Tracking error decision rules and accumulated wealth

There is compelling evidence that typical decision‐makers, including individual investors and even professional money managers, care about the difference between their portfolio returns and a reference point, or benchmark return. In the context of financial markets, likely benchmarks against which investors compare their own returns include easy‐to‐focus‐on numbers such as one's own past payoffs, historical average payoffs, and the payoffs of competitors. Referring to the gap between one's current portfolio return and the benchmark return as ‘tracking error’, this paper develops a simple model to study the consequences and possible origins of investors who use expected tracking error to guide their portfolio decisions, referred to as ‘tracking error types’. In particular, this paper analyses the level of risk‐taking and accumulated wealth of tracking error types using standard mean‐variance investors as a comparison group. The behaviour of these two types are studied first in isolation, and then in an equilibrium model. Simple analytic results together with statistics summarizing simulated wealth accumulations point to the conclusion that tracking error—whether it is interpreted as reflecting inertia, habituation, or a propensity to make social comparisons in evaluating one's own performance—leads to greater risk‐taking and greater shares of accumulated wealth. This result holds even though the two types are calibrated to be identically risk‐averse when expected tracking error equals zero. In the equilibrium model, increased aggregate levels of risk‐taking reduce the returns on risk. Therefore, the net social effect of tracking‐error‐induced risk‐taking is potentially ambiguous. This paper shows, however, that tracking error promotes a pattern of specialization that helps the economy move towards the path of maximum accumulated wealth.     

Modelling Cooperative Advertising Decisions in Franchising

Advertising fee decisions in franchise systems are a frequent source of conflict between franchisors and franchisees. Such disagreements persist because the win-win potential of vertical cooperative advertising is not well appreciated. Our paper introduces a formal normative approach for analyzing, understanding and subsequently making these vertical cooperative advertising decisions within a franchising context in a manner that results in optimal system-wide returns. The model demonstrates that cooperative determination of franchisor's and franchisee's advertising contributions may yield superior payoffs for both exchange partners than the total payoff if the franchisor and franchisee seek to optimize their individual objective functions. Three types of models are developed and evaluated (i.e. deterministic, stochastic and under conditions of differing perceptions of the sales response functions to advertising). Conclusions hold under all three model variants. Industry implications are also presented.     

Twitter reciprocal reply networks exhibit assortativity with respect to happiness

The advent of social media has provided an extraordinary, if imperfect, ‘big data’ window into the form and evolution of social networks. Based on nearly 40 million message pairs posted to Twitter between September 2008 and February 2009, we construct and examine the revealed social network structure and dynamics over the time scales of days, weeks, and months. At the level of user behavior, we employ our recently developed hedonometric analysis methods to investigate patterns of sentiment expression. We find users’ average happiness scores to be positively and significantly correlated with those of users one, two, and three links away. We strengthen our analysis by proposing and using a null model to test the effect of network topology on the assortativity of happiness. We also find evidence that more well connected users write happier status updates, with a transition occurring around Dunbar's number. More generally, our work provides evidence of a social sub-network structure within Twitter and raises several methodological points of interest with regard to social network reconstructions.     

A two-dimensional finite volume method for transient simulation of time- and scale-dependent transport in heterogeneous aquifer systems

In this paper, solute transport in heterogeneous aquifers using a modified Fokker-Plauck equation (MFPE) is investigated. This newly developed mathematical model is characterised with a time-, scale-dependent dispersivity. A two-dimensional finite volume quadrilateral mesh method (FVQMM) based on a quadrilateral background interpolation mesh is developed for analysing the model. The FVQMM transforms the coupled non-linear partial differential equations into a system of differential equations, which is solved using backward differentiation formulae of order one through five in order to advance the solution in time. Three examples are presented to demonstrate the model verification and utility. Henry's classic benchmark problem is used to show that the MFPE captures significant features of transport phenomena in heterogeneous porous media including enhanced transport of salt in the upper layer due to its parameters that represent the dependence of transport processes on scale and time. The time and scale effects are investigated. Numerical results are compared with published results on the same problems.     

