Updating preferences with multiple priors

We propose and axiomatically characterize dynamically consistent update rules for decision making under ambiguity. These rules apply to the preferences with multiple priors of Gilboa and Schmeidler (1989), and are the first, for any model of preferences over acts, to be able to reconcile typical behavior in the face of ambiguity (as exemplified by Ellsberg’s paradox) with dynamic consistency for all non-null events. Updating takes the form of applying Bayes’ rule to subsets of the set of priors, where the specific subset depends on the preferences, the conditioning event, and the choice problem (i.e., a feasible set of acts together with an act chosen from that set).Updating, dynamic consistency, ambiguity, Ellsberg, Bayesian, consequentialism

Speculative Trade and the Value of Public Information

In environments with expected utility, it has long been established that speculative trade cannot occur (Milgrom and Stokey [1982]), and that the value of public information is negative in economies with risk-sharing and no aggregate uncertainty (Hirshleifer [1971], Schlee [2001]). We show that these results are still true even if we relax expected utility, so that either Dynamic Consistency (DC) or Consequentialism is violated. We characterise no speculative trade in terms of a weakening of DC and find that Consequentialism is not required. Moreover, we show that a weakening of both DC and Consequentialism is sufficient for the value of public information to be negative. We therefore generalise these important results for convex preferences which contain several classes of ambiguity averse preferences

Confidence and ambiguity

This paper proposes a model of the decision-maker’s confidence in his probability judgements, in terms of an implausibility measure – a real-valued function on the set of probability functions. A decision rule is axiomatised according to which the decision-maker evaluates acts using sets of probability functions which vary depending on the agent’s implausibility measure and on what is at stake in the choice of the act. The framework proposed yields a natural notion of comparative aversion to lack of confidence, or ambiguity aversion, and allows the definition of an ambiguity premium. It is shown that these notions are equivalent and can be characterised in terms of the implausibility measure representing the agent’s confidence. A simple portfolio example is presented.Confidence; multiple priors; ambiguity aversion; ambiguity premium; implausibility measure

Rationality and dynamic consistency under risk and uncertainty

For choice with deterministic consequences, the standard rationality hypothesis is ordinality - i.e., maximization of a weak preference ordering. For choice under risk (resp. uncertainty), preferences are assumed to be represented by the objectively (resp. subjectively) expected value of a von Neumann{Morgenstern utility function. For choice under risk, this implies a key independence axiom; under uncertainty, it implies some version of Savage's sure thing principle. This chapter investigates the extent to which ordinality, independence, and the sure thing principle can be derived from more fundamental axioms concerning behaviour in decision trees. Following Cubitt (1996), these principles include dynamic consistency, separability, and reduction of sequential choice, which can be derived in turn from one consequentialist hypothesis applied to continuation subtrees as well as entire decision trees. Examples of behavior violating these principles are also reviewed, as are possible explanations of why such violations are often observed in experiments

Updating Ambiguity Averse Preferences

Dynamic consistency leads to Bayesian updating under expected utility. We ask what it implies for the updating of more general preferences. In this paper, we charac- terize dynamically consistent update rules for preference models satisfying ambiguity aversion. This characterization extends to regret-based models as well. As an appli- cation of our general result, we characterize dynamically consistent updating for two important models of ambiguity averse preferences: the ambiguity averse smooth am- biguity preferences (Klibanoff, Marinacci and Mukerji [Econometrica 73 2005, pp. 1849-1892]) and the variational preferences (Maccheroni, Marinacci and Rustichini [Econometrica 74 2006, pp. 1447-1498]). The latter includes max-min expected utility (Gilboa and Schmeidler [Journal of Mathematical Economics 18 1989, pp. 141-153]) and the multiplier preferences of Hansen and Sargent [American Economic Review 91(2) 2001, pp. 60-66] as special cases. For smooth ambiguity preferences, we also identify a simple rule that is shown to be the unique dynamically consistent rule among a large class of rules that may be expressed as reweightings of Bayes's rule.Updating, Dynamic Consistency, Ambiguity, Regret, Ellsberg, Bayesian, Consequentialism, Smooth Ambiguity

Platform Competition as Network Contestability

Recent research in industrial organisation has investigated the essential place that middlemen have in the networks that make up our global economy. In this paper we attempt to understand how such middlemen compete with each other through a game theoretic analysis using novel techniques from decision-making under ambiguity. We model a purposely abstract and reduced model of one middleman who pro- vides a two-sided platform, mediating surplus-creating interactions between two users. The middleman evaluates uncertain outcomes under positional ambiguity, taking into account the possibility of the emergence of an alternative middleman offering intermediary services to the two users. Surprisingly, we find many situations in which the middleman will purposely extract maximal gains from her position. Only if there is relatively low probability of devastating loss of business under competition, the middleman will adopt a more competitive attitude and extract less from her position.Comment: 23 pages, 3 figure

A Behavioral Characterization of Plausible Priors

One of the last great novels of José Saramago, Death with Interruptions, begins with an epigraph taken from Ludwig Wittgenstein: “If, for example, you were to think more deeply about death, then it would be truly strange if, in so doing, you did not encounter new images, new linguistic fields”. The aim of my paper is to ponder on what kind of a new language game the Portuguese writer is offering us in his book and how to interpret his investigations from the angle of another contemporary literary and philosophical thanatological discourses.One of the last great novels of José Saramago, Death with Interruptions, begins with an epigraph taken from Ludwig Wittgenstein: “If, for example, you were to think more deeply about death, then it would be truly strange if, in so doing, you did not encounter new images, new linguistic fields”. The aim of my paper is to ponder on what kind of a new language game the Portuguese writer is offering us in his book and how to interpret his investigations from the angle of another contemporary literary and philosophical thanatological discourses