Completing the State Space with Subjective States

We define an opportunity act as a mapping from an exogenously given objective state space to a set of lotteries over prizes, and consider preferences over opportunity acts. We allow the preferences to be possibly uncertainty averse. Our main theorem provides an axiomatization of the maxmin expected utility model. In the theorem we construct subjective states to complete the objective state space. As in E. Dekel et al. (Econometrica, in press), we obtain a unique subjective state space. We also allow for preference for flexibility in some of the subjective states and commitment in others. Journal of Economic Literature Classification Number: D81.     

Event-Separability in the Ellsberg urn

Ellsberg??s three-color urn involves two distinct sources of uncertainty??the color composition of the urn (which is subjective) and the identity of the drawn ball (which is objective)??and bets on it can involve mixed objective/subjective uncertainty. It is known that typical betting preferences on this urn violate both the Sure-Thing Principle and probabilistic sophistication over its mixed uncertainty but are consistent with both of them over its purely subjective uncertainty. In this paper, we show that the standard Ellsberg-type preference reversal is actually implied by the Independence Axiom over its purely objective uncertainty.     

Subjective Uncertainty over Behavior Strategies: A Correction

In order to model the subjective uncertainty of a player over the behavior strategies of an opponent, one must consider the player's beliefs about the opponent's play at information sets that the player thinks have probability zero. This corregendum uses “trembles” to provide a definition of the convex hull of a set of behavior strategies. This corrects a definition we gave in [E. Dekel, D. Fudenberg, and D. K. Levine, 1999, J. Econ. Theory89, 165-185], which led to two of the solution concepts we defined there not having the properties we intended. Journal of Economic Literature Classification Numbers: C72, D82, C610.     

Stationary cardinal utility and optimal growth under uncertainty

In the literature on multiperiod planning under uncertainty, it is generally postulated that preferences may be represented by a von Neumann-Morgenstern utility index that is additive over time. This paper accomplishes two objectives: First, an axiomatic basis is provided for a more general class of non-additive utility indices defined over infinite consumption streams. Second, this class of utility functions is applied to extend existing results (J. Econ. Theory4 (1972), 479–513; J. Econ. Theory11 (1975), 329–339) on the nature of optimal growth under uncertainty. Of particular interest are the existence and stability of a stochastic steady state.     

A theory of subjective compound lotteries

We develop a Savage-type model of choice under uncertainty in which agents identify uncertain prospects with subjective compound lotteries. Our theory permits issue preference; that is, agents may not be indifferent among gambles that yield the same probability distribution if they depend on different issues. Hence, we establish subjective foundations for the Anscombe-Aumann framework and other models with two different types of probabilities. We define second-order risk as risk that resolves in the first stage of the compound lottery and show that uncertainty aversion implies aversion to second-order risk which implies issue preference and behavior consistent with the Ellsberg paradox.     

Foreign trade,resource allocation,and structural adjustment in Yugoslavia: 1976–1980

A multisector computable general-equilibrium model for the Yugoslav economy is used to analyze some of the internal and external causes of the foreign-exchange crisis of the 1976–1980 period. Methodologically, its modeling approach, appropriately modified for institutional differences, can be used to study the behavior of socialist economies in which prices play a role in resource allocation. Empirically, the results suggest that internal policy errors and systemic factors were the predominant force behind Yugoslavia's growing foreign-exchange shortage between 1976 and 1980. J. Comp. Econ., March 1985, 9(1), pp. 46–70. University of California, Berkeley, California 94720.     

Preference for Flexibility and Dynamic Consistency

Dekel, Lipman, and Rustichini [3] characterize preferences over menus of lotteries that can be represented by the use of a unique subjective state space and a prior. We investigate what would be the appropriate version of Dynamic Consistency in such a setup. The condition we find, which we call Flexibility Consistency, is linked to a comparative theory of preference for flexibility. When the subjective state space is finite, we show that Flexibility Consistency is equivalent to a subjective version of Dynamic Consistency and that it implies that the decision maker is a subjective state space Bayesian updater. Later we characterize when a collection of signals can be interpreted as a partition of the subjective state space of the decision maker.     

