A Unique Costly Contemplation Representation

Abstract

We study preferences over menus which can be represented as if the individual is uncertain of her tastes, but is able to engage in costly contemplation before selecting an alternative from a menu. Since contemplation is costly, our key axiom, aversion to contingent planning, reflects the individual's preference to learn the menu from which she will be choosing prior to engaging in contemplation about her tastes for the alternatives. Our representation models contemplation strategies as subjective signals over a subjective state space. The subjectivity of the state space and the information structure in our representation makes it difficult to identify them from the preference. To overcome this issue, we show that each signal can be modeled in reduced form as a measure over ex post utility functions without reference to a state space. We show that in this reduced-form representation, the set of measures and their costs are uniquely identified. Finally, we provide a measure of comparative contemplation costs and characterize the special case of our representation where contemplation is costless. Copyright 2010 The Econometric Society.

The two kinds of free energy and the Bayesian revolution

“…Therefore, in this case, free energy can be seen as a certainty-equivalent value of the subordinate decision problems, i.e., the amount of utility the agent would have to receive to be indifferent between this guaranteed utility and the potential expected utility of the subsequent decision steps taking account the associated information processing costs. The special case (19) has been studied extensively in multiple contexts, including quantal response equilibria in the game-theoretic literature [10,14], rational inattention and costly contemplation [11,75], bounded rationality with KL costs [12,19], KL control [76,77], entropy regularization [8,9], robustness [15,16], the emergence of heuristics [78], thermodynamic models of computation [79], and the analysis of information flow in perception-action systems [17,18]. While (19) is often regarded as an abstract measure of uncertainty reduction or a generic proxy for information processing costs, it can also be viewed as a physical capacity constraint, where the information that is required to achieve a certain expected utility is considered to be sent over a channel to the actuator [24,[80][81][82][83].…”