THE 2009 LAWRENCE R. KLEIN LECTURE: DIVERSIFIED TREATMENT UNDER AMBIGUITY*

This article develops a broad theme about treatment under ambiguity through study of a particular decision criterion. The broad theme is that a planner may want to cope with ambiguity by diversification, assigning observationally identical persons to different treatments. Study of the minimax‐regret (MR) criterion substantiates the theme. The article significantly extends my earlier analysis of one‐period planning with an individualistic treatment and a linear welfare function. I show that MR treatment allocations are fractional in a large class of planning problems with nonlinear welfare functions, interacting treatments, learning, and noncooperative aspects.     

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.     

Regret aversion and opportunity dependence

This paper provides an axiomatic model of decision making under uncertainty in which the decision maker is driven by anticipated ex post regrets. Our model allows both regret aversion and likelihood judgement over states to coexist. Also, we characterize two special cases, minimax regret with multiple priors that generalizes Savage's minimax regret, and a smooth model of regret aversion.     

OPTIMISM AND PESSIMISM IN GAMES

This article considers the impact of ambiguity in strategic situations. It extends the existing literature on games with ambiguity‐averse players by allowing for optimistic responses to ambiguity. We use the CEU model of ambiguity with a class of capacities introduced by Jaffrray and Philippe (Mathematics of Operations Research 22 (1997), 165–85), which allows us to distinguish ambiguity from ambiguity‐attitude, and propose a new solution concept, equilibrium under ambiguity (EUA), for players who may be characterized by ambiguity‐preference. Applying EUA, we study comparative statics of changes in ambiguity‐attitude in games with strategic complements. This extends work in Eichberger and Kelsey (Journal of Economic Theory 106 (2002), 436–66) on the effects of increasing ambiguity if players are ambiguity averse.     

Minimax regret with imperfect ex-post knowledge of the state

We consider decision problems under complete ignorance and extend the minimax regret principle to situations where, after taking an action, the decision maker does not necessarily learn the state of the world. For example, if the decision maker only learns what the outcome is, then all she knows is that the actual state is one of the (possibly several) states that yield the observed outcome under the chosen action. We refer to this situation as imperfect ex-post information. We show that, given a choice between more information and less information, the decision maker prefers the latter. We also extend the framework to encompass the possibility of less than the extreme degree of pessimism that characterizes the minimax regret criterion.     

The weak core of simple games with ordinal preferences: implementation in Nash equilibrium

In a simple game, coalitions belonging to a given class are “absolutely powerful” while others have no power. We attempt to make this distinction operational. Toward this end, we propose two axioms on social choice correspondences, Strong Non-Discrimination and Exclusion. Strong Non-Discrimination describes circumstances under which certain coalitions, the losing coalitions, have no influence over social choice. Exclusion requires that there are situations in which certain coalitions, the winning coalitions, can exercise their power. We show that the weak core correspondence is the minimal correspondence satisfying Maskin Monotonicity and Strong Non-Discrimination. We also show that the weak core is the unique correspondence satisfying Nash implementability, Strong Non-Discrimination, and Exclusion.     

Fixed versus variable rate loans under regret aversion

This paper examines the optimal mix of fixed and variable rate loans of a competitive bank facing funding cost uncertainty, where the bank is not only risk averse but also regret averse. Regret aversion is characterized by a utility function that includes disutility from having chosen ex-post suboptimal alternatives. We show that a negative spread between fixed and variable rate loans is a necessary but not sufficient condition for the dominance of variable rate loans over fixed rate loans. If the bank optimally extends both fixed and variable rate loans, the total amount of loans depends neither on the bank's regret aversion nor on the funding cost uncertainty. The bank, however, optimally lends less should it be forced to assume the entire funding cost uncertainty by exclusively extending fixed rate loans. Finally, using a two-state example, we show that the bank optimally extends more (less) fixed rate loans than in the case of pure risk aversion if the high (low) marginal cost of funds is more likely to prevail. Regret aversion as such plays a crucial role in determining the bank's optimal choice between fixed and variable rate loans.     

