Uniqueness of stationary equilibria in bargaining one-dimensional policies under (super) majority rules

We consider negotiations selecting one-dimensional policies. Individuals have instantaneous preferences represented by continuous, concave and single-peaked utility functions, and they are impatient. Decisions arise from a bargaining game with random proposers and (super) majority approval, ranging from the simple majority up to unanimity. We provide sufficient conditions that guarantee the existence of a unique stationary subgame perfect equilibrium, and we provide its explicit characterization. The uniqueness of the equilibrium permits an analysis of the set of Pareto optimal voting rules. For symmetric distributions of peaks and uniform recognition probabilities unanimity is the unanimously preferred majority rule.     

Representative consumer's risk aversion and efficient risk-sharing rules

We study the representative consumer's risk attitude and efficient risk-sharing rules in a single-period, single-good economy in which consumers have homogeneous probabilistic beliefs but heterogeneous risk attitudes. We prove that if all consumers have convex absolute risk tolerance, so must the representative consumer. We also identify a relationship between the curvature of an individual consumer's individual risk sharing rule and his absolute cautiousness, the first derivative of absolute risk-tolerance. Furthermore, we discuss some consequences of these results and refinements of these results for the class of HARA utility functions.     

Optimal financial investments for non-concave utility functions

We prove a formula for the computation of optimal financial investments in an expected utility framework with arbitrary (not necessarily concave) utility functions. This extends classical results on optimal financial investments for strictly concave utility functions and is of importance particularly for applications of prospect theory where the utility function has a convex-concave shape.     

Optimal stopping with dynamic variational preferences

We solve optimal stopping problems in uncertain environments for agents assessing utility by virtue of dynamic variational preferences as in Maccheroni, Marinacci and Rustichini (2006) [16] or, equivalently, assessing risk in terms of dynamic convex risk measures as in Cheridito, Delbaen and Kupper (2006) [4]. The solution is achieved by generalizing the approach in Riedel (2009) [21] introducing the concept of variational supermartingales and variational Snell envelopes with an accompanying theory. To illustrate results, we consider prominent examples: dynamic multiplier preferences and a dynamic version of generalized average value at risk introduced in Cheridito and Tianhui (2009) [5].     

Uniqueness of asset prices in an exchange economy with unbounded utility

Summary. This paper studies conditions under which the price of an asset is uniquely determined by its fundamental value – i.e., no bubbles can arise – in Lucas-type asset pricing models with unbounded utility. After discussing Gilles and LeRoy's (1992) example, we construct an example of a two-period, representative agent economy to demonstrate that bubbles can arise in a standard model if utility is unbounded below, in which case the stochastic Euler equation may be violated. In an infinite horizon framework, we show that bubbles cannot arise if the optimal sequence of asset holdings can be lowered uniformly without incurring an infinite utility loss. Using this result, we develop conditions for the nonexistence of bubbles. The conditions depend exclusively on the asymptotic behavior of marginal utility at zero and infinity. They are satisfied by many unbounded utility functions, including the entire CRRA (constant relative risk aversion) class. The Appendix provides a complete market version of our two-period example. Received: January 22, 1996; revised version: February 18, 1997     

Robust monopoly pricing

We consider a robust version of the classic problem of optimal monopoly pricing with incomplete information. In the robust version, the seller faces model uncertainty and only knows that the true demand distribution is in the neighborhood of a given model distribution. We characterize the pricing policies under two distinct decision criteria with multiple priors: (i) maximin utility and (ii) minimax regret. The equilibrium price under either criterion is lower then in the absence of uncertainty. The concern for robustness leads the seller to concede a larger information rent to all buyers with values below the optimal price without uncertainty.     

Asset pricing in large information networks

We study asset pricing in economies with large information networks. We focus on networks that are sparse and have power law degree distributions, in line with empirical studies of large scale social networks. Our theoretical framework yields a rich set of novel asset pricing implications. We derive closed form expressions for price, volatility, profitability and trading volume, as functions of the network topology. We also study agent welfare and show that the network that optimizes total welfare is typically a uniform one with an intermediate degree of connectedness.     

Optimal size, optimal timing and optimal financing of an investment

Corporate investment is an important determinant of economic well-being. The existing literature identifies optimal investment size and timing without the possibility of debt financing, as well as the effect of debt financing on investment timing without the option to choose investment size. This paper contributes to the literature by identifying the optimal size, optimal timing and optimal financing for an investment when the firm controls all three decisions (as it usually does in practice). The investment size and investment trigger are generally positively related: when investment is delayed (accelerated) it is larger (smaller) in size, thus the overall effect on investment is ambiguous. However, when tax rate or bankruptcy cost is increased, the trigger rises and size falls, hence the effect on investment is unambiguously negative. The effect of debt financing on investment depends on the amount of debt used; with the optimal amount of debt, investment is delayed relative to the no-debt case, and this delay can be economically significant; however, the investment, when eventually made, will be larger in size. Overall, it is not appropriate to ignore either the firm’s ability to choose investment size or its option to use debt financing, when modeling the investment decision.     

HETEROGENEOUS RISK ATTITUDES IN A CONTINUOUS‐TIME MODEL*

We prove that every continuous‐time model in which all consumers have time‐homogeneous and time‐additive utility functions and share a common probabilistic belief and a common discount rate can be reduced to a static model. This result allows us to extend some of the existing results of the representative consumer and risk‐sharing rules in static models to continuous‐time models. We show that the equilibrium interest rate is lower and more volatile than in the standard representative consumer economy, and that the individual consumption growth rates are more dispersed than in the absence of uncertainty.     

