Von Neumann-Morgenstern Utility Function Research Articles

A multiplayer game model to detect insiders in wireless sensor networks.

Insiders might have incentives and objectives opposed to those of the belonging organization. It is hard to detect them because of their privileges that partially protect them. In Wireless Sensor Networks (WSNs), significant security issues arise, including compromised nodes by insiders that disrupt the normal network operation. Immediate defensive actions to isolate malicious nodes would mitigate any related impacts. A multiplayer game model is proposed as a solution to the problem of insider attacks in WSNs, the Game of Wireless Sensor Networks (GoWiSeN). It is an imperfect information game, formulated with the use of non-cooperative game theory, holding the assumption that all players are rational. The model consists of several Local Intrusion Detection Systems (LIDSs), which are located to different nodes and communicate with a Global Intrusion Detection System (GIDS). Each LIDS gives suggestions whether the monitoring node is trusted or not. The game is being played between a potential attacker, the nodes and the GIDS. The GIDS is responsible for making a final decision and for isolating a compromised node in case of an internal attack. The theoretical model represents these interactions in an extensive form game. The formal elements of the game are specified, the outcomes of the game are quantified by first specifying players’ preferences, and then, by using the von Neumann-Morgenstern utility function, and payoffs are obtained. The game is constructed and solved, by locating NE in pure and mixed strategies. Experimental evaluations conducted on real network datasets, using IDSs of different capabilities, simulate special cases and compromised nodes in a WSN, verify the model efficiency, and show how the game should be played.

The Standard Model of Rational Risky Decision-Making

Expected utility theory (EUT) is currently the standard framework which formally defines rational decision-making under risky conditions. EUT uses a theoretical device called von Neumann–Morgenstern utility function, where concepts of function and random variable are employed in their pre-set-theoretic senses. Any von Neumann–Morgenstern utility function thus derived is claimed to transform a non-degenerate random variable into its certainty equivalent. However, there can be no certainty equivalent for a non-degenerate random variable by the set-theoretic definition of a random variable, whilst the continuity axiom of EUT implies the existence of such a certainty equivalent. This paper also demonstrates that rational behaviour under utility theory is incompatible with scarcity of resources, making behaviour consistent with EUT irrational and justifying persistent external inconsistencies of EUT. A brief description of a new paradigm which can resolve the problems of the standard paradigm is presented. These include resolutions of such anomalies as instant endowment effect, asymmetric valuation of gains and losses, intransitivity of preferences, profit puzzle as well as the St. Petersburg paradox.

The Nash Solution as a von Neumann\u2013Morgenstern Utility Function on Bargaining Games

In this paper we prove that the symmetric Nash solution is a risk neutral von Neumann–Morgenstern utility function on the class of pure bargaining games. Our result corrects an error in Roth (Econometrica 46:587–594, 983, 1978) and generalizes Roth’s result to bargaining games with arbitrary status quo.

Optimal retirement and portfolio selection with consumption ratcheting

The purpose of this paper is to study the optimal retirement and consumption/investment decisions of an infinitely lived agent who does not tolerate any decline in his/her consumption throughout his/her lifetime. The agent receives labor income but suffers disutility from working until retirement. The agent’s optimization problem combines features of both singular control and optimal stopping. We use the martingale method and study the dual problem, which can be decoupled into a singular control problem and an optimal stopping problem. We provide a closed-form solution of the optimal strategies for the von Neumann–Morgenstern utility function. We show that the coefficient of relative risk aversion implied by the optimal portfolio (i.e., the implied coefficient of relative risk aversion, ICRRA) is a constant value smaller than 1. Moreover, we show that the ICRRA is independent of the agent’s felicity utility function and depends only on the subjective discount rate and market parameters.

Conditional Pure Strategy Dominance

Given a dynamic game with ordinal preferences, we deem a strategy sequentially rational if there exist a von Neumann-Morgenstern utility function that agrees with the assumed ordinal preferences and a conditional probability system with respect to which the strategy is a maximizer. We prove that this notion of sequential rationality is characterized by a notion of dominance, called Conditional B-Dominance, that extends Pure Strategy Dominance of Borgers (1993) to dynamic games represented in their extensive form. Additionally, we introduce an iterative procedure based on Conditional B-Dominance with a forward induction reasoning flavour, called Iterative Forward B-Dominance, that we prove satisfies nonemptiness. Finally, we show that Iterative Forward B-Dominance selects the unique backward induction outcome in generic dynamic games with perfect information.

Two-person Bargaining with Lexicographic Preferences

In bargaining theory a usual assumption is either that of von Neumann–Morgenstern utility functions or that of continuous preferences. In this note, we consider a bargaining model with lexicographic preferences for the two players. We show that the Rubinstein et al. (1992), definition can still be used to obtain a Nash solution. We also look briefly at the alternating offers approach.

