Menu-dependent self-control

The literature on self-control problems has typically put forth models that imply behavior that is consistent with the weak axiom of revealed preference (WARP). We argue that when choice is the outcome of some underlying internal conflict, the resulting choices may not be perfectly consistent across choice problems: an agent’s ability to resist temptation may well depend on what alternatives are available to him. We generalize Gul and Pesendorfer (2001) so that self-control weakens in the presence of temptation. To model choices from menus explicitly, we consider a choice correspondence as well as a preference over menus and relax both the Independence axiom for the preference and the WARP condition for the choice correspondence. The model is shown to unify a range of well-known findings in the experimental literature on choice under risk and over time within a single specification.     

Bad temptation

We study a static self-control model in which an agent’s preference, temptation ranking, and cost of self-control drive her choices among a finite set of options. We show it is without loss to assume the agent’s temptation ranking is the opposite of her preference. We characterize the model by relaxing the Weak Axiom of Revealed Preference (WARP), and exploit WARP violations to identify the model’s parameters.     

Reexamination on updating Choquet beliefs

Eichberger et al. (2007)  characterize the full Bayesian update rule for capacities. This paper shows that a conditional preference relation represented by the Choquet expected utility with respect to the updated capacity through the rule does not satisfy the axiom of Conditional Certainty Equivalence Consistency. A counterexample is provided and it is proved that a relaxation of the axiom maintains their results.     

On the computation of optimal monotone mean–variance portfolios via truncated quadratic utility

We report a surprising link between optimal portfolios generated by a special type of variational preferences called divergence preferences (see Maccheroni et al., 2006) and optimal portfolios generated by classical expected utility. As a special case, we connect optimization of truncated quadratic utility (see ?erný, 2003) to the optimal monotone mean–variance portfolios (see Maccheroni et al., 2009), thus simplifying the computation of the latter.     

Expected utility without bounds—A simple proof

We provide a simple proof for the existence of an expected utility representation of a preference relation with an unbounded and continuous utility function.     

Informativeness of experiments for MEU—A recursive definition

The well-known Blackwell theorem states the equivalence of statistical informativeness and economic valuableness. Çelen (2012) generalizes this theorem, which is well-known for subjective expected utility (seu), to maxmin expected utility (meu) preferences. We demonstrate that the underlying definition of the value of information used in Çelen (2012) is in contradiction with the principle of recursively defined utility. As a consequence, Çelen’s framework features dynamic inconsistency. Our main contribution consists in the definition of a value of information for meupreferences that is compatible with recursive utility and thus respects dynamic consistency.     

Existence of smooth utilities on Banach lattices

In this paper, we focus our attention on the representability of a preference relation by differentiable utility functions when the consumption sets belong to an infinite dimensional commodity space. We obtain sufficient conditions for the existence of a C^r function representing a preference relation defined on an open subset of a Banach lattice.     

A preference foundation for constant loss aversion

Following prospect theory and in particular the concept of loss aversion, introduced by Kahneman and Tversky (1979), we consider decision making under risk in which the decision maker’s preferences depend on a reference outcome. An outcome below this reference outcome is regarded as resulting from a loss: a loss decreases the decision maker’s basic utility more than a comparable gain increases this utility. An elegant and simple way to model this phenomenon was proposed by Shalev (2002): the utility of an outcome below the reference outcome is obtained from the basic utility by subtracting a multiple of the loss in basic utility: this multiple, the loss aversion coefficient, is constant across different reference outcomes. We provide a preference foundation for this loss aversion model.     

A characterization and an impossibility of finite length anonymity for infinite generations

In the context of ranking infinite utility streams, the impartiality axiom of finite length anonymity requires the equal ranking of any two utility streams that are equal up to a finite length permutation ( Fleurbaey and Michel, 2003). We first characterize any finite length permutation as a composition of a fixed step permutation and an “almost” fixed step permutation. We then show that if a binary relation satisfies finite length anonymity, then it violates all the distributional axioms that are based on a segment-wise comparison. Examples of those axioms include the weak Pareto principle and the weak Pigou-Dalton principle.     

Expected utility without continuity: A comment on Delbaen et al. (2011)

This paper presents preference axiomatizations of expected utility for nonsimple lotteries while avoiding continuity constraints. We use results by Fishburn (1975), Wakker (1993), and Kopylov (2010) to generalize results by Delbaen et al. (2011). We explain the logical relations between these contributions for risk versus uncertainty, and for finite versus countable additivity, indicating what are the most general axiomatizations of expected utility existing today.     

Generic non-existence of general equilibrium with EUU preferences under extreme ambiguity

In the presence of three or more realisations of the aggregate endowment that are extremely ambiguous, in the sense that all relative probabilities are admissible, if agents have preferences that are representable by expected uncertain utility functions (Gul and Pesendorfer, 2014), general equilibrium does not generically exist in finite economies. It always exists, however, in continuum economies.     

