A bilevel fuzzy principal-agent model for optimal nonlinear taxation problems

This paper presents a bilevel fuzzy principal-agent model for optimal nonlinear taxation problems with asymmetric information, in which the government and the monopolist are the principals, the consumer is their agent. Since the assessment of the government and the monopolist about the consumer’s taste is subjective, therefore, it is reasonable to characterize this assessment as a fuzzy variable. What’s more, a bilevel fuzzy optimal nonlinear taxation model is developed with the purpose of maximizing the expected social welfare and the monopolist’s expected welfare under the incentive feasible mechanism. The equivalent model for the bilevel fuzzy optimal nonlinear taxation model is presented and Pontryagin maximum principle is adopted to obtain the necessary conditions of the solutions for the fuzzy optimal nonlinear taxation problems. Finally, one numerical example is given to illustrate the effectiveness of the proposed model, the results demonstrate that the consumer’s purchased quantity not only relates with the consumer’s taste, but also depends on the structure of the social welfare.     

Optimal incentive contracts under relative income concerns

We are studying in this article an interplay between workers in organizations under the assumption that workers exhibit behavioral biases: envy, jealousy, or admiration toward the other coworkers’ compensation. We assume workers care about their relative position, and we study the impact of this assumption on their efforts and on their optimal incentive contracts. We explicitly solve for the optimal incentive contract of moral hazard a la Holmstrom and Milgrom (Econometrica 55:303–328, 1987). We model team production by agents in which each agent’s effort generates an observable signal and depends on efforts of other agents. One of the important findings is that an agent’s optimal effort is negatively impacted by the behavioral biases in other agents’ judgments. We also show envious behavior is destructive for organizations. Consistent with Tirole (Econometrica 69(1):1–35, 2001), our findings suggest that in the presence of agency problems induced by envy or jealousy, the optimal compensation exhibits high pay-for-performance sensitivity.     

Analysis of various optimal contracts in the problem of stimulation of agents by a principal in a model with two agents

This work is devoted to one section of a game theory popular in recent years, the theory of contracts and the problem of an agent and a principal. A principal tries to stimulate agents into making a number of contracts with clients using his resources in order to maximize his profits as a result. At the same time, the principal has limited information about the agents. He knows only the results he has obtained; he does not know their type or the efforts made. The strategy of the principal is an incentive scheme that shows the agent’s reward depending on his results. In turn, the agents try to maximize their benefits while having the right to turn down a contract. We do not consider models with random events, and we restrict ourselves to the deterministic case. The model thus does not fall under the heading of a moral hazard but is related to a situation of unfavorable selection.     

Optimal compensation with adverse selection and dynamic actions

We consider continuous-time models in which the agent is paid at the end of the time horizon by the principal, who does not know the agent’s type. The agent dynamically affects either the drift of the underlying output process, or its volatility. The principal’s problem reduces to a calculus of variation problem for the agent’s level of utility. The optimal ratio of marginal utilities is random, via dependence on the underlying output process. When the agent affects the drift only, in the risk- neutral case lower volatility corresponds to the more incentive optimal contract for the smaller range of agents who get rent above the reservation utility. If only the volatility is affected, the optimal contract is necessarily non-incentive, unlike in the first-best case. We also suggest a procedure for finding simple and reasonable contracts, which, however, are not necessarily optimal. Research supported in part by NSF grants DMS 04-03575 and 06-31298. We would like to express our gratitude to participants of the following seminars and conferences for useful comments and suggestions: UCLA (Econ Theory), Caltech (Econ Theory), Columbia (Probability), Princeton (Fin. Engineering), U. Texas at Austin (Math Finance), Banff Workshop on Optim. Problems in Fin. Econ, Kyoto U. (Economics), UC Irvine (Probability), Cornell (Fin. Engineering), Bachelier Seminar. Moreover, we are very grateful to the anonymous referee for helpful suggestions. The remaining errors are the authors’ sole responsibility.     

