Von Neumann-Morgenstern Research Articles

Strong and Weak Multivariate First-Order Stochastic Dominance

In this article we deal with three types of multivariate first-order stochastic dominance which serve for comparing random vectors. The first one is the strongest and it is generated by all non-decreasing multivariate utility functions. The second one, called weak multivariate stochastic dominance is defined by comparison of cumulative distribution functions of considered random vectors. The last one applies the univariate stochastic dominance notion to linear combinations of marginals. We compare these multivariate stochastic dominance relations among each other. Then we present important properties of strong and weak multivariate first-order stochastic dominance, in particular we describe their generators in the sense of von Neumann-Morgenstern utility functions and we explain their relation to joint and marginal distribution functions. Moreover, we discuss formulations of strong multivariate first-order stochastic dominance between random vectors with discrete distributions. Finally, we apply this stochastic dominance relation as a constraint to multivariate and multiperiod portfolio optimization problems.

Decision and Experienced Utility: Computational Applications in Privacy Decision Making

The existing computational models of privacy decisions are derived from expected utility theory, and can be equated with the von Neumann-Morgenstern (1953) perspective on decision utility. Here, I introduce experienced utility to privacy research, and shed light on the computational relations of experienced utility and decision utility, and computational applications of behavioral economics theories and concepts.

Rational expectations and farsighted stability

In the study of farsighted coalitional behavior, a central role is played by the von Neumann-Morgenstern (1944) stable set and its modification that incorporates farsightedness. Such a modification was first proposed by Harsanyi (1974) and has recently been re-formulated by Ray and Vohra (2015). The farsighted stable set is based on a notion of indirect dominance in which an outcome can be dominated by a chain of coalitional ‘moves’ in which each coalition that is involved in the sequence eventually stands to gain. However, it does not require that each coalition make a maximal move, i.e., one that is not Pareto dominated (for the members of the coalition in question) by another. Nor does it restrict coalitions to hold common expectations regarding the continuation path from every state. Consequently, when there are multiple continuation paths the farsighted stable set can yield unreasonable predictions. We resolve this difficulty by requiring all coalitions to have common rational expectations about the transition from one outcome to another. This leads to two related concepts: the rational expectations farsighted stable set (REFS) and the strong rational expectations farsighted stable set (SREFS). We apply these concepts to simple games and to pillage games to illustrate the consequences of imposing rational expectations for farsighted stability

Online Appendix for 'Competition and Networks of Collaboration'

I develop a model of collaboration between tournament participants in which agents collaborate in pairs, and an endogenous structure of collaboration is represented by a weighted network. The agents are forward-looking and capable of coordination; they value collaboration with others and higher tournament rankings. I use von Neumann-Morgenstern stable sets as a solution. I find stable networks in which agents collaborate only within exclusive groups. Both an absence of intergroup collaboration and excessive intragroup collaboration lead to inefficiency. I provide a necessary and sufficient condition for the stability of efficient outcomes in winner-takes-all tournaments. I show that the use of transfers does not repair efficiency.

Fair Stable Sets of Simple Games

Simple games are abstract representations of voting systems and other group-decision procedures. A stable set—or von Neumann-Morgenstern solution—of a simple game represents a “standard of behavior” that satisfies certain internal and external stability properties. Compound simple games are built out of component games, which are, in turn, “players” of a quotient game. I describe a method to construct fair—or symmetry-preserving—stable sets of compound simple games from fair stable sets of their quotient and components. This method is closely related to the composition theorem of Shapley (1963), and contributes to the answer of a question that he formulated: What is the set G of simple games that have a fair stable set? In particular, this method shows that the set G includes all simple games whose factors―or quotients in their “unique factorization” of Shapley (1967)―are in G, and suggests a path to characterize G.

