Utility Function For Money Research Articles

Identification of Biased Beliefs in Games of Incomplete Information Using Experimental Data

This paper studies the identification of players'; preferences and beliefs in empirical applications of discrete choice games using experimental data. The experiment comprises a set of games with similar features (e.g., two-player coordination games) where each game has different values for the players'; monetary payoffs. Each game can be interpreted as an experimental treatment group. The researcher assigns randomly subjects to play these games and observes the outcome of the game as described by the vector of players' actions. Data from this experiment can be described in terms of the empirical distribution of players' actions conditional on the treatment group. The researcher is interested in the nonparametric identification of players' preferences (utility function of money) and players' beliefs about the expected behavior of other players, without imposing restrictions such as unbiased or rational beliefs or a particular functional form for the utility of money. We show that the hypothesis of unbiased/rational beliefs is testable and propose a test of this null hypothesis. We apply our method to two sets of experiments conducted by Goeree and Holt (2001) and Heinemann, Nagel and Ockenfels (2009). Our empirical results suggest that in the matching pennies game, a player is able to correctly predict other player's behavior. In the public good coordination game, our test can reject the null hypothesis of unbiased beliefs when the payoff of the non-cooperative action is relatively low.

Harry G. Frankfurt, On Inequality. Princeton and Oxford: Princeton University Press, 2015

This book – or booklet, with 100 pages of large print – has not been written for an academic audience. While we should cherish the fact that philosophers write for a broader audience, in this case the merits are decidedly mixed. While its style is vivid and elegant, the book’s arguments are incomplete, some are set up against strawmen, and many are technically correct, but hardly relevant to today’s social and political circumstances. Frankfurt ignores essential pieces of scholarship, which makes him a poor ambassador for philosophy in the public sphere. And he seems oblivious to the way in which his book might be used by political actors who pursue policies that are diametrically opposed to what he claims to want. For philosophers who have followed Frankfurt’s writings, his arguments are not new; portions of them have been published in papers in 1987 (BEquality as a Moral Ideal^, Ethics 98(1), 21–43) and 1997 (BEquality and Respect^, Social Research 64(1), 3–15). Since then, the philosophical debate has moved on, and the world has changed dramatically. Frankfurt’s views, it seems, haven’t. Frankfurt presents a series of arguments in order to show that from a moral (rather than political or social, cf. 8) perspective, we should care more about everyone having enough than about individuals having equal amounts of money. For example, he criticizes arguments for equality based on the principle of diminishing marginal utility by pointing out, in a somewhat technical discussion, that there can be interdependencies between goods that imply that utility functions are often discontinuous, and that the utility function of money is likely to be different from that of other goods (17 ff.). He uses an example in which a certain threshold of resources is needed to survive to argue against a distribution that would be equal, but would let nobody survive (34 ff.); this is correct, but also too obvious to be worth insisting on. He also argues that if we are satisfied with life, we have no reason to strive for more – neglecting questions about whether money might, in a society without a social safety net, nonetheless be worth getting as a safety cushion against life’s misfortune. Against Isaiah Berlin, he holds that a presumption in favour of equality when dividing a cake results from the importance of Ethic Theory Moral Prac (2016) 19:823–825 DOI 10.1007/s10677-015-9678-1

Quantitative tests of the Perceived Relative Argument Model: comment on Loomes (2010).

Loomes (2010, Psychological Review) proposed the Perceived Relative Argument Model (PRAM) as a novel descriptive theory for risky choice. PRAM differs from models like prospect theory in that decision makers do not compare 2 prospects by first assigning each prospect an overall utility and then choosing the prospect with the higher overall utility. Instead, the decision maker determines the relative argument for one or the other prospect separately for outcomes and probabilities, before reaching an overall pairwise preference. Loomes (2010) did not model variability in choice behavior. We consider 2 types of "stochastic specification" of PRAM. In one, a decision maker has a fixed preference, and choice variability is caused by occasional errors/trembles. In the other, the parameters of the perception functions for outcomes and for probabilities are random, with no constraints on their joint distribution. State-of-the-art frequentist and Bayesian "order-constrained" inference suggest that PRAM accounts poorly for individual subject laboratory data from 67 participants. This conclusion is robust across 7 different utility functions for money and remains largely unaltered also when considering a prior unpublished version of PRAM (Loomes, 2006) that featured an additional free parameter in the perception function for probabilities. (PsycINFO Database Record (c) 2014 APA, all rights reserved).

Human Preferences and Risky Choices

EDITORIAL article Front. Psychol., 15 November 2011Sec. Cognition volume 2 - 2011 | https://doi.org/10.3389/fpsyg.2011.00333

The generalized value at risk admissible set: constraint consistency and portfolio outcomes

Generalized value at risk (GVaR) adds a conditional value at risk or censored mean lower bound to the standard value at risk and considers portfolio optimization problems in the presence of both constraints. For normal distributions the censored mean is synonymous with the statistical hazard function, but this is not true for fat-tailed distributions. The latter turn out to imply much tighter bounds for the admissible portfolio set and indeed for the logistic, an upper bound for the portfolio variance that yields a simple portfolio choice rule. The choice theory in GVaR is in general not consistent with classic Von Neumann–Morgenstern utility functions for money. A re-specification is suggested to make it so that gives a clearer picture of the economic role of the respective constraints. This can be used analytically to explore the choice of portfolio hedges.

