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Models of Information Acquisition under Ambiguity

  • Author(s): Li, Jian
  • Advisor(s): Shannon, Chris
  • et al.
Abstract

This dissertation studies models of dynamic choices under uncertainty with endogenous information acquisition. In particular we are interested in exploring the interactions between ambiguity attitudes and the incentive to collect new information.

The first chapter explores the link between intrinsic preferences for information and ambiguity attitudes in settings with subjective uncertainty. We enrich the standard dynamic choice model in two dimensions. First, we introduce a novel choice domain that allows

preferences to be indexed by the intermediate information, modeled as partitions of the underlying state space. Second, conditional on a given information partition, we allow preferences over state-contingent outcomes to depart from expected utility axioms. In particular

we accommodate ambiguity sensitive preferences. We show that aversion to partial information is equivalent to a property of static preferences called Event Complementarity. We show that Event Complementarity and aversion to partial information are closely related to

ambiguity attitudes. In familiar classes of ambiguity preferences, we identify conditions that characterize aversion to partial information.

The second chapter extends the basic model to allow for choices from non-singleton menus after partial information is revealed, and studies the value of information under ambiguity. We show that the value of information is not monotonic under ambiguity. Intrinsic aversion

to partial information in the basic model is equivalent to a preference for perfect information in the extended model. Moreover, the value of information is not monotone in the degree of ambiguity aversion.

The third chapter studies the impact of ambiguity in a classic information acquisition model-the K-armed bandit problem. We consider a particular family of ambiguity averse preferences, the multiple-priors model [Marinacci, 2002]. A previous paper [Li, 2012] shows that major classic characterizations of optimal strategies in the K-armed bandit problems

extend to incorporate ambiguity in the multiple-priors model. Here we explore new implications of ambiguity on the optimal incentive to experiment. First, increasing ambiguity in the unknown arm reduces the incentive to experiment, while increasing risk in the unknown arm typically increases the incentive to experiment. This suggests that ambiguity can offer an explanation for the widely observed under-experimentation in novel technology and consumer products. Second, optimal experimentation in the multiple-priors bandit problem generally cannot be reduced to that in a classic bandit problem with an equivalent

single prior. In particular, the lower envelope of the classic single-prior Gittins-Jones index for every prior lying in the multiple-priors set can be strictly higher than the generalized multiple-prior Gittins-Jones index. In one-dimensional parametric family, we identify monotonicity conditions under which this discrepancy disappears so an equivalent single prior

exists.

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