Overcoming resistance against managed care \u2013 insights from a bargaining model

Recent healthcare reforms have sought to increase efficiency by introducing managed care (MC) while respecting consumer preferences by admitting choice between MC and conventional care. This article proposes an institutional change designed to let German consumers choose between the two settings through directing payments from the Federal Health Fund to social health insurers (SHIs) or to specialized MC organizations (MCOs). To gauge the chance of success of this reform, a game involving a SHI, a MCO, and a representative insured (RI) is analyzed. In a “three-player/three-cake” game the coalitions {SHI, MCO}, {MCO, RI}, and {SHI, RI} can form. Players’ possibility to switch between coalitions creates new outside options, causing the conventional bilateral Nash bargaining solution to be replaced by the so-called von Neumann-Morgenstern triple. These triples are compared to the status quo (where the RI has no threat potential) and related to institutional conditions characterizing Germany, the Netherlands, and Switzerland.

What Are Asset Demand Tests of Expected Utility Really Testing?*

Assuming the classic contingent claim setting, a number of financial asset demand tests of Expected Utility have been developed and implemented in experimental settings. However the domain of preferences of these asset demand tests differ from the mixture space of distributions assumed in the traditional binary lottery laboratory tests of von Neumann-Morgenstern Expected Utility preferences. We derive new sets axioms that are necessary and sufficient for preferences over contingent claims to be representable by an Expected Utility function. We also indicate the additional axioms required to extend the representation to the more general case of preferences over risky prospects.

The Degree Measure as Utility Function over Positions in Networks

In this paper, we connect the social network theory on centrality measures to the economic theory of preferences and utility. Using the fact that networks form a special class of cooperative TU-games, we provide a foundation for the degree measure as a von Neumann-Morgenstern expected utility function reflecting preferences over being in different positions in different networks. The famous degree measure assigns to every position in a weighted network the sum of the weights of all links with its neighbours. A crucial property of a preference relation over network positions is neutrality to ordinary risk. If a preference relation over network positions satisfies this property and some regularity properties, then it must be represented by a utility function that is a multiple of the degree centrality measure. We show this in three steps. First, we characterize the degree measure as a centrality measure for weighted networks using four natural axioms. Second, we relate these network centrality axioms to properties of preference relations over positions in networks. Third, we show that the expected utility function is equal to a multiple of the degree measure if and only if it represents a regular preference relation that is neutral to ordinary risk. Similarly, we characterize a class of affine combinations of the outdegree and indegree measure in weighted directed networks and deliver its interpretation as a von Neumann-Morgenstern expected utility function.

Bounded, Sigmoid Utility for Insurance Applications

Abstract Applying a well-known argument of Karl Menger to an insurance version of the St. Petersburg Paradox (in which the decision maker is confronted with losses, rather than gains), one can assert that von Neumann-Morgenstern utility functions are necessarily concave upward and bounded below as decision-maker wealth tends to negative infinity. However, this argument is subject to two potential criticisms: (1) infinite-mean losses do not exist in the real world; and (2) the St. Petersburg Paradox derives its force from empirical observation (i. e., that actual decision makers would not agree to an arbitrarily large insurance bid price to transfer an infinite-mean loss), and thus does not impart logical necessity. In the present article, these two criticisms are addressed in turn. We first show that, although infinite-mean insurance losses technically do not exist, they do provide a reasonable model for certain large (i. e., excess and reinsurance) property-liability indemnities. We then employ the Two-Envelope Paradox to demonstrate the logical necessity of concave-upward, lower-bounded utility for arbitrarily small (i. e., negative) values of wealth. Finally, we note that recognizing the bounded, sigmoid nature of utility functions challenges certain fundamental understandings in the economics of insurance demand, and can lead to vastly different conclusions regarding the bid price for insurance.

