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.     

Measuring systemic risk with regime switching in tails

This paper motivates the importance of modeling nonlinearities in measuring systemic risk. I capitalize this motivation by generalizing the CoVaR approach proposed by Adrian and Brunnermeier (2016) to allow it switching between a high and a normal risk regime filtered from data.. Considering the U.S. large bank holding companies (BHCs), this paper shows that modeling regime changes in tails is capable of capturing both amplification and mean-reversion effects of an adverse shock to a bank's balance sheet on the banking system. Using the Kolmogorov–Smirnov test statistics with and without bootstrapping, I perform the significance test to identify systemically important financial institutions (SIFIs), and the stochastic dominance test to rank the identified SIFIs. The stochastic dominance test raises the concern that the CoVaR measure underestimates systemic risk contributions for SIFIs but overestimates for non-SIFIs. Finally, applying the BHCs' characteristics and housing market price to forecast the regime-switching systemic risk out-of-sample, I obtain from 4- and 8-quarter-ahead horizons a desirable countercyclical, forward-looking measure of systemic risk.     

Increasing Dominance with No Efficiency Effect

I uncover a new force towards increasing dominance (the property whereby, in dynamic games, the leader tends to increase his or her lead in expected terms). The new effect results from the strategic choice of covariance in races. I assume that players must choose not the amount of resources to spend but how to allocate those resources. I show that, in equilibrium, the laggard chooses a less promising path, in effect trading off lower expected value for lower correlation with respect to the leader. This results in increasing dominance and holds true even if no joint-payoff (or efficiency) effect is present. Journal of Economic Literature Classification Numbers: C7, L1.     

On Choquet prices in a GEI-model with intermediation costs

This article analyses whether the representation of asset prices by Choquet integration can be justified from a general equilibrium point of view. We demonstrate that if transaction costs functionals are increasing in the volume of trade, positive homogeneous and satisfy an additivity condition, the equilibrium price functional typically does not satisfy all the Choquet properties. Whereas subadditivity and positive homogeneity can be shown to hold for the equilibrium price functional, this is generally not the case for monotonicity and additivity of prices for comonotone income streams.     

Bivariate almost stochastic dominance

Univariate almost stochastic dominance has been widely studied and applied since its introduction by Leshno and Levy (Manag Sci 48:1074–1085, 2002). This paper extends this construction to the bivariate case by means of suitable two-attribute utility functions. After having confined correlation aversion and correlation loving to some acceptable levels, bivariate almost stochastic dominance rules are introduced for the preferences exhibiting confined correlation aversion and confined correlation loving. The impact of a change in risk in terms of bivariate almost stochastic dominance on optimal saving is analyzed as an application, as well as the effect of envy and altruism on income distributions. Finally, alternative definitions of bivariate almost stochastic dominance are discussed, as well as testing procedures for such dominance rules in financial problems.     

On efficiency of the English auction

We study efficiency properties of the irrevocable exit English auction in a setting with interdependent values. Maskin (1992) [1] shows that the pairwise single-crossing condition is sufficient for efficiency of the English auction with two bidders and suggests that it is also a necessary condition. This paper clarifies and extends Maskin?s results to the case of N bidders. We introduce the generalized single-crossing condition—a fairly intuitive extension of the pairwise single-crossing condition—and prove that it is essentially a necessary and sufficient condition for the existence of an efficient equilibrium of the N-bidder English auction.     

Diversification of interdependent prospects

This paper extends the stochastic dominance approach to the problem of diversification of interdependent prospects. One basic result is that a risk averter should always mix any two identically distributed prospects, regardless of the nature of the interdependence between them. A similar result holds for the case of n prospects, provided all the joint distribution functions of dimension n ? 1 are identical. When the n-dimensional joint distribution function is symmetric, then the optimal strategy is to put an equal amount into each prospect. The paper also provides conditions which make diversification optimal in the absence of identical marginal distributions.     

Cost-Effective and Stochastic Dominance Approaches to Stochastic Pollution Control

Most economic studies of pollution externalities focus on the relative efficiency or cost-effectiveness of alternative pollution control instruments. Much less attention has been paid to policy goals and objectives. However, a comprehensive pollution control strategy depends on all of these choices. This paper examines several efficiency properties of cost-effective pollution control strategies in a stochastic setting when economic damages from pollution are unknown. A number of policy goals are considered. In this setting and under a primal approach, it is found that certain stochastic dominance conditions must be satisfied for the strategies to exhibit desirable efficiency properties. A dual approach to cost-effective pollution control, which is based on a stochastic dominance objective, is also considered.     

