Stochastic Utility Research Articles

Regret Analysis of Repeated Delegated Choice

We present a study on a repeated delegated choice problem, which is the first to consider an online learning variant of Kleinberg and Kleinberg, EC'18. In this model, a principal interacts repeatedly with an agent who possesses an exogenous set of solutions to search for efficient ones. Each solution can yield varying utility for both the principal and the agent, and the agent may propose a solution to maximize its own utility in a selfish manner. To mitigate this behavior, the principal announces an eligible set which screens out a certain set of solutions. The principal, however, does not have any information on the distribution of solutions nor the number of solutions in advance. Therefore, the principal dynamically announces various eligible sets to efficiently learn the distribution. The principal's objective is to minimize cumulative regret compared to the optimal eligible set in hindsight. We explore two dimensions of the problem setup, whether the agent behaves myopically or strategizes across the rounds, and whether the solutions yield deterministic or stochastic utility. We obtain sublinear regret upper bounds in various regimes, and derive corresponding lower bounds which implies the tightness of the results. Overall, we bridge a well-known problem in economics to the evolving area of online learning, and present a comprehensive study in this problem.

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].

Optimization of day-ahead pricing electricity markets based on a simplified methodology for stochastic utility function estimation

In the context of smart markets’ popularization, day-ahead pricing of electricity has been deployed more commonly as an attempt to improve the grid’s operation and maximize the socioeconomic welfare. However, estimating the utility function is necessary to maximize the socioeconomic welfare, which is not a trivial task. The utility function models the quality of life added by electricity consumption and depends on several factors, such as the consumer’s class (residential, commercial, industrial, etc.), income, climate conditions, and individual preferences. This paper presents a simplified methodology to estimate the utility function in the context of day-ahead pricing. The main benefit of the proposed method is that its application is straightforward since the modeling is mainly based on simple matrix equations. The demand elasticities (self- and cross-elasticities), which are general concepts in economics, are addressed as input parameters. Due to the inherent uncertainties related to human behavior, a stochastic utility function is proposed to enhance the model’s accuracy/robustness. The proposed model particularly thrives when the effects of cross-elasticities are significant but not massive (although procedures can be applied to mitigate the error if higher cross-elasticities are verified). By applying the proposed model to a hypothetical smart microgrid with 100 consumers and 24 daily periods (hourly prices), results demonstrate that it successfully provides the rates that maximize the socioeconomic welfare created by the market. In the case study, the conventional quadratic utility function implies an error of 73%, whereas the proposed model an error of 10%, highlighting the usefulness of the proposed model.

Analyzing Rail Traffic Diversion Based on Machine Learning Technique considering Transportation Security

Based on a stated preference survey, we comprehensively analyze the travel psychology of residents and the advantages and disadvantages of rail transit and conventional buses, travel time, travel cost, travel security, and vehicle comfort and investigate the relationship between the relevant influencing factors and the transition probability from rail transit to buses. A stochastic utility theory is introduced to describe the transfer behavior pertaining to travel modes, and a binary Logit model for diversion transfer is constructed. The decision tree is also used to predict the diversion transfer. Then, based on the large amount of travel willingness data obtained through the stated preference survey, a maximum likelihood estimation method is used to calibrate the parameters of the binary Logit model. The performance of the binary Logit proves to be better than that of the decision tree. Results show that the travel time most notably affects the passenger flow transfer, followed by the vehicle comfort. Finally, Guangzhou Rail Transit Line 3 is considered an example, and the diversion route planning and design are performed according to the constructed diversion transfer probability model to verify the effectiveness and practicability of the model. The research provides an effective theoretical basis and technical reference for other cities to perform rail traffic diversion planning. Based on these results, the following suggestions can be made: (1) the organization of public transportation routes, delivery volume, and travel speed outside should be improved; (2) undertaking combined operation of bus and rail transportation and integrated development is preferred; (3) the transportation management should focus on the comprehensive function development and hardware support of public transportation stations. The convenience and comfort of rail transit are closely related to the facilities and functions of the stations and their connections, which should be highly valued.

