Abstract

We characterize a generalization of discounted logistic choice that incorporates a parameter to capture different views the agent might have about the costs and benefits of larger choice sets. The discounted logit model used in the empirical literature is the special case that displays a “preference for flexibility” in the sense that the agent always prefers to add additional items to a menu. Other cases display varying levels of “choice aversion,” where the agent prefers to remove items from a menu if their ex ante value is below a threshold. We show that higher choice aversion, as measured by dislike of bigger menus, also corresponds to an increased preference for putting off decisions as late as possible.

Highlights

  • Data on dynamic choice let us distinguish between models of random choice that coincide in static settings, because these models have different implications for how the agent views his future randomizations over menus, and

  • The reason that αv is not equivalent to v in Discounted Adjusted Logit (DAL), as opposed to the usual affine uniqueness of expected utility, is that we set the parameter of the extreme-value distribution to 1, which fixes the multiplicative term in the utility function; this parallels our specification of a unit coefficient for adjusted entropy in Discounted Adjusted Entropy (DAE) and of W = exp(1 · v) in Discounted Adjusted Luce (DALu)

  • This paper provides an axiomatic characterization of three equivalent generalizations of discounted logit, namely discounted adjusted logit, discounted adjusted entropy, and discounted adjusted Luce

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Summary

INTRODUCTION

This leads us to propose a generalization of discounted logit called Discounted Adjusted Logit (DAL), where the attractiveness of menus is adjusted to reflect the agent’s “choice aversion” and reduce or eliminate the option value of additional items To make this first step in characterizing dynamic stochastic choice, we maintain the Independence of Irrelevant Alternatives (IIA) assumption throughout the paper, so that static choice in our model is logit, and can be represented by a random utility model where the payoff shocks are independent and identically distributed (i.i.d.) with extreme-value type-1 distributions; see, for example, Anderson, De Palma, and Thisse (1992). The relative entropy cost function corresponds to κ = 1 in an alternative representation we call Discounted Adjusted Entropy or DAE In this case, adding an good item to a singleton menu has no effect on the menu’s value, as the agent will choose to randomize uniformly and incur no attention cost while receiving an equivalent current outcome. Form was recently used by Swait and Marley (2013) to model stochastic choice as the result of balancing multiple goals

DYNAMIC CHOICE PROBLEMS
CHOICE RULES AND THEIR REPRESENTATIONS
Work or College?
Durable Goods
Magazine Subscriptions
Choice Aversion
Immediate versus Delayed Consequences
Horizon Effects
Choosing When to Choose
AXIOMATIZATION
Logit-esque Axioms
Tying Choices in Different Time Periods
Stationarity and Impatience
Representation Theorem
Relation to the Literature
Conclusion
Proof of Proposition 1
Recursive Representations
Necessity
Proof of Lemma 5
Proof of Theorem 1
Proof of Proposition 2
Proof of Proposition 4
Proof of Proposition 5
Full Text

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