The effects of environmental taxes and quotas on the optimal timing of emission reductions under Choquet–Brownian uncertainty

The effects of two environmental policy options for the reduction of pollution emissions, i.e. taxes and non-tradable quotas, are analyzed. In contrast to the prior literature this work endogenously takes into account the level of emissions before and after the adoption of the new environmental policy. The level of emissions is determined by solving the firm's profit maximization problem under taxes and fixed quotas. We find that the optimal adoption threshold under taxes is always larger than the adoption threshold under fixed quota, even in a setting characterized by ecological uncertainty and ambiguity – in the form of Choquet–Brownian motions – on future costs and benefits over adopting environmental policies.     

基于后悔规避的投资组合模型及其实证分析

由于人的情感、认知等因素对投资活动有直接影响,本文在投资活动中引入人的情感因素,提出了基于后悔规避的投资者效用函数,该效用函数是期末财富和预期财富的函数。建立了存在无风险资产时的最优投资组合模型,发现基于后悔规避投资组合模型的组合前沿存在两基金分离的现象。对我国上海股票市场进行了实证分析,得到了基于后悔规避投资组合模型的组合前沿,并验证了组合前沿存在两基金分离现象的结论。     

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.     

Adverse selection under ignorance

Summary. We examine an adverse selection relationship in which the principal may ignore the ex ante distribution of the agent's types. The principal's behavior is described by a disutility function that covers the standard minimax regret and minimax loss criteria. We show that the incentive compatible and individually rational mechanism, which minimizes the maximal (or the minimal) principal's disutility over a set of priors, requires the efficient agents to realize the corresponding first-best actions and may demand actions lower than the first-best ones from less efficient agents. We also analyze the qualitative differences between the case in which the principal considers regrets and the case in which he considers losses. Received: 19 October 1998; revised version: 9 November 1999     

Non-cooperative solutions for estate division problems

In an estate division problem an estate has to be divided among several players whose total entitlement to the estate exceeds its size. This paper extends the non-cooperative approach through a claim game, as initiated by O?Neill (1982), by allowing players to put multiple claims on the same part of the estate, and by considering the case where individual entitlements may exceed the estate. A full characterization of the set of Nash equilibria of the claim game is obtained both for restricted estate division problems, where individual entitlements do not exceed the estate, and for the general case. Variations on the claim game are considered, which result in proportional division in equilibrium.     

The minimum approval mechanism implements the efficient public good allocation theoretically and experimentally

We propose the minimum approval mechanism (MAM) for a standard linear public good environment with two players. Players simultaneously and privately choose their contributions to the public good in the first stage. In the second stage, they simultaneously decide whether to approve the otherʼs choice. Both contribute what they choose in the first stage if both players approve; otherwise, both contribute the minimum of the two choices in the first stage. The MAM implements the Pareto-efficient allocation in multiple solution concepts including backward elimination of weakly dominated strategies (BEWDS), limit logit agent quantal response equilibrium, subgame perfect minimax regret equilibrium, level-k thinking, and diagonalization heuristics. Moreover, the MAM is unique under plausible conditions. Overall, contributions in the MAM experiment averaged 94.9%. Quantifying subjectsʼ responses to the questionnaire reveal heterogeneous reasoning processes and highlight the importance of developing mechanisms that implement the desired social choice outcome in multiple solution concepts.     

Modelling under ambiguity with dynamically consistent Choquet random walks and Choquet–Brownian motions

Ambiguity is pervasive in many environments and is increasingly being introduced into economic and financial models. This paper characterises ambiguity in the form of newly defined Choquet random walks: discrete-time binomial trees with capacities instead of exact probabilities on their branches. We describe the axiomatic basis of Choquet random walks, including dynamic consistency. We also discuss the convergence of Choquet random walks to Choquet–Brownian motion in continuous time. In contrast to previous literature, we derive tractable stochastic processes that allow for a wide range of ambiguity preferences to be represented in continuous time (including ambiguity-seeking preferences). Finally, we apply Choquet–Brownian ambiguity to a model of stationary inter-temporal portfolio choice. We find that both the mean and the variance of the underlying stochastic process are modified. This result opens the way for qualitative and quantitative results that differ from those of standard expected utility models and other models that feature ambiguity.     

Minimax regret and strategic uncertainty

This paper introduces a new solution concept, a minimax regret equilibrium, which allows for the possibility that players are uncertain about the rationality and conjectures of their opponents. We provide several applications of our concept. In particular, we consider price-setting environments and show that optimal pricing policy follows a non-degenerate distribution. The induced price dispersion is consistent with experimental and empirical observations (Baye and Morgan (2004) [4]).     