The deliberative relevance of refraining from deciding: A response to McKenna and Pereboom

Readers familiar with Harry Frankfurt’s argument that we do not need leeway-liberty (or the power to bring about alternative possible actions or intentions) to be morally responsible will probably also know that the most famous and popular response on behalf of leeway-libertarianism remains a dilemma posed in similar forms by David Widerker, Robert Kane, and Carl Ginet: either the agent retains significant residual leeway in Frankfurt-style cases, or these cases beg the question by presupposing causal determinism. In the last few years, there have been several different attempts to defend Frankfurtian critiques of PAP in response this dilemma. In a novel approach, Derk Pereboom and Michael McKenna present cases in which all deliberatively relevant or “robust” alternatives are blocked, but the agent’s act or decision is not determined. Pereboom and McKenna argue that any plausible leeway-condition on responsibility must characterize the required alternatives as robust in two ways: being voluntary performances and having a practical relevance accessible to the agent’s mind. I agree with the requirement of robustness, and argue that we can build this notion into a complex concept of agent-possibility, or “agentive-can.” However, I argue that both McKenna’s and Pereboom’s conceptions of robustness are too demanding: they exclude alternatives that are intuitively relevant. Moreover, I argue that the alternative of refraining from deciding, or voluntarily failing to decide, is robust in the right sense. In agreement with a tradition running from Ockham back through Scotus to Aquinas, I argue that this robust alternative is necessary for responsibility. If the Frankfurt-controller eliminates it, then the agent’s responsibility is undermined. In particular, I argue that Pereboom’s tax evasion cases do not refute this leeway-condition on moral responsibility.     

Optimization and mechanism design

Mechanism design is about optimizing the allocation of resources when the parameters needed to determine an optimal allocation are privately held by the agents who will consume the resources. An agent’s report of her information will influence the resulting allocation which in turn will affect her utility. In such a situation, how can one simultaneously elicit the information that is privately held and choose the optimal allocation? This paper illustrates how standard results in linear programming play a role in the analysis of mechanism design problems. It is not a comprehensive survey. Rather, it focuses on two variations of a particular problem: the allocation of a single object.     

Avoidance Control on Time Scales

We consider dynamic systems on time scales under the control of two agents. One of the agents desires to keep the state of the system out of a given set regardless of the other agent’s actions. Leitmann’s avoidance conditions are proved to be valid for dynamic systems evolving on an arbitrary time scale.     

基于委托—代理下的模糊报童问题

在委托-代理关系中.代理人的私人信息对委托人的决策会产生重要影响.因此,为了获取代理人的真实信息.设计一个有效的激励机制是委托人的核心问题.本文基于需求依赖于代理人的努力水平和模糊市场条件的假设,利用委托一代理相关理论,探讨了模糊报童问题的激励机制问题.首先讨论了委托人最优产量的确定问题.然后分别给出了可观测和不可观测两种努力水平下的最优激励机制,最后分析了模糊市场条件对委托一代理双方利益的影响.     

On optimizing a linear objective function subjected to fuzzy relation inequalities

In this paper, we extend Guo and Xia’s necessary condition which has been presented by Guo and Xia (Fuzzy optimizat Decis Mak 5: 33–47, 2006) in order to study the finitely many constraints of fuzzy relation inequalities and optimize a linear objective function on this region which is defined by the fuzzy max–min operator. The new condition provides a means for removing the unnecessary paths resulting from Guo and Xia’s paths. Also, an algorithm and two numerical examples are offered to abbreviate and illustrate the steps of the resolution process of the problem.     

Recursiveness of indifference prices and translation-invariant preferences

We consider an economic agent with dynamic preferences over a set of uncertain monetary payoffs. We assume that preferences are updated in a time-consistent way as more information is becoming available. Our main result is that the agent’s indifference prices are recursive if and only if the preferences are translation-invariant. The proof is based on a characterization of time-consistency of dynamic preferences in terms of indifference sets. As a special case, we obtain that expected utility leads to recursive indifference prices if and only if absolute risk aversion is constant, that is, the Bernoulli utility function is linear or exponential.     

