Stochastic Utility Maximization Research Articles

Pure strategy Nash equilibria for bargaining models of collective choice

This paper considers pure strategy Nash equilibria of non-cooperative legislative bargaining models. In contrast to existing legislative bargaining models, we derive legislators behavior from stochastic utility maximization. This approach allows us to prove the existence of a stationary Pure Local and Global Nash Equilibrium under rather general settings. The mathematical proof is based on a fixed point argument, which can also be used as a numerical method to determine an equilibrium. We characterize the equilibrium outcome as a lottery of legislators’ proposals and prove a Mean Voter Theorem, i.e., proposals result dimension-by-dimension as a weighted mean of legislators’ ideal points and are Pareto-optimal. Based on a simple example, we illustrate different logic of our model compared to mixed strategy equilibrium of the legislative bargaining model suggested by Banks and Duggan (Am Polit Sci Rev 94(1):73–88. https://doi.org/10.2307/2586381, 2000).

Test Score Algorithms for Budgeted Stochastic Utility Maximization

Motivated by recent developments in designing algorithms based on individual item scores for solving utility maximization problems, we study the framework of using test scores, defined as a statistic of observed individual item performance data, for solving the budgeted stochastic utility maximization problem. We extend an existing scoring mechanism, namely, the replication test scores, to incorporate heterogeneous item costs as well as item values. We show that a natural greedy algorithm that selects items solely based on their replication test scores outputs solutions within a constant factor of the optimum for the class of functions satisfying an extended diminishing returns property. Our algorithms and approximation guarantees assume that test scores are noisy estimates of certain expected values with respect to marginal distributions of individual item values, thus making our algorithms practical and extending previous work that assumes noiseless estimates. Moreover, we show how our algorithm can be adapted to the setting in which items arrive in a streaming fashion while maintaining the same approximation guarantee. We present numerical results, using synthetic data and data sets from the Academia.StackExchange Q&A forum, which show that our test score algorithm can achieve competitiveness and in some cases better performance than a benchmark algorithm that requires access to a value oracle to evaluate function values. Funding: This research was supported, in part, by the Institute for Basic Science [Grants IBS-R029-C1, IBS-R029-Y2].

Dynamic micro-assignment modeling approach for integrated multimodal urban corridor management

Development and analysis of demand management strategies for integrated multimodal urban corridor management requires application of a new generation of demand modeling and network analysis tools. This paper describes the development of a dynamic trip micro-assignment and (meso) simulation system that incorporates individual tripmaker choices of travel mode, departure time and route in multimodal urban transportation networks (with different travel modes such as drive alone, shared ride, bus rapid transit and metro rail). These travel choice dimensions are integrated in a stochastic utility maximization framework that considers multiple user decision criteria such as travel time, travel cost, schedule delay, as well as travel time reliability. A variational inequality model is first proposed to describe the general stochastic dynamic traffic user equilibrium problem. For a typical case that assumes the logit-based alternative choice model, this paper develops an equivalent gap function-based optimization formulation and a heuristic iterative solution procedure. Based on a multi-dimensional network representation, an efficient time-dependent least cost path algorithm is embedded to generate an intermodal route choice set that recognizes time-dependent mode transfer costs and feasible mode transfer sequences. A two-stage estimation procedure that can systematically utilize historical static demand information, time-dependent link counts, as well as empirically calibrated stochastic departure time choice models is proposed to infer commuters’ preferred arrival time distribution, which is important in modeling departure time choice dynamics. A case study based on a large-scale multimodal transportation network (adapted from the Baltimore–Washington corridor) is presented to illustrate the capabilities of the methodology and provide insight into the potential benefit of integrated multimodal corridor management.

Discrete choice and stochastic utility maximization

Discrete choice models are usually derived from the assumption of random utility maximization. We consider the reverse problem, whether choice probabilities are consistent with maximization of random utilities. This leads to tests that consider the variation of these choice probabilities with the average utilities of the alternatives. By restricting the range of the average utilities we obtain a sequence of tests with fewer maintained assumptions. In an empirical application, even the test with the fewest maintained assumptions rejects the hypothesis of random utility maximization.

Discrete Choice and Stochastic Utility Maximization

Discrete choice models are usually derived from the assumption of random utility maximization. We consider the reverse problem, whether choice probabilities are consistent with maximization of random utilities. This leads to tests that consider the variation of these choice probabilities with the average utilities of the alternatives. By restricting the range of the average utilities we obtain a sequence of tests with fewer maintained assumptions. In an empirical application, even the test with the fewest maintained assumptions rejects the hypothesis of random utility maximization.

Investigation of the Stochastic Utility Maximization Process of Consumer Brand Choice by Semiparametric Modeling

ABSTRACT The se of nonparametric methods, which posit fewer assumptions and greater modelu flexibility than parametric methods, could provide useful insights when studying brand choice. It was found, however, that the data requirement for a fully nonparametric brand choice model is so greatthat obtaining such large data sets is difficult even in mar keting. Semiparametric methods balance model flexibility and data requirement by imposing some parametric structure on components that are not sensitive to such assumptions while leaving the essential component nonparametric. In this paper, the authors compare two semiparametric brand choice models that are based on the generalized additive models (GAM). One model is specified as a nonparametric logistic regression of GAM (Hastie and Tibshirani 1986) with one equation for each brand. The other model is a multinomial logit (MNL) formulation with a nonparametric utility function, which is derived by extending the GAM framework (Abe 1999). Both models assume a parametric distribution for the random component, but capture the response of covariates nonparametrically. The competitive structure of the logistic regression formulation is specified by data through nonparametric response functions of the attributes forthe competitive brands, whereas that of the MNL formulation is guided by the choice theory of stochastic utility maximization (SUM). Simulation study and application to actual scanner panel data seem to support the behavioral assumption of SUM. In addition, if we relax the SUM assumption by letting data specify the competitive structure, a substantially larger amount of data, perhaps an order of magnitude more, would be required. Therefore, if alternative brands are chosen carefully, nonparametric relaxation to capture cross effect (i.e., nonparametrization of the MNL structure) may not be warranted unless the size of database becomes substantially larger than the one currently used.

