Agent's Utility Function Research Articles

Predestination and the Protestant Ethic

This paper shows an equivalence result between the utility functions of secular agents who abide by a moral obligation to accumulate wealth and those of religious agents who believe that salvation is immutable and preordained by God. This result formalizes Weber’s renowned thesis on the connection between the worldly asceticism of Protestants and the religious premises of Calvinism. Furthermore, ongoing economies are often modeled with preference relations such as \Keeping up with the Joneses which are not associated with religion. Our results relate these secular economies of today and economies of the past shaped by religious ideas.

Mechanism design for one-facility location game with obnoxious effects on a line

In this paper, we introduce obnoxious effects into obnoxious facility location games on a line, where each agent i has a private location xi on a closed interval [0,1] and one facility will be built on a location y in the interval according to the bids of all the agents. In addition, there are two thresholds d1 and d2 in the utility function of each agent, where 0≤d1≤d2≤1. Denote d(y,xi)=|y−xi| to be the distance between agent i and the facility on the location y. The utility function of agent i is 0 if d(y,xi) is at most d1; 1 if d(y,xi) is at least d2; otherwise a linear increasing function between 0 and 1. Each agent attempts to get the largest utility while the social welfare is to maximize the sum of all the agents' utilities.The classic obnoxious facility game [4,11] is a special case of our problem when d1=0 and d2=1. In this work, we first study the hardness of approximate mechanism design on this generalized problem, which states that our problem cannot admit any deterministic strategy-proof mechanism with bounded approximation ratio if d1≥12. Then we limit the thresholds to some ranges, both deterministic and randomized strategy-proof mechanisms are studied, and the approximation ratios vary with the specific values of d1 and d2.

Consumption-Portfolio Choice with Preferences for Cash

This paper studies a consumption-portfolio problem where money enters the agent's utility function. We solve the corresponding Hamilton-Jacobi-Bellman equation and provide closed-form solutions for the optimal consumption and portfolio strategy both in an infinite- and finite-horizon setting. For the infinite-horizon problem, the optimal stock demand is one particular root of a polynomial. In the finite-horizon case, the optimal stock demand is given by the inverse of the solution to an ordinary differential equation that can be solved explicitly. We also prove verification results showing that the solution to the Bellman equation is indeed the value function of the problem. From an economic point of view, we find that in the finite-horizon case the optimal stock demand is typically decreasing in age, which is in line with rules of thumb given by financial advisers and also with recent empirical evidence. Our results are robust to introducing recursive utility.

Bayesian Learning Without Recall

We analyze a model of learning and belief formation in networks in which agents follow Bayes rule yet they do not recall their history of past observations and cannot reason about how other agents' beliefs are formed. They do so by making rational inferences about their observations which include a sequence of independent and identically distributed private signals as well as the actions of their neighboring agents at each time. Successive applications of Bayes rule to the entire history of past observations lead to forebodingly complex inferences: due to lack of knowledge about the global network structure, and unavailability of private observations, as well as third party interactions preceding every decision. Such difficulties make Bayesian updating of beliefs an implausible mechanism for social learning. To address these complexities, we consider a Bayesian without Recall model of inference. On the one hand, this model provides a tractable framework for analyzing the behavior of rational agents in social networks. On the other hand, this model also provides a behavioral foundation for the variety of non-Bayesian update rules in the literature. We present the implications of various choices for the structure of the action space and utility functions for such agents and investigate the properties of learning, convergence, and consensus in special cases.