Stronger measures of higher-order risk attitudes

This paper aims to extend the results by Ross (1981) [15] and by Modica and Scarsini (2005) [13] to stochastic dominance of degree 4 and over. Specifically, it is shown that Ross' approach can be extended to any order of risk attitude beyond the generalization proposed by Modica and Scarsini by means of sth degree increase in risk defined by Ekern (1980) [8].     

Asymmetric first price auctions

A new approach to asymmetric first price auctions is proposed which circumvents the need to examine bidding strategies directly. Specifically, the ratio of bidders' (endogenous) payoffs is analyzed and compared to the ratio of the (exogenous) distribution functions that describe beliefs. Most of the results are inferred from this comparison. In the existing theoretical literature, assumptions of first order stochastic dominance or stronger imply that the latter ratio has very specific properties, but no such assumptions are imposed here. It is proven that first order stochastic dominance is necessary for bidding strategies not to cross. When this assumption is relaxed in the numerical literature it is done in a manner that leads to exactly one crossing. However, it is straightforward to construct examples with several crossings. Finally, bid distributions will cross in auctions with two bidders whenever second order (but not first order) stochastic dominance applies.     

Pricing decisions and strategies selection of dominant manufacturer in dual-channel supply chain

This paper investigates the dominance strategies exerted by the dominant manufacturer for maintaining its dominant position in the channel system which is operating substitutable products and what influences they have on members of the whole channel system and the consumers. As to the channel system with two manufacturers and one retailer, the pricing decisions are depicted to compare the optimal choices made by the system members under the dominant manufacturer's wholesale price dominance strategy and channel dominance strategy, respectively. It shows that only the dominant manufacturer can necessarily benefit from the wholesale price dominance strategy. Furthermore, both dominant manufacturer and retailer can benefit from the channel dominance strategy, and consumers can also benefit from it. The channel dominance strategy, however, is not always the optimal choice for the dominant manufacturer. Whatever dominance strategy is it, the weak manufacturer will suffer loss, but in the channel dominance strategy, the market share proportion of the weak manufacturer will increase under certain circumstances.     

Legal conflicts of interest of the revolving door

This paper analyzes the conflicts of interest arising from the “revolving door”. The revolving door is a common phenomenon, and it is unlikely that most of it can be explained by ‘regulatory capture’, a practice that is unlawful. Therefore, there is a need for a new framework.This paper proposes a framework wherein conflicts of interest arising from the revolving door are not unlawful, as is in the case of regulatory capture, but still lead to economic distortions. The paper introduces a market for bureaucratic capital, which explains why in equilibrium, the government allows this unethical, yet not unlawful, conflict of interest to persist. Our first result is that the political elite finds it optimal to allow the existence of the revolving door, as well as the creation of bureaucratic capital. The second result is that in equilibrium, the revolving door leads to an excessive level of bureaucratic capital. As a consequence, the interconnection of elites and the existence of the revolving door actually lead to lower economic growth.     

Technology adoption in markets with network effects: Theory and experimental evidence

We examine a technology-adoption game with network effects in which coordination on either technology A or technology B constitutes a Nash equilibrium. Coordination on technology B is assumed to be payoff dominant. We define a technology’s critical mass as the minimal share of users, which is necessary to make the choice of this technology the best response for any remaining user. We show that the technology with the lower critical mass implies risk dominance and selection by the maximin criterion. We present experimental evidence that both payoff dominance and risk dominance explain participants’ choices in the technology-adoption game. The relative riskiness of a technology can be proxied using either technologies’ critical masses or stand-alone values absent any network effects.     

Incentive monotonicity and equilibrium selection in 2×2 matrix games

For the class of 2×2 matrix games with two strict Nash equilibria the paper introduces an equilibrium refinement called incentive monotonicity. It selects the risk-dominant equilibrium if interests are conflicting, while it remains silent in games with common interests. These results suggest that the equilibrium-selection problem might be more difficult in games with common interests, which is certainly the case if risk dominance and payoff dominance go in opposite directions.     