Tax Revenue Potential and Effort in Ethiopia: a Comparative Analysis of Stochastic Frontier Analysis vs Utility Maximisation Function as a New Measure of Tax Effort

This article tests the new measure of tax efforts following Dalamagas et al (2019) who argued that in the context of the Arrow-Debreu economy, with fixed labour supply and no savings, disposable income is equal to private consumption, a utility function with two arguments, income, and government spending, is maximised concerning direct and indirect tax rates. The optimal level of tax revenue is derived from a utility maximisation process and is shown to be equal to the difference between income and consumption. As a robustness check, the results of the utility maximisation function were compared to the findings of the stochastic frontier model. Each model records very near results for tax effort, tax potential, and tax gaps. The empirical findings revealed that Ethiopia has a large tax gap and poor tax effort, which is primarily due to policy choices and enforcement procedures.

Optimization of Day-Ahead Pricing Electricity Markets Based on a Simplified Methodology for Stochastic Utility Function Estimation

Optimization of Day-Ahead Pricing Electricity Markets Based on a Simplified Methodology for Stochastic Utility Function Estimation

Dual‐Channel Dynamic Pricing in the Presence of Low‐Carbon Preference

This paper investigates the dynamic pricing strategy for perishable products sold through online and offline channels with the consideration of consumers’ low‐carbon preferences. The MNL stochastic utility model is used to describe the purchasing decisions of consumers with different low‐carbon preferences. On this basis, we establish a dual‐channel dynamic pricing model for perishable products to maximize the firm’s expected revenue by using the dynamic programming method. We also study the influence of consumers’ low‐carbon preferences on optimal prices. The conclusions show that the low‐carbon utility and the proportion of consumers with high low‐carbon preference have positive effects on the optimal prices of the dual sales channels. Moreover, consumers are more inclined to purchase products through the online channel in the presence of low‐carbon preference, so the optimal price of the online channel product is higher than that of the offline channel product.

Trial and Error Learning for Dynamic Distributed Channel Allocation in Random Medium

This paper considers the problem of fully distributed channel allocation in clustered wireless networks when the propagation medium is random. We extend here the existing Trial and Error (TE) framework developed in the deterministic case and for which strong convergence properties hold. We prove that using directly this solution in the random context leads to unsatisfactory solutions. Then we propose an adaptation of the original Trial and Error Learning (TEL) algorithm, called Robust TEL (RTEL), assuming that the random channel effects translate into a bounded stochastic disturbance of the utility function. The solution consists in introducing thresholds in the transitions of the TEL’s Finite State Controller (FSC). We prove that this new solution restores the good convergence property inherited from the TEL. Furthermore, we provide analysis of the stochastic utilities in the Rayleigh fading case in order to check the bounded assumption. Finally, we develop an online algorithm that dynamically estimates the optimal threshold values to adapt to the instantaneous disturbance. Numerical results corroborate our theoretical claims.

Stability Analysis Model of Eco Economic System based on Discrete Selection

The internal structure of eco-economic system is relatively complex, and its stability is easily affected by external environmental factors such as region, which results in poor accuracy of die results of its analysis. Based on this, the stability analysis model of eco-economic system based on discrete selection is proposed. In order to improve the accuracy of eco-economic system analysis, the characteristics of discrete selection model are analyzed. Based on the principles of scientificity, practicability, regionality, operability and dynamic, and the comprehensive development of four sub-systems of economy, land, environment and society, the indexes of economy, land, environment and society are selected to build the stability evaluation of eco-economic system Price index system: through adjusting the structure of resource utilization, the indexes are selected hierarchically to truly reflect the structure of resource utilization. The weight of each index is obtained by AHP, and the component of each index in the evaluation system is reasonably divided. According to the theory of stochastic utility, the elements of discrete selection model are analyzed, and then the discrete selection model is constructed. By studying the close degree of each evaluation object and ideal solution, the stability analysis of ecological economic system is realized. The experimental results show that the influence of the proposed model on net income per unit is relatively stable at the positive and negative balance points, which is consistent with the actual situation., and the shortest analysis time is 1.2 min, which is feasible.