Uncertainty avoidance and the rate of business ownership across 21 OECD countries, 1976–2004

Persistent differences in the level of business ownership across countries have attracted the attention of scientific as well as political debate. Cultural as well as economic influences are assumed to play a role. This paper deals with the influence of cultural attitudes towards uncertainty on the rate of business ownership across 21 OECD countries. First, the concepts of uncertainty and risk are elaborated, as well as their relevance for entrepreneurship. An occupational choice model is introduced to underpin our reasoning at the macro-level. Second, regression analysis using pooled macro data for 1976, 1990 and 2004 and controlling for several economic variables, yields evidence that uncertainty avoidance is positively correlated with the prevalence of business ownership. According to our model, a restrictive climate of large organizations in high uncertainty avoidance countries pushes individuals striving for autonomy towards self-employment. Regressions for these 3 years separately show that in 2004, this positive correlation is no longer found, indicating that a compensating pull of entrepreneurship in countries with low uncertainty avoidance may have gained momentum in recent years. Third, an interaction term between uncertainty avoidance and GDP per capita in the pooled panel regressions shows that the historical negative relationship between GDP per capita and the level of business ownership is substantially weaker for countries with lower uncertainty avoidance. This suggests that rising opportunity costs of self-employment play a less important role in this cultural environment, or are being compensated by increasing entrepreneurial opportunities.

Choice under uncertainty with the best and worst in mind: Neo-additive capacities

We develop the simplest generalization of subjective expected utility that can accommodate both optimistic and pessimistic attitudes towards uncertainty—Choquet expected utility with non-extreme-outcome-additive (neo-additive) capacities. A neo-additive capacity can be expressed as the convex combination of a probability and a special capacity, we refer to as a Hurwicz capacity, that only distinguishes between whether an event is impossible, possible or certain. We show that neo-additive capacities can be readily applied in economic problems, and we provide an axiomatization in a framework of purely subjective uncertainty.     

Core allocations and the dimension of the cone of efficiency price vectors

Let (R₁,…,R_k) be an arbitrary partition of the grand coalition in an atomless exchange economy with k “large enough.” We prove that an optimal allocation x belongs to the core if and only if x cannot be improved upon by any coalition that includes at least one of the R_i's. K is “large enough” if k ? r + 1, where r is the linear dimension of the cone P of the efficiency price vectors for x. Recall that it is always true that r ? n, when n is the number of commodities in the market, and that under differentiability and interiority r = 1; thus k can be chosen to be 2 (i.e., for any coalition R, an allocation x belongs to the core of the market if and only if x is not blocked by any coalition that either contains R or contains its complement).     

Free access vs private ownership: A comparison

Weitzman (J. Econ. Theory8 (1974), 225–234) has established that under free access properties of average or better quality will be overutilised relative to the efficient private property equilibrium. This leaves open the question of what happens to the low quality properties. It is shown here that there are conflicting considerations and the outcome is ambigous. Necessary and sufficient conditions are obtained for less of a variable input to be attracted to a site when access is free than when a private owner makes a charge for access.     

SUBJECTIVE EVALUATION IN AGENCY CONTRACTS*

We study how a principal uses her subjective evaluation of the agent's performance in an incentive contract. It is shown that the subjective evaluation can be used either 1) when there is no other information about the agent's performance and the principal is able to discard money, or 2) when the principal chooses between wage payment based on subjective evaluation by foregoing objective evaluation, and the one based only on the objective evaluation and when the subjective evaluation is sufficiently accurate. The principal pays a high fixed wage when her rating at the subjective evaluation is above a certain level. On the other hand, when it is below that level, she either pays a low fixed wage or obtains objective evaluation and pays based on its outcome.     

Individual option prices for climate change mitigation

Willingness-to-pay for climate change mitigation depends on people's perceptions about just how bad things will get if nothing is done. Individual subjective distributions for future climate conditions are combined with stated choices over alternative climate policies to estimate individual option prices (the appropriate ex ante welfare measure in the face of uncertainty) for climate change mitigation. We find statistically significant sensitivity of estimated option prices to both expected future conditions and uncertainty about future conditions.     

Rational responses and rational conjectures

This paper utilizes a pure-trade imperfect-competition model and discusses the rationality problem arising from the fact that agents have to make conjectures about the markets to set prices optimally. The objective is to show that there may be inefficient allocations with the agents behaving rationaly. In the same context Hahn (Rev. Econ. Stud.45 (1978), 1–17) proposed a notion of rationality under which the existence results obtained were negative. This paper argues that Hahn's is a strong notion of rationality that requires the mechanism to be incentive compatible. Thus, an alternative notion that refers exclusively to the rationality of the conjectures is proposed, and positive results on existence obtained.     

