Paradox of the absent minded driver

However, problems still exist when there are more than one action optimals. Always EXIT at an intersection would give the highest payoff of 7.

However, there are other stable points aka action optimals. The equilibrium is determined by outside forces such as customs and traditions. I find this explanation unconvincing. Even if a game of coordination is played between different persons, each person picking the stable point with the highest payoff is still a very plausible outcome.

The given rationale for picking a lower payoff strategy at the action stage, i. It is a self-locating probability. As I have argued in anthropic paradoxes, self-locating probabilities are not valid concepts. Because of its primitive nature, there is no way to define an inherent reference class nor assign any probability distribution.

There is only one legitimate payoff function the one at the planning stage. The driver should keep his original strategy when arriving at an intersection simply because there is no new information. Here the original coin is tossed after the first awakening on Monday afternoon.

A second, inconsequential coin toss is added on Tuesday afternoon. This format is similar to the absent-minded driver problem. Nonetheless, I think it is an excellent example. In the first part, the author reviews four types of time consistency. One of his innovative contributions is the definition of gt-time consistency: a decision maker reviewing his strategy at an information set believes that this review is done at the first node. We find it hard to make sense of this assumption.

One possible interpre- tation is that the decision maker infers from his desire to change the plan that it must be the first time the information set has been reached since changes would be made the first time the opportunity arises. It is not clear, however, why a decision maker who draws inferences from his desire to change the strategy should not also make inferences from his unwillingness to change it. When the original plan is confirmed, why should his inference exclude the possibility of being at the second intersection?

In the second part of the paper, the author proposes an alternative model for decision problems with imperfect recall. This model contains some of the elements Fagin et al. Gilboa Gilboa excludes any form of preplanning.

The basic formalization of the problem defuses any paradoxical aspects. Most game theorists think of a game as a physical description of a situation. Indeed, the game has also an asymmetric equilibrium in which one agent exits and the other continues.

This equilibrium has a payoff of 2 which cannot be achieved in the original decision problem. For further discussion of this point and the connection between the Gilboa and Aumann, Hart, and Perry papers see Lipman.

If the scenario must include details about the way that the decision maker reasons, we have one. If they require that the process of reasoning be derived from primitive assumptions which induce consistent behavior, well, obviously such a scenario, by definition, will not display a paradox.

The ex-ante payoff and the payoff at the information set differ unless a is equal to 1. He would refuse an offer of 4r3 to quit the game once it had started, yet at the bar would believe this to be a fair offer.

The authors compare two probabilistic models. This measure corresponds to our definition of z-consistency. In this case, the induced beliefs are the frequency probabilities. However, ex-ante expected utility differs from the expected utility at the information set. The comparison of ex-ante and ex-post payoffs of a fixed strategy is the sole objective of Grove and Halpern.

For a discussion of this issue we refer the readers to Lipman. Despite all that has been said we are still confused about its resolution. We do not find it surprising that the paradox disappears when interpre- tative ambiguities are removed by making specific assumptions. However, the suggestions by different eminent scholars are far from coinciding. The availability of random elements is not at all obvious.

One is the following. This reinforces our view as to the presence of interpretative ambiguities in the model. We believe we have a consensus on this issue. Details such as strategy recall, circumstances which induce a decision maker to reassess his strategy, and so on, are recognized to be crucial for the analysis of such decision problems. There is less of a consensus about the next step. Some believe that the standard model of extensive games can tackle these issues successfully.

Others think that there is a need to expand the model to allow explicit consideration of the above elements. We see no justification for ruling out a priori that a decision maker could consider a change in his plan beyond the instance of the deliberation.

Every point of view can be criticized in such terms. As formal theoreticians we can at most clarify some of the logic of these ways. Aumann, R. Binmore, K. Guth et al. Dekel, E. Kreps and K. Wallis, Eds.. Press, Cambridge. Fagin, R. Gilboa, I. Grove, A. Halpern, J. Lipman, B.