A game theoretical approach for distributed resource allocation with uncertainty

PurposeThe paper aims to build the connections between game theory and the resource allocation problem with general uncertainty. It proposes modeling the distributed resource allocation problem by Bayesian game. During this paper, three basic kinds of uncertainties are discussed. Therefore, the purpose of this paper is to build the connections between game theory and the resource allocation problem with general uncertainty.Design/methodology/approachIn this paper, the Bayesian game is proposed for modeling the resource allocation problem with uncertainty. The basic game theoretical model contains three parts: agents, utility function, and decision-making process. Therefore, the probabilistic weighted Shapley value (WSV) is applied to design the utility function of the agents. For achieving the Bayesian Nash equilibrium point, the rational learning method is introduced for optimizing the decision-making process of the agents.FindingsThe paper provides empirical insights about how the game theoretical model deals with the resource allocation problem uncertainty. A probabilistic WSV function was proposed to design the utility function of agents. Moreover, the rational learning was used to optimize the decision-making process of agents for achieving Bayesian Nash equilibrium point. By comparing with the models with full information, the simulation results illustrated the effectiveness of the Bayesian game theoretical methods for the resource allocation problem under uncertainty.Originality/valueThis paper designs a Bayesian theoretical model for the resource allocation problem under uncertainty. The relationships between the Bayesian game and the resource allocation problem are discussed.

Information Avoidance

We commonly think of information as a means to an end. However, a growing theoretical and experimental literature suggests that information may directly enter the agent's utility function. This can create an incentive to avoid information, even when it is useful, free, and independent of strategic considerations. We review research documenting the occurrence of information avoidance, as well as theoretical and empirical research on reasons why people avoid information, drawing from economics, psychology, and other disciplines. The review concludes with a discussion of some of the diverse (and often costly) individual and societal consequences of information avoidance. (JEL D82, D83)

Research Policies Rewarding Quantity: Estonia and Ukraine

This article is resting on the theoretical model of Braun (2003) describing the delegation modes for public funding of research in the principal-agent framework. It aims to show by using the conceptualisation of utility functions of principal and agents on the various levels, how different motivations for producing different kinds of research outputs emerge for researchers and universities or public research organisations in Estonia and Ukraine. The article attempts to offer one explanation to why in some quantitative research output indicators both countries perform very well compared to much lower levels of innovation system indicators otherwise. Estonia is rewarding publications and Ukraine is rewarding utility model applications throughout different levels of the system.

Consumption-Portfolio Choice with Preferences for Cash

This paper studies a consumption-portfolio problem where money enters the agent's utility function. We solve the corresponding Hamilton-Jacobi-Bellman equation and provide closed-form solutions for the optimal consumption and portfolio strategy both in an infinite- and finite-horizon setting. For the infinite-horizon problem, the optimal stock demand is one particular root of a polynomial. In the finite-horizon case, the optimal stock demand is given by the inverse of the solution to an ordinary differential equation that can be solved explicitly. We also prove verification results showing that the solution to the Bellman equation is indeed the value function of the problem. From an economic point of view, we find that in the finite-horizon case the optimal stock demand is typically decreasing in age, which is in line with rules of thumb given by financial advisers and also with recent empirical evidence.

Willingness to Pay of the Expo-Power Utility Decision Maker to Limit Climate Change

This paper extends the work of Pindyck by taking into consideration a large class family of different utility functions of economic agents. As in Pindyck, instead of consideringa social utility function that is characterized by constant relative risk aversion (C.R.R.A), we use the expo-power utility function of Saha. In fact, depending on the choice of the expo-power utility function parameters, we cover a diverse range1of utility functions and besides covering the other utility functions that a C.R.R.A omits, Expo-power function permits usto discern if under the other behaviors of economic agents, the willingness to pay remainsmore affected by uncertain outcomes than certain outcomes, when we vary the expectationand standard deviation of the temperature distribution probability. Our paper has maintained the small-tailed gamma distributions of temperature and economic impact of Pindyck, notonly because they hinder infinite future welfare losses (for an exponential utility function), but because it is easy to change some moments of the distribution (jointly or holding the othersfixed) while studying how uncertainty influences the willingness to pay as explained in Pindyck.

Automated Multilateral Negotiation on Multiple Issues with Private Information

In this paper, we propose and analyze a distributed negotiation strategy for a multi-agent, multi-attribute negotiation in which the agents have no information about the utility functions of other agents. We analytically prove that, if the zone of agreement is nonempty and the agents concede up to their reservation utilities, agents generating offers using our offer-generation strategy, namely the sequential projection strategy, will converge to an agreement acceptable to all the agents; the convergence property does not depend on the specific concession strategy. In considering agents’ incentive to concede during the negotiation, we propose and analyze a reactive concession strategy. Through computational experiments, we demonstrate that our distributed negotiation strategy yields performance sufficiently close to the Nash bargaining solution and that our algorithms are robust to potential deviation strategies. Methodologically, our paper advances the state of the art of alternating projection algorithms, in that we establish the convergence for the case of multiple, moving sets (as opposed to two static sets in the current literature). Our paper introduces a new analytical foundation for a broad class of computational group decision and negotiation problems.