The relationship between revealed preference and the Slutsky matrix

This paper presents a method of calculating the utility function from a smooth demand function whose Slutsky matrix is negative semi-definite and symmetric. The calculated utility function is the unique upper semi-continuous function corresponding with the demand function. Moreover, we present an axiom for demand functions. We show that under the strong axiom, this new axiom is equivalent to the existence of the corresponding continuous preference relation. If the demand function obeys this axiom, the calculated utility function is also continuous. Further, we show that the mapping from the demand function into a continuous preference relation is continuous, which ensures the applicability of our results for econometrics. Moreover, if this demand function satisfies the rank condition, then our utility function is smooth. Finally, we show that under an additional axiom, the above results hold even if the demand function has corner solutions.     

A utility representation theorem with weaker continuity condition

We prove that a mixture continuous preference relation has a utility representation if its domain is a convex subset of a finite dimensional vector space. Our condition on the domain of a preference relation is stronger than Eilenberg (1941) and Debreu (1959, 1964), but our condition on the continuity of a preference relation is strictly weaker than the usual continuity assumed by them.     

Risk and prices in separable utility functions

Many decision problems involve more than one attribute. Separable multi-attribute utility functions are commonly used to model preferences in such situations. We consider the case in which one attribute can be identified as money. The price at which non-monetary attributes may be substituted by money, the relation of this price to a decision-maker's wealth, and the implications on attitudes toward risk are examined for additively and multiplicatively separable multi-attribute utility functions. In particular, it is shown that additive separability, price independent of wealth and monetary risk-aversion are mutually inconsistent.     

Reconciling introspective utility with revealed preference: Experimental arguments based on prospect theory

In an experiment, choice-based (revealed-preference) utility of money is derived from choices under risk, and choiceless (non-revealed-preference) utility from introspective strength-of-preference judgments. The well-known inconsistencies of risky utility under expected utility are resolved under prospect theory, yielding one consistent cardinal utility index for risky choice. Remarkably, however, this cardinal index also agrees well with the choiceless utilities, suggesting a relation between a choice-based and a choiceless concept. Such a relation implies that introspective judgments can provide useful data for economics, and can reinforce the revealed-preference paradigm. This finding sheds new light on the classical debate on ordinal versus cardinal utility.     

The shared reward dilemma on structured populations

In this paper we study the recently introduced “shared reward dilemma” (Cuesta et al. in J Theor Biol 251:253–263, 2008) in the presence of a structure governing the interactions among the population. The shared reward dilemma arises when the prisoner’s dilemma is supplemented with a second stage in which a fixed reward is equally distributed among all cooperators. We first extend our previous results on the equilibrium structure of this game to the case of a one-shot game taking place on a regular network. Subsequently, we consider an evolutionary version of the game on both lattices and random networks. We show that the evolutionary game on graphs exhibits important differences with the case of well-mixed populations. In particular, there exists an important parameter range in which the cooperation is boosted and a single cooperator can invade a population of defectors. We study the dependence of the cooperation levels on the neighborhood size, finding that on random networks the level of cooperation reached decreases as the neighborhood size increases. Moreover, square lattices favor cooperation more than random networks, and on them cooperation may be almost full for certain parameter regions even for large neighborhood sizes. Further, we show that the effect of the population structure is never detrimental for cooperation. We interpret our results in terms of weak versus strong temptation and discuss the nontrivial issues involved in trying to promote cooperation exogenously by means of such a reward mechanism.     

Measuring utility from demand

This study presents a new method to calculate a preference relation from a demand function. Our method works well under the weak axiom and can calculate a smooth utility function if the demand function obeys the strong axiom. Further, if the demand function is derived from a customary utility function, our method restores the original preference. Our method provides a complete and rigorous proof of Samuelson’s conjecture. In addition to these results, we guarantee the recoverability: i.e., the uniqueness of the preference relation corresponding to a demand function.     

Representation of transferable utility games by coalition production economies

We prove that, by the method of construction of a coalition production economy due to Sun et al. [Sun, N., Trockel, W., Yang, Z., 2008. Competitive outcomes and endogenous coalition formation in an n$n$-person game. Journal of Mathematical Economics 44, 853–860], every transferable utility (TU) game can be generated by a coalition production economy. Namely, for every TU game, we can construct a coalition production economy that generates the given game. We briefly discuss the relationship between the core of a given TU game and the set of Walrasian payoff vectors for the induced coalition production economy.     

A customer’s utility measure based on the reliability of multi-state systems

The main focus of this paper is on the development of utility measures for dynamic multi-state systems that have M + 1 discrete states of working efficiency. To develop the utility measures for multi-state systems, we assume that the degradation of the multi-state systems follows a non-homogeneous semi-Markov process together with a backward recurrence time process and that the system can directly degrade into any lower state. The measure considers the immediate utility derived from the state of the system occupancy and the utility due to the system survival expectations derived from its reliability. Moreover, in order to measure the customer’s cumulative utility, the discounted non-homogeneous continuous time semi-Markov process with rewards is implemented. In such a way, the higher order moments of the reward process can be evaluated and then, in particular, the expectation and the standard deviation of the consumer’s accumulated discounted utility. These statistic indices are useful both to the industry in order to compare different system designs offered by the market and to the market itself, in order to know the customer’s utility deriving from the goods she/he consumes. Finally, a numerical example shows the possibility of implementing the model in real-life problems.