Satisficing and optimality in 2×2 common interest games

Summary. The paper studies the evolution of cooperation when satisficing players repeatedly play a symmetric two-by-two game of common interest. We show that if initial aspiration levels are sufficiently close to the efficient payoff and aspiration adjusts at a sufficiently slow speed then the unique long run state will be the efficient outcome. In the special case of coordination games, the more tension there is between payoff dominance and risk dominance, the longer it takes for the system to lock into the payoff dominant outcome. Received: June 23, 1997; revised version: November 19, 1997     

Second-best efficiency of allocation rules: strategy-proofness and single-peaked preferences with multiple commodities

We study strategy-proof allocation rules in economies with perfectly divisible multiple commodities and single-peaked preferences. In this setup, it is known that the incompatibility among strategy-proofness, Pareto efficiency and non-dictatorship arises in contrast with the Sprumont (Econometrica 59:509–519, 1991) one commodity model. We first investigate the existence problem of strategy-proof and second-best efficient rules, where a strategy-proof rule is second-best efficient if it is not Pareto-dominated by any other strategy-proof rules. We show that there exists an egalitarian rational (consequently, non-dictatorial) strategy-proof rule satisfying second-best efficiency. Second, we give a new characterization of the generalized uniform rule with the second-best efficiency in two-agent case.     

On bidding with securities: Risk aversion and positive dependence

DeMarzo et al. (2005) consider auctions in which bids are selected from a completely ordered family of securities whose values are tied to the resource being auctioned. The paper defines a notion of relative steepness of families of securities and shows that a steeper family provides greater expected revenue to the seller. Two assumptions are: the buyers are risk neutral; the random variables through which values and signals of the buyers are realized are affiliated. We show that this revenue ranking holds for the second price auction in the case of risk aversion. However, it does not hold if affiliation is relaxed to a less restrictive form of positive dependence, namely first order stochastic dominance (FOSD). We define the relative strong steepness of families of securities and show that it provides a necessary and sufficient condition for comparing two families in the FOSD case. All results extend to the English auction.     

Undominated directions of tax reform

This article considers the reform of a commodity tax system. Consumers' preferences over directions of tax reform are constructed from indirect utility functions. A Wicksellian decision procedure is used to define a dominance relation on the set of directions of change; direction x dominates direction y if and only if (a) everybody prefers x to y or (b) x is the status quo and at least one person prefers x to y. A number of characterizations of undominated directions of change are provided. A related unanimity rule procedure, which does not single out the status quo for special treatment, is also considered. Particular attention is paid to the issue of whether Wicksellian reforms preserve production efficiency. Remarks on the relationship between this work, previous work in optimal taxation theory, and social choice theory are also provided.     

Pure exchange equilibrium of dynamic economic models

This paper studies competitive equilibrium over time of a one good model in which the agents are members of a population which grows at a constant rate. Each agent lives for n periods and in the i-th period of his life receives an endowment of e_i units of goods. Goods can neither be produced nor stored. The model is thus the n-period generalization of the two- and three-period models studied by Samuelson in [4]. We seek to ascertain the structure of the time paths of consumption in these models. Our results can be summarized roughly as follows: In general, there will exist two kinds of steady state paths, (i) golden rule paths in which the rate of interest equals the growth rate of population and (ii) “balanced” paths in which the aggregate assets or indebtedness of the society as a whole is zero (a fundamental fact about dynamic models is that it is possible for aggregate debt not to equal aggregate credit as it must in the static case). A model is termed classical if in the golden rule state aggregate assets are negative (or debt positive) and Samuelson (following [4]) in the opposite case. It is conjectured that the golden rule program is globally stable in the classical case and the balanced program is stable in the Samuelson case. This is established for the special case n = 2.     

Contract renegotiation in a continuous state space

Summary. When players are unable to write complete state contingent contracts it is shown, within the context of a non-cooperative contracting-renegotiation game, that the only subgame perfect equilibrium allocations are those that correspond to the set of first-best allocations. Players are able to implement this set of allocations by signing an initial contract that is subsequently renegotiated in all states of the world. The contracting-renegotiation problem is complicated in an interesting way by assuming that the state space is continuous. The issue of the existence of an initial contract, that is subsequently renegotiated to the set of first-best allocations, must be resolved. Unlike Aghion, Dewatripont and Rey [1994], the results here do not require nor depend upon the comonotonicity of the objective functions. Received: January 27, 1995; revised version July 1, 1996