Using fuzzy measures and habitual domains to analyze the public attitude and apply to the gas taxi policy

Public acceptance and support are the crucial keys for implementing public policies successfully. Thus, the understanding of public acceptance or rejection towards the policy, as well as the important attributes of concern, could be very helpful to implementing the policy. However, most conventional attitude models could not approximate people's subjective evaluation process exactly by virtue of the additivity and independence assumptions. Additionally, people's decision behavior is deeply affected by their existing habits. Since habitual domains exist in the decision process, if the government can change or extend people's habitual thinking in favor of the public policy, the policy will receive satisfactory acceptance. Therefore, this study uses the habitual domain theory to analyze the public's attitude towards public policies. Furthermore, general fuzzy measures and fuzzy integrals, which require only boundary conditions and monotonicity, are also applied to develop a public attitude analysis model. An empirical study on the compress natural gas (CNG) taxi policy in Taipei City is conducted to show the applicability of the proposed model. The empirical results indicate that there are significant differences between the public's concern and governmental publicity, and some valuable strategies are suggested to the government.     

Surplus efficiency of ex ante investments in matching markets with nontransferabilities

Does a competitive equilibrium in a matching market provide adequate incentives for investments made before the market when utility is not perfectly transferable? In a one-sided market with a continuum of agents and finite types there is a constrained surplus efficient equilibrium, when a social planner can only affect investments but not payoffs nor matches, if an equal treatment property holds in equilibrium. Sufficient (but not full) utility transferability in a well defined sense implies this property. Ex post efficiency of payoffs (i.e., individual payoffs maximize the surplus in each match) alone is not sufficient to ensure that equilibrium investments maximize aggregate surplus.     

Mathematica™ in context

Aspects of the problem of teaching introductory undergraduate mathematics are considered in the context of both an increased participation rate in higher education as well as increasingly sophisticated computational technology. In particular, some of the changes in student and governmental expectations of course outcomes are canvassed, and an ongoing project initiated as a response both to these changes and to the availability of modern computational algebra systems that have sophisticated user interfaces is described. The project's aim is to develop students' mathematical understanding by undertaking practical laboratory work focused on applications that are perceived by students to be relevant to their social context and employment aspirations.     

Preference modelling by estimating local utility functions for multiobjective optimization

This paper is intended to design goal programming models for capturing the decision maker's (DM's) preference information and for supporting the search for the best compromise solutions in multiobjective optimization. At first, a linear goal programming model is built to estimate piecewise linear local utility functions based on pairwise comparisons of efficient solutions as well as objectives. The interactive step trade-off method (ISTM) is employed to generate a typical subset of efficient solutions of a multiobjective problem. Another general goal programming model is then constructed to embed the estimated utility functions in the original multiobjective problem for utility optimization using ordinary nonlinear programming algorithms. This technique, consisting of the ISTM method and the newly investigated search process, facilitates the identification and elimination of possible inconsistent information which may exist in the DM's preferences. It also provides various ways to carry out post-optimality analysis to test the robustness of the obtained best solutions. A modified nonlinear multiobjective management problem is taken as example to demonstrate the technique.     

中国地方政府财政民生支出效率实证分析

利用DEA方法计算出2009-2013年5年间全国31个省份财政民生支出资金配置的综合技术效率、纯技术效率、规模效率三种效率值,分析出各省份政府财政民生支出所处规模报酬阶段.结果显示:大部分省份的政府财政民生支出DEA得分在0.9以上,说明虽然效率没有达到最优水平,但是总体来说效率水平还是比较高的.另外,各省市财政民生产出存在较大的差异,东部地区综合产出水平高于中西部地区,其中,西部地区效率最低,改进空间最大.     

Cooperative games with imcomplete information

A bargaining solution concept which generalizes the Nash bargaining solution and the Shapley NTU value is defined for cooperative games with incomplete information. These bargaining solutions are efficient and equitable when interpersonal comparisons are made in terms of certainvirtual utility scales. A player's virtual utility differs from his real utility by exaggerating the difference from the preferences of false types that jeopardize his true type. In any incentive-efficient mechanism, the players always maximize their total virtual utility ex post. Conditionally-transferable virtual utility is the strongest possible transferability assumption for games with incomplete information.     

