I would like to dedicate this paper to the memory of Louis-André Gérard-Varet. His premature death in January 2001 deprived us all of a genuinely broad theoretical economist with deep foundational interests. He was one of the few to be conversant with the intricacies of the theory of subjective probability, and he himself co-authored a formal reconstruction of the Impartial Observer Theorem (d'Aspremont and Gérard-Varet, 1991). At the time of publishing this alternative reconstruction, I cannot refrain from remembering his exceptionally active intelligence, as well as the fruitful interchanges we had.

Instrumental rationality requires that an agent selects those actions that give her the best outcomes. This is the principle of consequentialism. It may be that it is not the only requirement of this form of rationality. Considerations other than the outcomes may enter the picture as well. However, the outcome(s) of an action always play a role in determining its rationality. Seen in this light consequentialism is a minimum requirement of instrumental rationality. Therefore, any theory that tries to spell out the implications of instrumental rationality, in particular expected utility theory, should subscribe to the principle of consequentialism. Or so it seems.

The concept of patience describes a person's ability to make prolonged efforts towards future goals, and his or her ability to consider long-term future consequences. Clearly, patience is a capacity that comes by degrees. On the following pages, a person will be said to be patient to the extent that his actions are motivated by future consequences. Hence, a person is not patient if he has the ability to see long-term consequences, while being unable to take these consequences into consideration when he decides how to act.

On many occasions, individuals are able to coordinate their actions. The first empirical evidence to this effect has been described by Schelling (1960) in an informal experiment. His results were corroborated many years later by Mehta et al. (1994a,b) and Bacharach and Bernasconi (1997). From the point of view of mainstream game theory, the success of individuals in coordinating their actions is something of a mystery. If there are two or more strict Nash equilibria, mainstream game theory has no means of explaining why people tend to choose their part of one and the same equilibrium. Textbooks (see, e.g., Rasmusen, 1989 and Kreps, 1990) refer to the fact that players may use focal points (see Schelling (1960)) or social conventions (see Lewis (1969)). Both notions cannot easily be incorporated into mainstream game theory, however. The notion of social conventions has recently been extensively studied in the context of evolutionary game theory where a population of agents interacts with each other. The central focus of this paper, however, is on situations where a few players play a game only once and I study how they may coordinate their actions.

The relationship between extensive and normal form analyses in non-cooperative game theory seems to be dominated, at least traditionally, by the so-called ‘sufficiency of the normal form principle’, according to which all that is necessary to analyse and ‘solve’ an extensive game is already in its normal form representation. The traditional defence of the sufficiency principle, that Myerson (1991, p. 50) attributes to von Neumann and Morgenstern, holds that, with respect to extensive games, it can be assumed without loss of generality, that players formulate simultaneously and independently their strategic plans at the beginning of the game – a situation which, it is claimed, is exactly described by the normal representation of an extensive game.

Keynes's A Treatise on Probability (Keynes, 1921) contains some quite unusual concepts, such as non-numerical probabilities and the ‘weights of the arguments’ that support probability judgements. Their controversial interpretation gave rise to a huge literature about ‘what Keynes really did mean’, also because Keynes's later views in macroeconomics ultimately rest on his ideas on uncertainty and expectations formation.

We should like to thank our editorial assistant, Jonas Josefsson, our copy-editor, Ann Broome, and all the following people for generously giving their time as referees in the year up to July 2001.