On the Optimal Investment

In 1988 Dybvig introduced the payoff distribution pricing model (PDPM) as an alternative to the capital asset pricing model (CAPM). Under this new paradigm agents preferences depend on the probability distribution of the payoff and for the same distribution agents prefer the payoff that requires less investment. In this context he gave the notion of efficient payoff. Both approaches run parallel to the theory of choice of von Neumann-Morgenstern (1947), known as the Expected Utility Theory and posterior axiomatic alternatives. In this paper we consider the notion of optimal payoff as that maximizing the terminal position for a chosen preference functional and we investigate the relationship between both concepts, optimal and efficient payoffs, as well as the behavior of the efficient payoffs under different market dynamics. We also show that path-dependent options can be efficient in some simple models.

ITG 1000, Risk Detection and Accounting Information: a Theoretical Analysis on the Cost versus Benefit for Micro and Small Enterprises

This essay aims to discuss aspects related to the incentives that individuals face with regard to the adoption or not of ITG 1000, as well as the possible scenarios resulting from the responses of these individuals to such incentives. It was assumed as a basic premise that there is no executive inter-relationship between keeping only the cash book ledger, or adopting ITG 1000, and other economic choices. The discussion is based on the assumptions of economic rationality and assumes that individuals, under uncertainty, will behave in a manner attributable to Von Neumann-Morgenstern. In addition, it was guided by the classical model proposed by Allingham and Sandmo (1972), referring to the economic theory of tax evasion. It may be noted that the successful adoption of ITG 1000 can be achieved with an awareness of the segments involved and with the prohibition and penalizing of adverse behavior, permitting one to infer that the adoption of the 1000 ITG is much more dependent on the accounting class’s actions, rather than a management decision itself.

일반적 효용함수 하에서 대출제약의 정도와 최적 소비 및 투자

I study optimal consumption and investment choices of an infinitely-lived economic agent with a general time-sepa- rable von Neumann-Morgenstern utility under general borrowing constraints against future labor income. An explicit solution is provided by the dynamic programming method. It is shown that the optimal consumption and risky invest- ment decrease as the borrowing constraints become stronger.

Debunking the Monday Irrationality through the External Affection of Investors

This study aims to reveal the mechanism of the influences of the full moon and high temperatures on investors’ Monday irrationality. In contrast to other studies, this research was built under a retroductive approach by using a time series quasi experimental study. Investors were directly assessed for their irrationality by using an adapted psychometric test on 4 occasions. The results indicate that there were indeed effects of the full moon and high temperatures on investors’ irrationality. Because the full moon and high temperatures frequently occurred on Mondays, it is most probably those two variables that were the drivers of the Monday irrationality. In the end, we concluded that the rational behaviour assumption can no longer be held. Instead of rationality, the investors were quasi rational. The utility function of Von Neumann-Morgenstern in decision making has to be replaced by the hedonic utility.

An Alternative Proof of the Characterization of Core Stability for the Assignment Game

Solymosi and Raghavan (2001) characterize the stability of the core of the assignment game by means of a property of the valuation matrix. They show that the core of an assignment game is a von Neumann-Morgenstern stable set if and only if its valuation matrix has a dominant diagonal. Their proof makes use of some graph-theoretical tools, while the present proof relies on the notion of buyer-seller exact representative in Nunez and Rafels (2002).

Theory of Generalized Risk Attitudes

This paper develops a theory of risk attitudes that can be applied in a broad array of settings, including those in which the decision maker (DM) abides by a preference model other than the expected utility model and in which decisions are being made over multiattribute alternatives. The theory is based on (i) a set of plausible axioms in which the DM’s preferences over consequences and lotteries are defined separately and (ii) the premise that a risk neutral DM is indifferent between a lottery and the average (in terms of preference) of the outcomes obtained from infinite repetition of the lottery. We show that, under these assumptions, a risk neutral DM seeks to maximize the expectation of classic cardinal utility (i.e., measurable value). This means, in particular, that the DM’s risk attitude in expected utility theory is related to the transformation function between the classic cardinal utility function and the von Neumann-Morgenstern utility function. The results also suggest that the applicability of the conventional definitions of risk attitudes may be limited to settings in which the DM’s classic cardinal utility function is linear and that a more generalized treatment of risk attitudes is required for settings in which this is not the case.