Randomized stopping games and Markov market games

We study nonzero-sum stopping games with randomized stopping strategies. The existence of Nash equilibrium and ɛ-equilibrium strategies are discussed under various assumptions on players random payoffs and utility functions dependent on the observed discrete time Markov process. Then we will present a model of a market game in which randomized stopping times are involved. The model is a mixture of a stochastic game and stopping game. Research supported by grant PBZ-KBN-016/P03/99.     

The role of utility interdependence in public good experiments

A popular approach to explain over-contribution in public good games is based on the assumption that people care (either positively or negatively) about the utility of other participants. Over-contribution then is an outcome of utility maximization where utility depends on subjects’ own payoffs as well as on the payoffs of other players. In this paper, I study to what extent this assumption of utility interdependence is responsible for over-contribution. I design three treatments where subjects’ decisions cannot affect opponents’ payoffs and thus utility interdependence cannot explain cooperative behavior. The main result is that while average contribution in these treatments is below the benchmark it nonetheless stays well above zero. Even when no one benefits from subjects’ generosity the average contributions are as high as one third of the endowment and are only 25% below those in the benchmark level. This suggests that utility interdependence is not the main factor responsible for over-contribution. I would like to thank my dissertation advisor Shyam Sunder for his valuable suggestions that helped improve this paper. I am also grateful to Dan Levin, Ben Polak, Klaus Schmidt, Andrew Schotter, Anat Bracha, Danielle Catambay, Rodney Chan, two anonymous referees and the anonymous Associate Editor for their comments and suggestions. Participants of the 17th International Conference on Game Theory at Stony Brook University, 2006 ESA International Meeting and 10th Biennial Behavioral Decision Research in Management Conference provided a valuable feedback at earlier stages of the paper. Finally, I would like to thank the Whitebox Fellowship for its generous support of this study.     

Scarcity,competition, and value

We suggest a value for finite coalitional games with transferable utility that are enriched by non-negative weights for the players. In contrast to other weighted values, players stand for types of agents and weights are intended to represent the population sizes of these types. Therefore, weights do not only affect individual payoffs but also the joint payoff. Two principles guide the behavior of this value. Scarcity: the generation of worth is restricted by the scarcest type. Competition: only scarce types are rewarded. We find that the types’ payoffs for this value coincide with the payoffs assigned by the Mertens value to their type populations in an associated infinite game.     

HOW RAPID SHOULD EMISSION REDUCTION BE? A GAME‐THEORETIC APPROACH

Abstract In this paper, we search for multistage realization of international environmental agreements. To analyze countries' incentives and the results of their interactions, we mathematically represent players' strategic preferences and apply a game‐theoretic approach to make predictions about their outcomes. The initial decision on emissions reduction is determined by the Stackelberg equilibrium concept. We generalize Barrett's static “emission” model to a dynamic framework and answer the question “how rapid should the emission reduction be?” It appears that sharper abatement is desirable in the early term, which is similar to the conclusion of the Stern review. Numerical example demonstrates that abatement dynamics of the coalition and the free‐rider differ when discounting of the future payoffs increases. We show that without incentives from external organizations or governments, such pollution reduction path can actually lead to a decline in the agreement's membership size.     

Toward eudaimonology: notes on a quantitative framework for the study of happiness

After noting factors (concern for others, ignorance, irrationality) accounting for the divergences between preference and happiness, the question of representing the preference of an individual by a utility function is discussed, taking account of lexicographic ordering, imperfect discrimination and the corresponding concepts of semiorder and sub-semiorder. Methods to improve upon the interpersonal comparability of measures of happiness such as pinning down the dividing line of zero happiness and the use of a just perceivable increment of happiness are discussed. The relation of social welfare to individual welfare (i.e. happiness) is then considered. Some reasonable set of axioms ensuring that social welfare is a separable function of and indeed an unweighted sum of individual welfares are reviewed. Finally, happiness is regarded as a function of objective, institutional and subjective factors; an interdisciplinary approach is needed even for an incomplete analysis.     