The magnitude effect: Temporal discount rates and restaurant tips

Decision makers show a larger subjective temporal discount rate for small magnitudes than for large ones. That is, they demand a larger percent increase in value to compensate for a delay when they are waiting for a small amount of money than for a large amount. Prelec and Loewenstein (1991; see also Loewenstein & Prelec, 1992) proposed an increasing proportional sensitivity account of this magnitude effect. This account surmises that the magnitude effect stems from the utility function for money and is consequently not unique to intertemporal choice. One study tested this prediction by demonstrating the magnitude effect in two domains: intertemporal choice and tipping for restaurant meals, haircuts, and taxi rides. In intertemporal choice, subjects showed a larger discount rate for smaller monetary amounts. They also tipped a larger percentage on small bills than on large bills. Thus, both domains showed the magnitude effect; however, the size of the effect was not well correlated between domains.

Weighing risk and uncertainty.

Decision theory distinguishes between risky prospects, where the probabilities associated with the possible outcomes are assumed to be known, and uncertain prospects, where these probabilities are not assumed to be known. Studies of choice between risky prospects have suggested a nonlinear transformation of the probability scale that overweights low probabilities and underweights moderate and high probabilities. The present article extends this notion from risk to uncertainty by invoking the principle of bounded subadditivity: An event has greater impact when it turns impossibility into possibility, or possibility into certainty, than when it merely makes a possibility more or less likely. A series of studies provides support for this principle in decision under both risk and uncertainty and shows that people are less sensitive to uncertainty than to risk. Finally, the article discusses the relationship between probability judgments and decision weights and distinguishes relative sensitivity from ambiguity aversion. Decisions are generally made without definite knowledge of their consequences. The decisions to invest in the stock market, to undergo a medical operation, or to go to court are generally made without knowing in advance whether the market will go up, the operation will be successful, or the court will decide in one's favor. Decision under uncertainty, therefore, calls for an evaluation of two attributes: the desirability of possible outcomes and their likelihood of occurrence. Indeed, much of the study of decision making is concerned with the assessment of these values and the manner in which they are—or should be— combined. In the classical theory of decision under risk, the utility of each outcome is weighted by its probability of occurrence. Consider a simple prospect of the form (x, p) that offers a probability p to win $jc and a probability 1 — p to win nothing. The expected utility of this prospect is given by pu(x) + (1 — p)w(O), where u is the utility function for money. Expected utility theory has been developed to explain attitudes toward risk, namely, risk aversion and risk seeking. Risk aversion is denned as a preference for a sure outcome over a prospect with an equal or greater expected value. Thus, choosing a sure $100 over an even chance to win $200 or nothing is an expression of risk aversion. Risk seeking is exhibited if a prospect is preferred to a sure outcome with equal or greater expected value. It is commonly assumed that people are risk averse, which is explained in expected utility theory by a concave utility function. The experimental study of decision under risk has shown that people often violate both the expected utility model and the

Scale convergence and utility measurement

In order to investigate derived scales for the utility, or subjective value of money, subjects were instructed to perform four tasks: in two tasks, they judged “ratios” and “differences” of strengths of preference for monetary amounts; in two other tasks, they judged the values of gambles from buyer's or seller's points of view. The two arrays of data for “ratios” and “differences” were consistent with the hypothesis that most subjects used only one operation to compare monetary amounts, although a few subjects appeared to use two operations. The buyer's and seller's prices would lead to two different utility functions for money under expected utility theory, subjective expected utility theory, or any theory that is additive across outcomes. However, configural-weight utility theory can predict these changes in rank order with an invariant utility function, by postulating that the configurai weight of the smaller amount depends on point of view. The data also reveal systematic violations of dominance (monotonicity) that can be described by assuming that the configurai weight of zero, when it is the lower value, has smaller weight at low probabilities than nonzero outcomes. Disregarding the minority of subjects who appeared to utilize two operations for judging “ratios” and “differences” in utility, the majority of the data can be well-approximated using a single scale of utility, the subtractive model for “ratio” and “difference” comparisons, and the configurai weight, rank-dependent model for buyer's and seller's prices.

Utility Functions for Nonmonetary Events

Six experiments are described that use magnitude estimation methods to characterize a nonlinear (approximately square root) utility function for money

Risk Aversion in the Small and in the Large

This paper concerns utility functions for money. A measure of risk aversion in the small, the risk premium or insurance premium for an arbitrary risk, and a natural concept of decreasing risk aversion are discussed and related to one another. Risks are also considered as a proportion of total assets.

Utility functions of money for clear games

AbstractIn this paper we discuss the question of clearness of K‐games for catalogues as defined by Jentzsch in Ref. [4]. It is proved that when the coalition K has at least two members, a necessary and sufficient condition that all money games played by K will be clear is that the utility functions for money of the players of K are linear in money. In the proof we assume that the utility functions are concave.