Automated Multilateral Negotiation on Multiple Issues with Private Information

In this paper, we propose and analyze a distributed negotiation strategy for a multi-agent multi-attribute negotiation in which the agents have no information about the utility functions of other agents. We analytically prove that, if the zone of agreement is non-empty and the agents concede up to their reservation utilities, agents generating offers using our offer-generation strategy, namely the sequential projection strategy, will converge to an agreement acceptable to all the agents; the convergence property does not depend on the specific concession strategy. In considering agents’ incentive to concede during the negotiation, we propose and analyze a reactive concession strategy. We demonstrate through computational experiments that our distributed negotiation strategy yields performance sufficiently close to the Nash bargaining solution, and that our algorithms are robust to potential deviation strategies. Methodologically, our paper advances the state of the art of alternating projection algorithms, in that we establish the convergence for the case of multiple, moving sets (as opposed to two, static sets in the current literature). Our paper introduces a new analytical foundation for a broad class of computational group decision and negotiation problems.

An optimal consumption, investment and voluntary retirement choice problem with disutility and subsistence consumption constraints: A dynamic programming approach

In this paper, we investigate an optimal consumption/portfolio problem of an agent with voluntary retirement and subsistence consumption constraints before retirement. We assume that the agent's utility function of consumption is of CRRA type and the agent suffers a utility loss from labor before retirement. We use the dynamic programming method to obtain explicit forms of the optimal consumption/portfolio and retirement time.

Self‐Insurance, Self‐Protection, and Saving: On Consumption Smoothing and Risk Management

This article studies the effect of risk preferences on self‐insurance and self‐protection in a two‐period expected utility framework. Here the investment to reduce risk precedes its effect. In contrast to single‐period models, self‐insurance and self‐protection react similarly when the agent's utility function becomes more concave. Effort is increased if and only if current consumption is sufficiently large. However, if we introduce endogenous saving, an agent with more concave utility always selects more self‐insurance, but will select more self‐protection if and only if the probability of loss is small enough. These latter results concur with those in standard monoperiodic models with no saving.

Analysis Method based on Rough Attack-defense Bayes Game Model

In order to solve the strategic interdependence question during the attack and defense process in a complex network, the dissertation proposes an analysis method based on rough attack-defense Bayes game model. After defining the inner structure of attacking agent and defense agent, the dissertation extends traditional object Petri Net and introduces rough set theory into node domain and transition domain, then propose the network attack-defense confrontation model. By dividing domain attack strategy set into equivalence classes, the extraction method of characteristic attack strategy set is given. Then the rough game model and utility function of attack and defense agents are defined, accordingly, the solution of Bayes equilibrium strategy and maximal attack and defense strategy set are proposed. The analysis method can reduce the scale of strategic space of the game model, and suitable for researching on complex network attack and defense action.

Recognizing Coverage Functions

A coverage function $f$ over a ground set $[m]$ is associated with a universe $U$ of weighted elements and $m$ sets $A_1,\ldots,A_m \subseteq U$, and for any $T\subseteq [m]$, $f(T)$ is defined as the total weight of the elements in the union $\cup_{j\in T} A_j$. Coverage functions are an important special case of submodular functions, and arise in many applications, for instance, as a class of utility functions of agents in combinatorial auctions. Naïve representations of coverage functions have size exponential in $m$, and in algorithmic applications, an access to a value oracle is assumed. In this paper, we ask whether one can recognize if a given oracle is that of a coverage function or not. We demonstrate an algorithm which makes $O(m|U|)$ queries to an oracle of a coverage function and completely reconstructs it. This is polynomial time whenever $|U|$ is polynomially bounded implying the function has a succinct description. To complement the above result, we show a negative result. We prove that “noncoverageness” needs large certificates---there exists a function which is not coverage and yet any algorithm making fewer than $2^{m-1}$ queries cannot distinguish this function from some coverage function. Our positive result shows that the property of coverageness has $O(m|U|)$-query proximity oblivious testers, while our negative result shows an exponential lower bound. We believe our lower bound also goes through for general property testers, and provide some evidence of the same.