Global stability of delay-distributed viral infection model with two modes of viral transmission and B-cell impairment

This paper formulates a virus dynamics model with impairment of B-cell functions. The model incorporates two modes of viral transmission: cell-free and cell-to-cell. The cell-free and cell-cell incidence rates are modeled by general functions. The model incorporates both, latently and actively, infected cells as well as three distributed time delays. Nonnegativity and boundedness properties of the solutions are proven to show the well-posedness of the model. The model admits two equilibria that are determined by the basic reproduction number R₀. The global stability of each equilibrium is proven by utilizing Lyapunov function and LaSalle's invariance principle. The theoretical results are illustrated by numerical simulations. The effect of impairment of B-cell functions and time delays on the virus dynamics are studied. We have shown that if the functions of B-cell is impaired, then the concentration of viruses is increased in the plasma. Moreover, we have observed that increasing the time delay will suppress the viral replication.     

Baseline models are not “finishline” models: A sympathetic critique of Mayhew's strategy

A rationalist view of Relative Deprivation is possible if it is represented with extended preference. In the social movements studies, the concept of relative deprivation has been treated as an intervening variable, which is determined by the interpersonal comparisons and causes the social movements. The most important problem is whether a relatively deprived individual has an incentive for social movements or not. On the one hand he has different reference persons to whom he experiences relative deprivation and a sense of his subjective welfare, which make him behave in respective ways. But on the other hand he can behave in only one way at one time. We formalize the concept of the relative deprivation and construct the model that the relative deprivation and his preference in the ordinary sense are both the factors determining his behavior. Then it is deduced that there's no effect of the feeling relative deprivation for each individual to decide his way under some adequate conditions. So it should be concluded that the concept of the relative deprivation is not effective to explain social movements or social change in collectivities.     

The influence of random interactions and decision heuristics on norm evolution in social networks

In this paper we explore the effect that random social interactions have on the emergence and evolution of social norms in a simulated population of agents. In our model agents observe the behaviour of others and update their norms based on these observations. An agent’s norm is influenced by both their own fixed social network plus a second random network that is composed of a subset of the remaining population. Random interactions are based on a weighted selection algorithm that uses an individual’s path distance on the network to determine their chance of meeting a stranger. This means that friends-of-friends are more likely to randomly interact with one another than agents with a higher degree of separation. We then contrast the cases where agents make highest utility based rational decisions about which norm to adopt versus using a Markov Decision process that associates a weight with the best choice. Finally we examine the effect that these random interactions have on the evolution of a more complex social norm as it propagates throughout the population. We discover that increasing the frequency and weighting of random interactions results in higher levels of norm convergence and in a quicker time when agents have the choice between two competing alternatives. This can be attributed to more information passing through the population thereby allowing for quicker convergence. When the norm is allowed to evolve we observe both global consensus formation and group splintering depending on the cognitive agent model used.     

Stability of solutions for Ky Fan's section theorem with some applications

In this paper, we prove that “most of” problems in Ky Fan's section theorem (in the sense of Baire category) are essential and that for any problem in Ky Fan's section theorem, there exists at least one essential component of its solution set. As applications, we deduce both the existence of essential components of the set of Ky Fan's points based on Ky Fan's minimax inequality theorem and the existence of essential components of the set of Nash equilibrium points for general n-person non-cooperative games with non-concave payoffs.     

Common resources, optimality and taxes in dynamic games with increasing number of players

In the paper we examine the problem of exploitation of a common renewable resource. We use two kinds of models of this problem: games with finitely many players and games with a continuum of players. Equilibria in both cases are calculated and the payoffs are compared with payoffs in the situation in which each player behaves as a single owner of the resource. Various concepts of optimality are considered: optimality in the sense of property, Pareto optimality, maximization of a social welfare function of specific type and environmental sustainability. Another issue is the problem of enforcement of assumed profiles by so-called “linear” tax systems. Special attention is paid to the comparison of games with finitely many players and their continuum-of-players limit game.