THE SIZE DISTRIBUTION OF INCOME: AN INTERNATIONAL COMPARISON

This paper collects and extends the available data on size distribution of income by country, and then uses these data to develop an hypothesis about the relation of stage and mode of development to the distribution of income. In particular, the author attributes the increase in income inequality which often occurs in the early stages of economic development to the uneven spread of capitalist modes of production, which leads to a dualism which separates the capitalist sector from the rest of the economy. The author goes on to discuss the role of this dualism in increasing the inequalities existing in the society. Finally, the author contrasts the income distributions found in socialist countries with those of capitalist ones, and concludes that it is not economic growth per se , but rather the capitalist mode of production, which creates income inequalities in developing countries.     

Spillovers through backward linkages from multinationals: Measurement matters!

We argue that the measures of backward linkages used in recent papers on spillovers from multinational companies are potentially problematic, as they depend on a number of restrictive assumptions, namely that (i) multinationals use domestically produced inputs in the same proportion as imported inputs, (ii) multinationals have the same input sourcing behaviour as domestic firms, irrespective of their country of origin, and (iii) the demand for locally produced inputs by multinationals is proportional to their share of locally produced output. We discuss why these assumptions are likely to be violated in practice, and provide alternative measures that overcome these drawbacks. Our results, using plant level data for Ireland, clearly show that the choice of backward linkage measure and thus, the assumptions behind it, matters greatly in order to draw possible conclusions regarding the existence of foreign direct investment (FDI)-related spillovers. Using the standard measure employed in the literature we fail to find robust evidence for spillovers through backward linkages. However, when we use alternative measures of backward linkages that relax assumptions (i)–(iii), we find robust evidence for positive FDI backward spillover effects.     

Consistent firm choice and the theory of supply

Summary. This paper analyzes the problem of deriving predictions, regarding supply behavior of a competitive firm, from prior consistency postulates about input-output choices made by such a firm. It extends the literature by introducing a consistency postulate for firm choice, which is weaker than profit-maximization. This consistency postulate is nevertheless both necessary and sufficient for supply responses predicted by the standard theory of firm choice based on the postulate of profit-maximization. Furthermore, our rationality postulate, in conjunction with another condition, is shown to be equivalent to firm choice behavior that can be rationalized in terms of profit maximization.Received: 11 April 2003, Revised: 26 April 2004, JEL Classification Numbers: D21.Indraneel Dasgupta: I thank Bhaskar Dutta and two anonymous referees for helpful comments on earlier versions.     

A comparison of regret-based and utility-based discrete choice modelling – an empirical illustration with hospital bed choice

There is some concern that the unobserved preference heterogeneity in random utility maximization theory-based discrete choice experiment modelling is an important source of error variability. The randomness in utility is often interpreted as interpersonal preference heterogeneity but it can also be intrapersonal random variation in preferences. We compare utility maximization and regret minimization-based choice models’ sensitivity to individual heterogeneity, examine differences between two consecrated models and validate with empirical illustrations. We use frequency of category (public, semi-private, and private) of bed chosen from Swiss cross-sectional datasets (2007–2012) to compare two approaches – utility maximization and regret minimization by applying multinomial logit (MNL) models in regard to the variances in utility (regret) function, goodness-of-fit and predicted marginal effects (pseudo-elasticity) of additional payment. We find parameters with the same sign and estimates with almost same order of magnitude in both the approaches. The statistical significance of attribute effects is consistent in all variants of utility -based MNL models while effects of different attributes are significant only in heteroskedastic extreme value (HEV) variant of regret-based MNL models. This empirical illustration suggests that HEV variant of regret-based models perform better in capturing attribute effects in choice behaviour.     

Income distributions and decomposable divergence measures

Inequality indices evaluate the divergence between the income distribution and the hypothetical situation where all individuals receive the mean income, and are unambiguously reduced by a Pigou–Dalton progressive transfer. This paper proposes a new approach to evaluate the divergence between any two income distributions, where the latter can be a reference distribution for the former. In the case where the reference distribution is perfectly egalitarian – and uniquely in this case – we assume that any progressive transfer reduces the divergence, and that the divergence can be additively separated into inequality and efficiency loss. We characterize the unique class of decomposable divergence measures consistent with these views. We derive the associated relative and absolute subclasses, and we illustrate the applicability of our results. This approach extends the generalized entropy studied in inequality measurement.