The optimal reservation utility in models of decision making in arranged marriages

Abstract

The notion of a reservation quality or utility is a key feature of Batabyal's (2003a) recent analysis of decision making in arranged marriages. In this model, the magnitude of the reservation utility has a nontrivial impact on the decision to accept or decline a marriage proposal. Even so, Batabyal (2003a) treats the marrying agent's reservation utility as an exogenous variable. Consequently, the purpose of this article is to endogenize the reservation utility variable in the context of a dynamic and stochastic model of decision making in arranged marriages. Our analysis leads to two results. First, we demonstrate that the optimal reservation utility is the solution to a particular maximization problem. Second, we show that theoretical circumstances exist in which the optimal reservation utility is unique.

Acknowledgement

Batabyal acknowledges financial support from the Gosnell endowment at RIT. The usual disclaimer applies.

Notes

¹ The concept of a reservation value – value denoting variables such as price, quality, revenue, utility and wage – has been used to analyse questions in many different areas of economics such as family economics (Hatcher, 2002), information economics (Tirole, 1986), labour economics (Groot and Oosterbeek, 1994) and natural resource economics (Batabyal, 2003b). The reader should note that although Batabyal (2003a) uses the term ‘reservation quality,’ in the rest of this article, we shall use the more familiar term ‘reservation utility’ to refer to our marrying agent's threshold level of utility.

² Without loss of generality, in the rest of this article we shall suppose that the utility of an arbitrary marriage proposal is given by a nonnegative real number. As such, the lowest possible utility is zero and the highest possible utility is (in principle) ∞.

³ For textbook accounts of the Poisson process, see Ross (1996, pp. 59–97, 2003, pp. 288–348).