A target-oriented approach: a "one-size" model to suit humans and econs behaviors

Thaler and Sunstein (2008) introduce two stereotypical decision makers: the Econs, imaginary people who always behave as strictly rational expected utility maximizers, and the Humans, real people subject to ordinary behavioral biases. This note sheds light on how the axiomatic target-oriented approach introduced by Castagnoli and Li Calzi (1996) may fit well the behavior of both of them. We show that although Econs and Humans use a different language, they maximize the same functional, e.g. the probability of meeting the goal. So declaring the probability distribution of the goal permits to elicit the agent utility function. A number of different distributions for goals are discussed and the family of the skew normal ones is proposed for its user-friendly flexibility. We show how moving the skewness parameter along its range every stereotypical decision maker’s profile may be modelled.

Multidimensional Spatial Voting with Non-separable Preferences

In most multidimensional spatial models, the systematic component of agent utility functions is specified as additive separable. We argue that this assumption is too restrictive, at least in the context of spatial voting in mass elections. Here, assuming separability would stipulate that voters do not care about how policy platforms combine positions on multiple policy dimensions. We present a statistical implementation of Davis, Hinich, and Ordeshook's (1970) Weighted Euclidean Distance model that allows for the estimation of the direction and magnitude of non-separability from vote choice data. We demonstrate in a Monte-Carlo experiment that conventional separable model specifications yield biased and/or unreliable estimates of the effect of policy distances on vote choice probabilities in the presence of non-separable preferences. In three empirical applications, we find voter preferences on economic and socio-cultural issues to be non-separable. If non-separability is unaccounted for, researchers run the risk of missing crucial parts of the story. The implications of our findings carry over to other fields of research: checking for non-separability is an essential part of robustness testing in empirical applications of multidimensional spatial models.

Risk aversion, prudence and mixed optimal saving models

The paper studies risk aversion and prudence of an agent in the face of a risk situation with two parameters, one described by a fuzzy number, the other described by a fuzzy variable. The first contribution of the paper is the characterization of risk aversion and prudence in mixed models by conditions on the concavity and the convexity of the agent's utility function and its partial derivatives. The second contribution is the building of mixed models of optimal saving and their connection with the concept of prudence and downside risk aversion.

STABILITY OF THE EXPONENTIAL UTILITY MAXIMIZATION PROBLEM WITH RESPECT TO PREFERENCES

This paper studies stability of the exponential utility maximization when there are small variations on agent's utility function. Two settings are considered. First, in a general semimartingale model where random endowments are present, a sequence of utilities defined on converges to the exponential utility. Under a uniform condition on their marginal utilities, convergence of value functions, optimal payoffs, and optimal investment strategies are obtained, their rate of convergence is also determined. Stability of utility‐based pricing is studied as an application. Second, a sequence of utilities defined on converges to the exponential utility after shifting and scaling. Their associated optimal strategies, after appropriate scaling, converge to the optimal strategy for the exponential hedging problem. This complements Theorem 3.2 in [Nutz, M. (2012): Risk aversion asymptotics for power utility maximization. Probab. Theory & Relat. Fields 152, 703–749], which establishes the convergence for a sequence of power utilities.

Environmental consciousness, economic growth, and macroeconomic instability

This paper develops an endogenous growth model to examine the linkages between environmental consciousness and economic growth. It is found that macroeconomic instability can arise in a simple AK-type growth model when the pollution externality is present only in the agent's utility function. It is also found that the impact of environmental consciousness on the economic growth rate is ambiguous. The economic systems (a decentralized versus centralized economy) and the ecological evolution (the specific pollution growth rate) are two crucial factors that determine the relationship between environmental consciousness and economic growth.