Testing the consistency of nested logit models with utility maximization

This paper provides simple necessary conditions for testing the local consistency of nested logit models with stochastic utility maximization. A graphical analysis illustrates the extent to which these conditions extend the range of admissible dissimilarity coefficients beyond the unit interval.

On the compatibility of nested logit models with utility maximization: A comment

Börsch-Supan (1990) gives a sufficient condition for the compatibility of choice probabilities with stochastic utility maximization on an interval. We show that the necessary and sufficient conditions for global compatibility as derived by Daly and Zachary (1979) and McFadden (1981) also apply if the nonrandom components are restricted to a closed interval. Hence, this case gives no further restrictions on the choice probabilities.

On the compatibility of nested logit models with utility maximization

The paper examines the relationship between the nested multinomial logit (NMNL) model and rational consumer behavior. We show that the Daly-Zachary-McFadden (DZM) condition of the validity of stochastic utility maximization in NMNL models is unnecessarily strong and leads too often to rejection of NMNL models with large dissimilarity parameters. In many cases, the distribution of the stochastic utility components in the NMNL model can be modified in a way that preserves the NMNL choice probabilities on a subset of R I , where I is the number of alternatives in the choice set. On this subset, the DZM condition can be violated without violating the restrictions of stochastic utility maximization.

Discrete Choice Theory and the General Equilibrium of Employment, Housing, and Travel Networks in a Lowry-Type Model of the Urban Economy

Five influential paradigms established by Beckmann, Lowry, Wilson, Mills, and McFadden are unified by developing a long-run economic general equilibrium model of urban land-use based on probabilistic discrete choice theory. The model takes into account the interdependence of export-oriented and service employment with population. Households' choices of employment type, employment location, type and location of housing, shopping destination, and choice of travel routes in the journey to work and journey to shop are determined simultaneously by means of stochastic utility maximization. Firms' choices of building type and location and landowners' choices of land-use type and density are determined by means of stochastic profit maximization. Travel occurs on a congestible link—node network. The model determines the wage rate for each employment type in each zone, the price of floor space for each building type in each zone, the price of land in each zone, the price of the locally traded composite commodity in each zone, and the peak and off-peak congested travel-cost and travel-time for each link of the network. The quantity of land which remains undeveloped is also determined. I formulate a nonlinear mathematical programming problem which is equivalent to the general equilibrium problem. Using this formulation, I prove the existence and uniqueness of the general equilibrium in all the prices and physical allocations.

A nested logit model of travel mode to work and auto ownership

Estimating the demand for urban passenger travel is very useful in transport planning. This study estimates a joint model of choice for both auto ownership and travel mode to work in Karachi, Pakistan. The model used for analysis is based on stochastic utility maximization and is estimated utilizing nested logit techniques. The purpose of the study is to measure the impact of various policy changes on welfare. The model reveals that the decision to own a car is made simultaneously with the decision regarding mode of travel to work. However, the study shows that had this simultaneity been ignored, the loss in terms of bias in the estimated coefficients would not have been large. The model has several advantages over conventional transport demand models. It is estimated using a small household sample; it is behavioral and responsive to more important policy instruments available to a planner; it allows one to make welfare comparisons between various policy regimes; and it enables one to calculate the effect of a policy change or change in the attributes of various modes on the demand for each mode and auto ownership.

Discrete choice theory, information theory and the multinomial logit and gravity models

The strong “similarity” between “information minimizing” and “utility maximizing” models of spatial interaction has been known for some time (see Anas 1975, Williams, 1977), but the extent of this “similarity” has been underestimated. This paper proves that the two approaches are identical in that the multinomial logit model can be derived and identically estimated by either method. It is also proved that the doubly-constrained gravity model derived by Wilson (1967) is identical to a multinomial logit model of joint origin-destination choice, consistent with stochastic utility maximization. It follows that behaviorally valid “gravity models” can be estimated from disaggregated data on individual choices. In closure, “behavioral demand modeling”, which follows McFadden (1973), and “entropy-maximizing modeling”, which follows Wilson (1967), should be seen as two equivalent views of the same problem. The behavioral content of models estimated by either approach is entirely determined by the model specification and data aggregation beliefs of the analysts, and not by any inherent structural property of the models themselves.

The Impact of Transit Investment on Housing Values: A Simulation Experiment

This paper uses a joint-choice logit model of travel demand and residential location to simulate the impact of urban rapid-transit investment on housing values within a radial corridor. The model developed is a clean break with the traditional urban economic theory. Instead the heterogeneous nature of travel and location decisions is recognized and the logit model, consistent with stochastic utility maximization, is employed. Simulation experiments reveal that the aggregate increase in property values caused by transit's impact on work trips is highly sensitive to the aggregate number of vacancies within the corridor. Under reasonable assumptions, transit investment tends to lower central-city property values, to increase central-city vacancies, and to raise suburban property values. It tends to help the poor move further away from the center and penetrate the inner suburbs. Depending on several influences, aggregate property values can increase or decrease and the change can often be statistically insignificant. Calculations show that an equitable taxation (and compensation) of property-value changes may raise a small to modest proportion of a transit system's construction cost. Several considerations suggest that even these modest estimates might be optimistic. These results help develop an improved perspective on ‘value-capture policy’ which has not, up to now, benefited from quantitative analysis. Major extensions of the model are briefly considered.