Aggregation and the existence of a social utility function

In a well-known paper Gorman (Econometrica21 (1953)) established that the necessary and sufficient condition for the existence of an aggregate, or social, utility function, independent of the distribution of income, is that all individuals' income consumption paths be parallel straight lines. Recently Chipman (J. Econ. Theory8 (1974)), building on the paper of Hurwicz and Uzawa (in “Preference Utility and Demand”) has shown that if the distribution of income is proportional and individual preferences are homothetic, aggregate consumption behavior obeys the necessary integrability conditions. It is shown here that the consistency of aggregate behavior can be derived from more general conditions than the ones used by Chipman and Gorman. Examples of demand systems from which aggregate behavior implies a social utility function are provided. It is then shown that if individual demand functions are linear in income—a form employed by both Gorman and Chipman—it is not necessary that the distribution of income be fixed.     

Socialism and incentives: Developing a framework

This paper proposes a framework for comparative analysis of economic systems that is broad enough to encompass not only variants of socialism, but also laissez-faire and other cases. The two basic components of the framework deal with information and incentives. A central problem is that of designing an incentive-compatible, informationally decentralized mechanism satisfying the requirements of optimality and fairness. Recent results show that there are limitations on the design of such mechanisms; in particular, it may be impossible to avoid lowering the level of satisfaction of some members of society in order to achieve equity and efficiency. J. Comp. Econ., Sept. 1979, 3(3), pp. 207–216. University of Minnesota, Minneapolis, Minnesota 55455.     

Willingness-to-pay for urban ecosystem services provision under objective and subjective uncertainty

There is growing concern that failure to acknowledge the risk and uncertainty surrounding ecosystem services (ES) delivery could have adverse effects on support for ES policy intervention in the long run. However, acknowledging risk may reduce support for policy interventions in the short term. In this paper, we sought to determine whether willingness-to-pay (WTP) for urban forest ES in Southampton, UK is affected by objective and subjective uncertainty surrounding ES delivery. We conducted a discrete choice experiment with a split sample design: one with a scenario specifying risky ES outcomes and one where zero risk was implied. Respondents’ subjective certainty surrounding the provision of ES was determined before and after the choice questions. Despite respondents’ risk aversion, introducing an objective likelihood attribute did not reduce WTP compared to the scenario with implied certain ES outcomes. Furthermore, whilst WTP for the overall scheme was found to be adversely affected by the presence of risk around ES outcomes, subjective uncertainty seemed to reduce WTP more than objective probabilities. Our results therefore support the idea that both objective probabilities and subjective uncertainty should be explicitly incorporated in the design of stated preference studies for ES valuation.     

Resource egalitarianism with a dash of efficiency

We study the problem of defining inequality-averse social orderings over allocations of commodities when individuals have different preferences. We formulate a notion of egalitarianism based on the axiom that any dominance between consumption bundles should be reduced. This Dominance Aversion requirement is compatible with Consensus, a version of the Pareto principle saying that an allocation y is better than x whenever everybody finds that everyone?s bundle at y is better than at x. We characterize a family of multidimensional leximin orderings satisfying Dominance Aversion and Consensus.     

A Suggested Interpretation of Some Experimental Results on Preplay Communication

M. Rabin (1994, J. Econ. Theory63, 370-391) proposes a model of behavior in two-person complete-information games with preplay communication, using non-equilibrium notions in the spirit of rationalizability to derive lower bounds on players' expected payoffs when players have unlimited communication opportunities. This paper adapts Rabin's model so that it can be used to analyze the results of the experiments of R. Cooper et al. (1989, Rand J. Econ.20, 568-587) on structured preplay communication in the Battle of the Sexes and the results of the unstructured bargaining experiments of Roth, Malouf, and Murnighan. Adding empirically motivated restrictions that allow the model to predict the payoff effects of changes in bounded communication possibilities like those in the experiments, it is shown that the data from both experiments are generally consistent with Rabin's model, and with the predictions of the extended model. Journal of Economic Literature Classification Numbers: C70, C72, C78, C91.     

How Communication Improves Efficiency in Bargaining Games

We study a double auction with two-sided private information and preplay communication, for which Myerson and Satterthwaite (1983, J. Econ. Theory28, 265–281) showed that all equilibria are inefficient and the Chatterjee–Samuleson linear equilibrium is most efficient. Like several others, we find that players use communication to surpass equilibrium levels of efficiency, especially when the communication is face-to-face. Our main contribution is an analysis of how communication helps the parties achieve such high levels of efficiency. We find that when preplay communication is allowed, efficiency above equilibrium levels is a result of what we call “dyadic” strategies that allow the parties to coordinate on a single price that reflects both parties' valuations. Journal of Economic Literature Classification Numbers: C78, D82.