Abstract
Hitherto, the analysis was confined to deterministic choice problems with full information. The individual confronted with the decision tree of Figure 11.1, for instance, is completely informed about future preferences and all future subtrees. Prom a descriptive point of view this is a highly unrealistic assumption. One may whish to accomodate uncertainty with respect to future preferences and subtrees. Both can be easily accomodated by incorporating chance nodes into the decision tree framework. One should point out that uncertainty does not change the basic undercurrents. If in the preceding chapters we had allowed for uncertainty, some of the essential aspects might have been obscured. It is primarily for this reason, that the inclusion of uncertainty has been deferred until now.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Notes
That is, the number of departing branches and the associated propabilities are unaffected as one “reduces” X(nt) to some lottery ξ(nt).
This definition is equivalent to the notion of “dynamically consistent” preferences as used by Machina (1989) and McClennen (1988, 1990).
Abundant evidence exists on people violating the Independence Axiom. For a recent review of this literature see Seidl (1996b).
LaValle and Fishburn (1987) denote trees with identical opportunity sets as strategically equivalent.
A number of studies of dynamic choice under uncertainty are concerned with the timing of resolution of uncertainty. Examples are Chew and Epstein (1989), Epstein and Zin (1989), Johnsen and Donaldson (1985), Kreps and Porteus (1978), and Seiden (1978).
Other important contributions to the discussion on dynamic consistency and consequentialism are Hammond (1988, 1989), Machina (1989), McClennen (1990), and Weiler (1978).
A quasi-ordering is a binary relation which is reflexive and transitive but not necessarily complete. Recall that not all sets in L(nt) necessarily represent opportunity sets. For this reason, in contractible models featuring uncertainty, the shadow preferences form a quasi-ordering but not necessarily an ordering.
Note that for the case of certainty α(n0) = α(n0), and to each option β(n0) only one option β(n0) exists, and thus, only one truncated option β(nt) ∈G(nt). Hence, Definition 11.17 simplifies to Definition 8.4.
Note that α(n1) = α′(n1) = α(n1).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
von Auer, L. (1998). An Extension to Uncertainty. In: Dynamic Preferences, Choice Mechanisms, and Welfare. Lecture Notes in Economics and Mathematical Systems, vol 462. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58879-2_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-58879-2_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64320-3
Online ISBN: 978-3-642-58879-2
eBook Packages: Springer Book Archive