Li, Hualin
(2020)
Essays on decision making under variable information.
PhD thesis, University of Glasgow.
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Abstract
This thesis is composed of three chapters that invoke axiomatic approaches to study models of decision making under objective and variable information.
In Chapter 1, we propose a model of choice from choice architectures that refer to environments where alternatives are presented with objective and observable choicerelevant information. We identify choice architectures by directed graphs on sets of alternatives where directed edges represent choicerelevant information about the alternatives. In this domain, a choice function hence singles out a vertex from each given directed graph, whereas a choice correspondence assigns to every directed graph a set of vertices. A choice function and choice correspondence are respectively characterised by a choice procedure that separates the role of information processing from that of preferences. Notably, both choice procedures suggest the same machinery of information processing that is hinged on properties of directed graphs, hence being objective and predictable. We then explore its implications on the formation mechanism of consideration sets and the sources of the stochasticity of choice. Later in the chapter, we also study the applications in terms of demand shaping and revealing equilibrium, respectively.
Chapter 2 considers decision making under uncertainty with objective and variable information structures. We take as primitive a family of informationdependent preferences over subjective acts indexed by partitions of the state space. Each partition corresponds to an information structure. We characterise a utility representation that comprises an affine utility index over simple lotteries, a unique capacity over the state space, and for each partition, a probability measure on the $\sigma$algebra generated by the partition. We find that such a representation is equivalent to the Choquet expected utility representation with specific machinery of nonadditive belief formation. We then connect the utility representation to the definition of comparative uncertainty aversion to explore the characteristic conditions related to the translatability of uncertainty attitude among variable information structures.
In Chapter 3, we explicitly incorporate framing of information into decision making under uncertainty. As in Chapter 2, we also study a family of partitionindexed preferences over subjective acts, where we interpret each partition as a frame of information. Under a modest set of axioms, we characterise a general utility representation, which we call frameadaptive expected utility. Having the general utility representation, we focus on two parameterised forms of frameadaptive expected utility featuring attitude towards informativeness and degree of salience, respectively. We then apply the frameadaptive models to the definition of comparative uncertainty aversion and that of definitive uncertaintyaversion to study the translatability of uncertainty attitude among variable frames of information. We also conduct a comparative analysis and find that the decision maker's reaction to information frames plays a role in modifying the degree of uncertainty attitude revealed from choices. Later in the chapter, we relate frameadaptivity to ambiguityaversion and argue that the latter can be viewed as a manifestation of the decisionmaker performing frameadaptive reasoning.
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