Asymmetric reaction is rational behavior

DeBondt and Thahler (1995) point out that while von Neumann-Morgenstern (1947) utility functions, the axioms of cardinal utility (Copeland and Weston, 1992), risk aversion, rational expectations, etc., have formed the basis for theories of choice under uncertainty, research in behavioral science, has either compromised these foundations or outright rejected them. For example, although most asset-pricing models assume symmetry in valence and strength of within-moment preferences, Kahenman and Travesky’s prospect theory, and Kahneman, Knetsch and Thaler (1990) empirical findings establishes that a pattern of behavior contrary to rational expectations. Requiring investors to be utility maximizers, and using an approach similar to Scott-Horvath (1980), this paper argues that the finding investors weighing losses more than gains (Kahneman, Knetsch and Thaler, 1990), is in fact the very foundation of rational behavior.

Statistical Rationality and Equilibrium: A Theory of Statistical Games

Through building the statistical structure of game theory, this paper develops a paradigm of rationality and equilibrium to model collective and interactive behaviors for various economic ecologies from a perfect organizing corporation to a complete freedom population such as an anarchy. In addition to the employment of the theory of von Neumann-Morgenstern expected utility, this paper constructs a rational evaluation system for collective ecologies by introducing the postulates that a free behavior tends to be a uniform distribution. The equilibrium structure that is described by its properties of completeness, simplicity and efficiency, is examined through managing rational behavioral patterns of collective ecologies and their interactive mechanisms. The Pareto optimality of an equilibrium such as the cooperative solution to a game of prisoner's dilemma could be approached within a certain interactive mechanism.

How non-arbitrage, viability and numéraire portfolio are related

This paper proposes two approaches that quantify the exact relationship among the viability, the absence of arbitrage, and/or the existence of the num\'eraire portfolio under minimal assumptions and for general continuous-time market models. Precisely, our first and principal contribution proves the equivalence among the No-Unbounded-Profit-with-Bounded-Risk condition (NUPBR hereafter), the existence of the num\'eraire portfolio, and the existence of the optimal portfolio under an equivalent probability measure for any "nice" utility and positive initial capital. Herein, a 'nice" utility is any smooth von Neumann-Morgenstern utility satisfying Inada's conditions and the elasticity assumptions of Kramkov and Schachermayer. Furthermore, the equivalent probability measure ---under which the utility maximization problems have solutions--- can be chosen as close to the real-world probability measure as we want (but might not be equal). Without changing the underlying probability measure and under mild assumptions, our second contribution proves that the NUPBR is equivalent to the "{\it local}" existence of the optimal portfolio. This constitutes an alternative to the first contribution, if one insists on working under the real-world probability. These two contributions lead naturally to new types of viability that we call weak and local viabilities.

Differentiability of Von Neumann-Morgenstern Utility Functions

This paper studies necessary and sufficient preference-based conditions for differentiability of risk averse (prudent, or temperate) von Neumann-Morgenstern utility functions. The very idea to devise those conditions is based on the reverse claim of an old observation by Arrow that a risk-averse expected-utility maximizer will always accept a sufficiently small stake in any positive expected-value bet if her von Neumann-Morgenstern utility function is differentiable.

HOW TO PREPARE FOR RETIREMENT? OPTIMAL SAVING, LABOR SUPPLY, AND INVESTMENT STRATEGY

In this paper we study consumption-labor supply decision of an agent who prepares for retirement at a known time in the future. The agent is assumed to have a preference which is represented by the von Neumann-Morgenstern utility function in which the felicity function has constant relative risk aversion over the composite of consumption and leisure. The composite is obtained by the Cobb-Douglas function. A general problem has been studied by Bodie et al. (2004). We contribute to the literature by deriving the Slutsky equations and conducting comparative statics. In particular, we show that wealth effect can exhibit an interesting property depending upon the time until retirement, as the interest rate increases.