Risk minimization and optimal derivative design in a principal agent game

We consider the problem of Adverse Selection and optimal derivative design within a Principal–Agent framework. The principal’s income is exposed to non-hedgeable risk factors arising, for instance, from weather or climate phenomena. She evaluates her risk using a coherent and law invariant risk measure and tries minimize her exposure by selling derivative securities on her income to individual agents. The agents have mean–variance preferences with heterogeneous risk aversion coefficients. An agent’s degree of risk aversion is private information and hidden from the principal who only knows the overall distribution. We show that the principal’s risk minimization problem has a solution and illustrate the effects of risk transfer on her income by means of two specific examples. Our model extends earlier work of Barrieu and El Karoui (in Financ Stochast 9, 269–298, 2005) and Carlier et al. (in Math Financ Econ 1, 57–80, 2007). We thank Guillaume Carlier, Pierre-Andre Chiappori, Ivar Ekeland, Andreas Putz and seminar participants at various institutions for valuable comments and suggestions. Financial support through an NSERC individual discovery grant is gratefully acknowledged.     

Extension of the LINMAP for multiattribute decision making under Atanassov’s intuitionistic fuzzy environment

The aim of this article is further extending the linear programming techniques for multidimensional analysis of preference (LINMAP) to develop a new methodology for solving multiattribute decision making (MADM) problems under Atanassov’s intuitionistic fuzzy (IF) environments. The LINMAP only can deal with MADM problems in crisp environments. However, fuzziness is inherent in decision data and decision making processes. In this methodology, Atanassov’s IF sets are used to describe fuzziness in decision information and decision making processes by means of an Atanassov’s IF decision matrix. A Euclidean distance is proposed to measure the difference between Atanassov’s IF sets. Consistency and inconsistency indices are defined on the basis of preferences between alternatives given by the decision maker. Each alternative is assessed on the basis of its distance to an Atanassov’s IF positive ideal solution (IFPIS) which is unknown a prior. The Atanassov’s IFPIS and the weights of attributes are then estimated using a new linear programming model based upon the consistency and inconsistency indices defined. Finally, the distance of each alternative to the Atanassov’s IFPIS can be calculated to determine the ranking order of all alternatives. A numerical example is examined to demonstrate the implementation process of this methodology. Also it has been proved that the methodology proposed in this article can deal with MADM problems under not only Atanassov’s IF environments but also both fuzzy and crisp environments.     

Moral coherence,moral worth and explanations of moral motivation

Moral internalism and moral externalism compete over the best explanation of the link between judgment and relevant motivation but, it is argued, they differ at best only verbally. The internalist rational-conceptual nature of the link’ as accounted by M. Smith in The Moral Problem is contrasted to the externalist, also rational, link that requires in addition support from the agent’s psychological-dispositional profile; the internalist link, however, is found to depend crucially on a, similarly to the externalist, psychologically ‘loaded’ profile. It is also argued that the differentiation of the two competing explanations is insufficient partly because they both fail to consider crucial quantitative parameters of the judgment-motivation link. Such parameters become very important particularly in the light of Smith’s claim that this link is grounded on the observable “striking fact” where changes in the set of one’s moral beliefs systematically bring about changes in one’s moral behavior. Examples of algorithms measuring moral coherence and moral worth are provided to serve as evidence for what it comes down to, vis-à-vis the alleged fact, only a verbal dispute between the two camps. Finally, the ‘misfiring’ of these explanations is understood in connection to the irreducibility of concepts such as ‘moral worth’, and/or, ‘moral sensitivity’.     

Multi-fuzzy sets: An extension of fuzzy sets

In this paper we propose a method to construct more general fuzzy sets using ordinary fuzzy sets as building blocks. We introduce the concept of multi-fuzzy sets in terms of ordered sequences of membership functions. The family of operations T, S, M of multi-fuzzy sets are introduced by coordinate wise t-norms, s-norms and aggregation operations. We define the notion of coordinate wise conjugation of multifuzzy sets, a method for obtaining Atanassov’s intuitionistic fuzzy operations from multi-fuzzy sets. We show that various binary operations in Atanassov’s intuitionistic fuzzy sets are equivalent to some operations in multi-fuzzy sets like M operations, 2-conjugates of the T and S operations. It is concluded that multi-fuzzy set theory is an extension of Zadeh’s fuzzy set theory, Atanassov’s intuitionsitic fuzzy set theory and L-fuzzy set theory.     