Multi-party stochastic energy scheduling for industrial integrated energy systems considering thermal delay and thermoelectric coupling

Multi-dimensional stochastic factors challenge the interactive energy scheduling of the industrial integrated energy system (IIES). Previous research focuses on either deterministic energy scheduling or individual stochastic scheduling while neglecting complicated interactions among uncertain parties, which brings the research gaps about stochastic multi-party’s interaction. In this regard, a multi-party stochastic energy scheduling approach in IIES is proposed based on the stochastic game. A decentralized decision support system is considered, and a stochastic utility model is designed for decentralized IUs with multi-dimensional stochastic factors from photovoltaic (PV) production and IIES parameters, enabling them to participate in the multi-energy scheduling with their own strategies. A stochastic game model is developed considering the thermoelectric coupling and the IUs’ interaction. The co-decision mechanism, recognizing different transfer times of electrical and thermal energy, is built based on the state transition within the game. Moreover, a distributed solution algorithm that includes the Markov decision process and iterative method is designed to address the problem of the “curse of dimensionality” arising from multiple stochastic factors. Finally, case studies with realistic data from an industrial park in Guangdong Province, China, are designed to show the effectiveness of the proposed approach, which enhances IUs’ profits by 9.4% and fits flexible load strategies and price strategies. The decentralized system can also reduce the computation time by 70.1% compared to the centralized system. Through analyzing different number of scenarios and intervals for PV generation, electrical and thermal load, the conclusion has obtained that increase the number of scenarios has a negative effect on IUs’ decision, but increase the number of load intervals contributes to more specific results and higher utility.

General framework of opening and closing shops over a spatial network based on stochastic utility under competitive and time-bounded environment

General framework of opening and closing shops over a spatial network based on stochastic utility under competitive and time-bounded environment

Research on Airport Taxi Problem Based on Cell Transmission Simulation Model

In order to solve the decision-making problem of taxi drivers at the airport, it constructed a non-aggregate stochastic utility model, a cell transmission simulation model, and a queuing model. Besides, it used software programming and drawing software such as MATLAB, SPSS, EXCEL, and rapid flow chart comprehensively. Finally, this paper solves the taxi problem at the airport and gives relevant suggestions.

MIXTURE OF CONSISTENT STOCHASTIC UTILITIES AND A PRIORI RANDOMNESS

The purpose of this paper is to develop an explicit construction of consistent utilities, using the stochastic flows approach developed in El Karoui & Mrad (2013, 2020). Starting from a family of utility functions indexed by some parameter [Formula: see text] (for example, the risk aversion coefficient or any other parameter), the idea is to randomize [Formula: see text] and to construct nonstandard stochastic utility processes. Two approaches are developed. The first one consists of building directly from the class [Formula: see text] a global utility [Formula: see text] as a sup-convolution. The second approach which is very different, consists to define from the class [Formula: see text] of monotonic optimal processes, associated with the class [Formula: see text], a global pair [Formula: see text] as a mixture. The nonstandard stochastic utility is then obtained by composing stochastic flows and is interpreted as the aggregate utility of all considered agents.

Concavity, stochastic utility, and risk aversion

This paper studies the relation between concavity, stochastic or state-dependent utility functions, and risk aversion. Using the common definition of risk aversion, but modified for state-dependent preferences, we show that concavity does not imply risk aversion. Instead, it implies a weaker version of risk aversion, defined herein, and called risk aversion for independent gambles. Furthermore, to characterise the economic meaning of concavity, we define two new risk aversion notions, called uniform risk aversion and uniform risk aversion for independent gambles, respectively. We show that concavity is equivalent to uniform risk aversion for independent gambles, and that concavity plus some additional conditions are equivalent to uniform risk aversion.

Recover Dynamic Utility from Observable Process: Application to the Economic Equilibrium

Decision making under uncertainty is often viewed as an optimization problem under choice criterium, but its calibration raises the inverse problem to recover the criterium from the data. An example is the theory of preference by Samuelson in the 40s, \cite{samuelson1938}. The observable is a so-called increasing characteristic process $\mbX=(\scX_t(x))$ and the objective is to recover a dynamic stochastic utility $\bfU$ in the sense where $U(t,\scX_t(x))$ is a martingale. A linearized version is provided by the first order conditions $U_x(t,\scX_t(x))=Y_t(u_z(x)$, and the additional martingale conditions of the processes $\scX_x(t,x)Y_t(u_z(x))$ and $\scX_t(x)Y_t(u_z(x))$. When $\mbX$ and $\bfY$ are regular solutions of two SDEs with random coefficients, under strongly martingale condition, any revealed utility is solution of a non linear SPDE, and is the stochastic value function of some optimization problem. More interesting is the dynamic equilibrium problem as in He and Leland \cite{HL}, where $Y$ is coupled with $\scX$ so that the monotonicity of $Y_t(z,u_z(z)) $ is lost. Nevertheless, we solve the He \& Leland problem (in random environment), by characterizing all the equilibria: the adjoint process still linear in $y$ (GBM in Markovian case) and the conjugate utilities are a deterministic mixture of stochastic dual power utilities. Besides, the primal utility is the value function of an optimal wealth allocation in the Pareto problem.