The relationship between risk attitudes and heuristics in search tasks: A laboratory experiment

Experimental studies of search behavior suggest that individuals stop searching earlier than the optimal, risk-neutral stopping rule predicts. Two different classes of decision rules could generate this behavior: rules that are optimal conditional on utility functions departing from risk neutrality, or heuristics derived from limited cognitive processing capacities and satisficing. To discriminate between these possibilities, we conducted an experiment that consists of a search task as well as a lottery task designed to elicit utility functions. We find that search heuristics are not related to measures of risk aversion, but to measures of loss aversion.     

The robustness of robust implementation

We show that a mechanism that robustly implements optimal outcomes in a one-dimensional supermodular environment continues to robustly implement ε-optimal outcomes in all close-by environments. Robust implementation of ε-optimal outcomes is thus robust to small perturbations of the environment. This is in contrast to ex-post implementation which is not robust in this sense as only trivial social choice functions are ex-post implementable in generic environments.     

Consumption Commitments and Employment Contracts

We examine an economy in which the cost of consuming some goods can be reduced by making commitments that reduce flexibility. We show that such consumption commitments can induce consumers with risk-neutral underlying utility functions to be risk averse over small variations in income, but sometimes to seek risk over large variations. As a result, optimal employment contracts will smooth wages conditional on being employed, but may incorporate a possibility of unemployment.     

Dual theory of choice with multivariate risks

We propose a multivariate extension of Yaari?s dual theory of choice under risk. We show that a decision maker with a preference relation on multidimensional prospects that preserves first order stochastic dominance and satisfies comonotonic independence behaves as if evaluating prospects using a weighted sum of quantiles. Both the notions of quantiles and of comonotonicity are extended to the multivariate framework using optimal transportation maps. Finally, risk averse decision makers are characterized within this framework and their local utility functions are derived. Applications to the measurement of multi-attribute inequality are also discussed.     

Misery loves company: Social regret and social interaction effects in choices under risk and uncertainty

Extensive field evidence shows individuals? decisions in settings involving uncertainty depend on their peers? decisions. One hypothesized cause of peer group effects is social interaction effects: an individual?s utility from an action is enhanced by others taking the same action. We employ a series of controlled laboratory experiments to study the causes of peer effects in choice under uncertainty. We find strong peer group effects in the laboratory. Our design allows us to rule out social learning, social norms, group affiliation, and complementarities as possible causes for the observed peer group effects, leaving social interaction effects as the likely cause. We use a combination of theory and empirical analysis to show that preferences including “social regret” are more consistent with the data than preferences including a taste for conformity. We observe spillover effects, as observing another?s choice of one risky gamble makes all risky gambles more likely to be chosen.     

Risk Aversion and the Investment Horizon: A New Perspective on the Time Diversification Debate

Investment managers generally subscribe to the principle of time diversification. This implies that a larger portion of the portfolio should be devoted to risky assets as the investment horizon increases. In contrast, academics have shown that for investors with utility functions characterized by constant relative risk aversion, the optimal asset-allocation strategy is independent of the investment horizon. The relative risk aversion in these studies is assumed to be constant both with respect to wealth as well as investment horizon. We suggest a utility function that explicitly captures the notion that individuals are more risk tolerant when the investment horizon is long, thereby validating the intuitively appealing time diversification argument.     

Utility Functions whose Parameters depend on Initial Wealth

Conventional one-period utility functions in Economics assume that initial wealth only enters preferences through the definition of final wealth. Consequently, those utility functions most utilized (i.e., exponential and quadratic) have implausible risk characteristics. The authors characterize a new class of utility function whose risk parameters depend upon initial wealth and obtain several desirable results. In particular, investors with quadratic and exponential utility functions can have decreasing risk aversion, and risky assets in a quadratic utility multi-asset environment do not have to be inferior as implied by the traditional framework.     

A new test for linear inequality constraints when the variance–covariance matrix depends on the unknown parameters

We extend Hansen’s (2005) test to testing hypotheses involving general inequality constraints where the variance–covariance matrix of the functions in the constraints depends on the unknown parameters. The test can be applied to a wider class of problems than Wolak’s (1991).     

Optimal risk sharing and borrowing constraints in a continuous-time model with limited commitment

We study a continuous-time version of the optimal risk-sharing problem with one-sided commitment. In the optimal contract, the agent?s consumption is a time-invariant, strictly increasing function of a single state variable: the maximal level of the agent?s income realized to date. We characterize this function in terms of the agent?s outside option value function and the discounted amount of time in which the agent?s income process is expected to reach a new to-date maximum. Under constant relative risk aversion we solve the model in closed-form: optimal consumption of the agent equals a constant fraction of his maximal income realized to date. In the complete-markets implementation of the optimal contract, the Alvarez–Jermann solvency constraints take the form of a simple borrowing constraint familiar from the Bewley–Aiyagari incomplete-markets models.     

Endogenous market power

In this paper we develop a framework to study markets with heterogeneous atomic traders. The competitive model is augmented as we provide traders with correct beliefs about their price impacts to define equilibrium with endogenously determined market power and show that such equilibrium exists in economies with smooth utility and cost functions and is generically determinate. Traders? price impacts depend positively on the convexity of preferences or cost functions of the trading partners and are subject to mutual reinforcement. Compared to the competitive model, the volume of trade is reduced, and hence is Pareto inefficient. The price effects of non-competitive trading depend on the convexity of marginal utility or cost function.     

Probabilistic sophistication and variational preferences

This paper shows that in the class of variational preferences the notion of probabilistic sophistication is equivalent to expected utility as long as there exists at least one event such that the independence axiom holds for bets on that event. This extends the result of Marinacci (2002) [13] and provides a novel interpretation of his result.