Trust and relational capital

Trust can be viewed at the same time as an instrument both for an agent selecting the right partners in order to achieve its own goals, and for an agent of being selected from other potential partners in order to establish with them a cooperation/collaboration and to take advantage from the accumulated trust. In this paper we will analyze trust as the agents’ relational capital. Starting from the classical dependence network with potential partners, we introduce the analysis of what it means for an agent to be trusted and how this condition could be strategically used from it for achieving its own goals, that is, why it represents a form of power. The idea of taking another agent’s point of view is especially important if we consider the amount of studies in social science that connect trust with social capital related issues. Although there is a big interest in literature about ‘social capital’ and its powerful effects on the wellbeing of both societies and individuals, often it is not clear enough what is it the object under analysis. Individual trust capital (relational capital) and collective trust capital not only should be disentangled, but their relations are quite complicated and even conflicting. To overcome this gap, we propose a study that first attempts to understand what trust is as capital of individuals. In which sense “trust” is a capital. How this capital is built, managed and saved. In particular, how this capital is the result of the others’ beliefs and goals. Then we aim to analytically study the cognitive dynamics of this object.     

Trust and relational capital

Trust can be viewed at the same time as an instrument both for an agent selecting the right partners in order to achieve its own goals, and for an agent of being selected from other potential partners in order to establish with them a cooperation/collaboration and to take advantage from the accumulated trust. In this paper we will analyze trust as the agents’ relational capital. Starting from the classical dependence network with potential partners, we introduce the analysis of what it means for an agent to be trusted and how this condition could be strategically used from it for achieving its own goals, that is, why it represents a form of power. The idea of taking another agent’s point of view is especially important if we consider the amount of studies in social science that connect trust with social capital related issues. Although there is a big interest in literature about ‘social capital’ and its powerful effects on the wellbeing of both societies and individuals, often it is not clear enough what is it the object under analysis. Individual trust capital (relational capital) and collective trust capital not only should be disentangled, but their relations are quite complicated and even conflicting. To overcome this gap, we propose a study that first attempts to understand what trust is as capital of individuals. In which sense “trust” is a capital. How this capital is built, managed and saved. In particular, how this capital is the result of the others’ beliefs and goals. Then we aim to analytically study the cognitive dynamics of this object.     

A note on the dynamics of incentive contracts

Laffont and Tirole (Econometrica 56:1153–1175) show that when uncertainty about an agent’s ability is small, the equilibrium must involve a large amount of pooling, but, whether the continuation equilibrium induced by an optimal first-period menu of contracts is partitional or not, remains unclear. They construct a non-partitional continuation equilibrium for a given first-period menu of contracts and conjecture that this continuation equilibrium need not be suboptimal for the whole game under small uncertainty. We show that, irrespective of the amount of uncertainty, this non-partitional continuation equilibrium generates a strictly smaller payoff for the principal than a different menu of contracts with a partitional continuation equilibrium. In this sense, Laffont and Tirole’s menu of contracts, giving rise to a non-partitional continuation equilibrium, is not optimal.     

Optimal derivatives design for mean–variance agents under adverse selection

We consider a problem of derivatives design under asymmetry of information: the principal sells a contingent claim to an agent, the type of whom he does not know. More precisely, the principal designs a contingent claim and prices it for each possible agent type, in such a way that each agent picks the contingent claim and pays the price that the principal designed for him. We assume that the preferences of the agent depend linearly on the parameters which determine the agent’s type; this model is rich enough to accommodate quadratic utilities. The problem then is reformulated as an optimization problem, where the optimization is performed within a class of convex functions. We prove an existence result for the provide explicit examples in the case when the agent is fully characterized by a single parameter