Approval-directed agency and the decision theory of Newcomb-like problems

Decision theorists disagree about how instrumentally rational agents, i.e., agents trying to achieve some goal, should behave in so-called Newcomb-like problems, with the main contenders being causal and evidential decision theory. Since the main goal of artificial intelligence research is to create machines that make instrumentally rational decisions, the disagreement pertains to this field. In addition to the more philosophical question of what the right decision theory is, the goal of AI poses the question of how to implement any given decision theory in an AI. For example, how would one go about building an AI whose behavior matches evidential decision theory’s recommendations? Conversely, we can ask which decision theories (if any) describe the behavior of any existing AI design. In this paper, we study what decision theory an approval-directed agent, i.e., an agent whose goal it is to maximize the score it receives from an overseer, implements. If we assume that the overseer rewards the agent based on the expected value of some von Neumann–Morgenstern utility function, then such an approval-directed agent is guided by two decision theories: the one used by the agent to decide which action to choose in order to maximize the reward and the one used by the overseer to compute the expected utility of a chosen action. We show which of these two decision theories describes the agent’s behavior in which situations.

Welfare maximization entices participation

We consider randomized public good mechanisms with optional participation. Preferences over lotteries are modeled using skew-symmetric bilinear (SSB) utility functions, a generalization of classic von Neumann–Morgenstern utility functions. We show that every welfare-maximizing mechanism entices participation and that the converse holds under additional assumptions. As a corollary, we obtain a characterization of an attractive randomized voting rule that satisfies Condorcet-consistency and entices participation. This stands in contrast to Moulin's well-known no-show paradox (Moulin, 1988), which shows that no deterministic voting rule can satisfy both properties simultaneously.

The role of risk aversion in public goods dilemmas with environmental uncertainty: an experimental analysis

ABSTRACTThe purpose of this study is to extend earlier research on environmental uncertainty in public goods dilemmas. The present paper reports the results of an experiment designed to examine the effect of risk aversion on public goods provision. A von Neumann–Morgenstern utility function with constant coefficient of relative risk aversion is used to investigate the impact of risk attitudes within a threshold public goods environment. The outcome of the threshold public goods experiment shows that subjects are indifferent to the changes in environmental conditions. Additionally, the analysis indicates that risk aversion is a significant determinant of voluntary public goods contribution level.

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.

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.

Measuring unfairness feeling in allocation problems

In this paper, we introduce a new measure of social fairness based on unfairness feelings of the players involved in an allocation problem, e.g., cake-cutting problem or shift scheduling. We only require that each player be described by a von Neumann–Morgenstern utility function. Next, we propose a social normalization of each player׳s utility function, based on how each player sees the other players׳ shares through her own utility function. Further, we extend this normalization idea to a setting where the players are represented by a weighted oriented graph, where the weights assess the relatedness of (or similarities between) the agents. Among other results, we establish some links between our measures of fairness and those classically used in the cake-cutting-problem literature.

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.

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.

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.

Foreign Exchange Derivatives and Bank Lending in China

With the reform of the RMB exchange rate regime, China’s banks expose to more exchange rate risks and use foreign exchange derivatives to manage these risks. This paper develops a theoretical model to examine the relationship between foreign exchange derivatives and the foreign currency lending in China’s banking sector. In our model, banks choose lending activities in a way analogous to Cournot competition commonly described in industrial organization. We find there is the positive effect of the derivatives position on the total loan volumes under the condition that the von Neumann-Morgenstern utility function of bank using derivatives displays either constant or decreasing absolute risk aversion. In the empirical section, we use Vector Autoregression (VAR) model with China’s monthly data over the period from Jan 2007 to Jun 2014. Based on techniques commonly used in the VAR literature, the main results suggest that the foreign exchange derivatives transaction has bi-directional Granger causality with bank’s foreign currency loan volume, and derivatives transaction has a significantly and persistently positive effect on bank lending. Furthermore, we find that derivatives transaction accounts for over 40 percent of variations in loan volume in the long run.

Interest-Rate Derivatives and Bank Lending in China

With interest rate liberalization, China’s commercial banks expose to more interest rate risks and use interest-rate derivatives to manage these risks. This paper develops a theoretical model, capturing the main characteristics of the banking sector in China, to analyze the effect of interest-rate derivatives on bank lending. In our model, banks choose lending activity in a way analogous to Cournot competition commonly described in industrial organization. We find the positive effect of interest-rate derivatives position on the total loan volumes in the credit market under the condition that the von Neumann-Morgenstern utility function of bank using derivatives displays either constant or decreasing absolute risk aversion and the derivatives market is unbiased. In the empirical section, we use Vector Autoregression (VAR) model with China’s monthly data over the period from Jan 2007 to Jun 2014. Based on techniques commonly used in the VAR literature, the main results suggest that the interest-rate derivatives market transaction has bi-directional Granger causality with bank loan growth, and derivatives transaction has a significantly and persistently positive effect on loan growth. Moreover, we find that derivatives transaction accounts for 20 percent of variations in bank loan growth in the long run.

Foreign Exchange Derivatives and International Trade in China

Our paper studies the effect of foreign exchange derivatives on international trade in China theoretically and empirically. On one hand, we build a two-stage model of an international Cournot duopoly under exchange rate uncertainty, which extends the model of Broll et al (2009). Our extended model shows foreign exchange derivatives hedging exchange rate risk have the positive effects on export and import level of the firm if the von Neumann-Morgenstern utility function of the firm displays either constant or decreasing absolute risk aversion and the derivatives market is unbiased. On the other hand, we use Bayesian Vector Autoregression (BVAR) model with China’s monthly data over the period from Oct 2006 to Dec 2014, and the empirical results are consistent with what the theoretical model predicts.