Concavity, Stochastic Utility, and Risk Aversion

This paper studies the relation between concavity, stochastic or state dependent utility functions, and risk aversion. Using the common definition of risk aversion, but modified for state dependent preferences, we show that concavity does not imply risk aversion. Instead, it implies a weaker version of risk aversion, defined herein, and called risk aversion for independent gambles. Furthermore, to characterize the economic meaning of concavity, we define two new risk aversion notions, called uniform risk aversion and uniform risk aversion for independent gambles, respectively. We show that concavity is equivalent to uniform risk aversion for independent gambles, and that concavity plus some additional conditions are equivalent to uniform risk aversion.

Error by omitted variables in regret-based choice models: formal and empirical comparison with utility-based models using orthogonal design data

Random regret minimization models have mostly relied on the assumption of identically and independently distributed error terms. Professionally designed stated choice experiments use various design and implementation principles to ensure that any errors meet this assumption. Based on the behavioral theory that individuals arrive at a decision by first processing the attribute values of a choice alternative according to an integration rule to derive the stochastic utility associated with the choice alternatives and then apply the deterministic utility maximizing rule, this assumption can be reasonable met for utility maximizing models. The question is whether this assumption is equally defendable for random regret minimization models in light of the difference in model specification, rooted in fundamental behavioral differences between the underlying decision theories. This study focuses on the effect of omitted variables which is one of main sources of error. Based on a formal analysis and empirical comparison, we argue and show that omitted variables cause correlation between unobserved regrets. Consequently, the independence assumption is difficult to defend because the omitted variables simultaneously affect the comparison of choice alternatives. To capture this effect, we propose an error components structure for regret-based choice models. Empirical results obtained for classic random regret-minimization models for two different data sets support our theoretical arguments. If these results can be generalized to other data sets, it is advisable to adopt an error components structure when estimating these classic random regret-minimization models unless one has reason to believe the effect of the omitted variables is small and therefore can be ignored.

Stochastic utilities with subsistence and satiation: Optimal life insurance purchase, consumption and investment

We introduce stochastic utilities such that utility of any fixed amount of interest is a stochastic process or random variable. Also, there exist stochastic (or random) subsistence and satiation levels associated with stochastic utilities. Then, we consider optimal consumption, life insurance purchase and investment strategies to maximize the expected utility of consumption, bequest and pension with respect to stochastic utilities. We use the martingale approach to solve the optimization problem in two steps. First, we solve the optimization problem with an equality constraint which requires that the present value of consumption, bequest and pension is equal to the present value of initial wealth and income stream. Second, if the optimization problem is feasible, we obtain the explicit representations of the replicating life insurance purchase and portfolio strategies. As an application of our general results, we consider a family of stochastic utilities which have hyperbolic absolute risk aversion (HARA).

A simple model explaining the interaction between special interest spending and voter choices

Abstract. This research develops a model of eligible voters rationally maximizing their stochastic utility functions in their decisions with respect to casting ballots in elections that result in voting decision being largely determined by social and psychological factors heterogeneously maleable by political expenditures. The wealthiest agents utilize their overwhelming financial resources to promote only candidates cooperating with their special interests to attract public attention, which exerts social pressure on voters to cast ballots only for those politicians who represent those agents. The model, which enables exacting computation of the benefits to politicians, special interest groups, and voters from their political actions, is shown to supply insightful explanations for the 2016 U.S. Presidential polling results for the four leading candidates. Voters were effectively swayed by large political expenditures to select from the two candidates who represented the agents providing the financial backing to market their special interests. Keywords. Special interests, Voter utility, Elections, Political marketing. JEL. D71, D72, F50.