: The Nobel Prize in Economic Science, 2005

Abstract

Robert Aumann and Thomas Schelling won the Nobel Prize in Economic Science in 2005. Their work in game theory shows two different approaches to understanding strategic interaction. Schelling's work on the strategic aspects of negotiations, focal points, and self-command is mathematically informal and is based on experimental and inductive knowledge of players' capabilities. Aumann's work on repeated games and common knowledge is mathematically deductive, and assumes highly rational agents. An exploration of their work allows for a comparison of these two approaches.

Notes

¹Schelling, now at the University of Maryland, taught at Harvard for most of his long career. Aumann teaches at Hebrew University of Jerusalem.

²Aumann, however, seems quite hostile to explanations based on behavioral economics, holding that experimental settings are too artificial and that departures from rationality do not show up in empirical work (Hart, 2005, pp. 31–35). He has discussed irrationality in game theory, however, and I consider this work below.

³Their other contributions that do not have a strategic (theoretic) component are not explored here for reasons of space. For a discussion of Schelling's relation to the Cold and Vietnam wars, see Sent (2007). Aydinonat (2007) investigates Schelling's model of residential segregation.

⁴This style can also be confusing for those used to another way of writing. Innocenti (2007, p. 2) points out, ‘Indeed, his books are so full of real people and case studies that one often gets the impression that the vast amount of telling anecdotes makes the reader miss the key point.’

⁵I have argued for a distinct but compatible thesis, that game theory was ignored by economists while general equilibrium theory was dominant, but when the latter was seen to become stalled in the early and mid 1970s, game theory (and other aspects of economics) came to be embraced by the economics profession (Rizvi, 1994a).

⁶Zeckhauser was writing at a time when Schelling was still at Harvard pursuing his long career there.

⁷All of these biographical details are taken from Aumann's account in an interview with Hart (2005).

⁸The lack of mention seems to be an indication of the increasingly bad odor in which general equilibrium theory has been held over the past 20 years, in an era in which game theory and other approaches are favored to it. The high level of citations reflects, however, the dominance of general equilibrium theory at a time when game theory was quiescent (see Rizvi, 1994b, for more on this argument).

⁹Aumann says, ‘It is difficult to imagine now how serious the Cold War was. People were really afraid that the world was coming to an end.’ Harold Kuhn and Oskar Morgenstern had started a consulting firm, Mathematica, in the early 1960s, and in 1964, it started to work for the US Arms Control and Disarmament Agency. Aumann and Mike Maschler were involved with Mathematica and saw repeated negotiations as repeated games. This thought inspired the work referred to in this paragraph (Hart, 2005, p. 9).

¹⁰Surprisingly, Lewis and Aumann gave the concept ‘common knowledge’ the same name (Hart, 2005, p. 17).

¹¹This has been the view of Reinhard Selten for some time, in contrast to Aumann's (Selten, 1985). Selten's first publication was an experimental study of oligopoly, he was an early admirer of Herbert Simon, and he wrote in his autobiographical comments upon winning the Nobel Prize that ‘At the University of Bonn my work [for the past 10 years] and that of most of my assistants is concentrated on experimental economics. It is our goal to help to build up a descriptive branch of decision and game theory which takes the limited rationality of human behavior seriously’ (Selten, 1994).

¹²Aumann recalls that the agreement theorem came out of conversations with Frank Hahn and Kenneth Arrow. When he showed the result to Arrow, however, Arrow would not believe, initially, that it was true. This shows the extent to which the agreement theorem is unsettling to economic theory (Hart, 2005, p. 17)

¹³The study of models in which agents may be unaware of something is in its infancy.

¹⁴It has been argued, however, that Schelling's involvement with the Vietnam War did not show this embeddedness and that his approach was too abstract to understand the true costs of the strategies he proposed. See Sent (2007).

¹⁵Norde et al. (1996). For more on this, see Rizvi (2005).