Subjective Expected Utility Theory with State-Dependent Preferences

This paper extends Savage′s subjective expected utility theory to include state-dependent preferences. The dependence of the decision maker′s preferences over consequences on the states of nature is represented by state-specific mappings of the set of consequences onto itself. Within this framework Savage′s postulates are reformulated and it is shown that there exist subjective expected utility representations of the preference relation over acts with unique, nonatomic, probability measure on the algebra of all events, and a state-dependent utility function over the set of consequences. Journal of Economic Literature Classification Number: D81.     

Bounded interpersonal inferences and decision making

Summary. Individual decision making is based on predictions about other players' choices as well as on valuations of reactions to predictions. In this sense, a player has a prediction-decision criterion for decision making. We develop a theory of prediction-decision criteria, which enables us to capture new phenomena on individual decision making in games. The decision making situation is described in the epistemic logic GL of shallow depths. There, each player considers his and other players' decision making down to some shallow depths. It is a point of our theory to investigate inferential complexities of interpersonal introspections. In particular, we can discuss a minimal epistemic inferential structure for prediction-decision making. We will find parallel structures in decision making and prediction making, which is called an inner parallelism. The climax of the paper is the consideration of inner parallelisms of prediction-decision making. Received: August 31, 2000; revised version: April 9, 2001     

A general structure theorem for the Nash equilibrium correspondence

I consider n-person normal form games where the strategy set of each player is a non-empty compact convex subset of an Euclidean space, and the payoff function of player i is continuous in joint strategies and continuously differentiable and concave in the player i's strategy. No further restrictions (such as multilinearity of the payoff functions or the requirement that the strategy sets be polyhedral) are imposed. I demonstrate that the graph of the Nash equilibrium correspondence on this domain is homeomorphic to the space of games. This result generalizes a well-known structure theorem in [Kohlberg, E., Mertens, J.-F., 1986. On the strategic stability of equilibria. Econometrica 54, 1003–1037]. It is supplemented by an extension analogous to the unknottedness theorems in [Demichelis S., Germano, F., 2000. Some consequences of the unknottedness of the Walras correspondence. J. Math. Econ. 34, 537–545; Demichelis S., Germano, F., 2002. On (un)knots and dynamics in games. Games Econ. Behav. 41, 46–60]: the graph of the Nash equilibrium correspondence is ambient isotopic to a trivial copy of the space of games.     

Decision and time from a Humean point of view

Until recently, little attention has been paid to the consequences of Hume’s theory of action for intertemporal decision. Yet in view of the recurring discussion concerning situations of conflicting choice between a close and a remote objective, which runs from Book 2 of the Treatise, to the second Enquiry, to the Dissertation, intertemporal decision appears, at least in part, to be an outcome of the role of the natural relation of contiguity in the formation of the structure of desires, and thus different from the structure of pleasure. This paper shows, and expresses formally, that Hume’s approach provides alternative conditions which explain time-consistency on the one hand, and dynamic time-inconsistency on the other, when the link between contiguity and the ’violence’ of the passions is taken into account. The possibility of time-inconsistency is acknowledged by Hume as giving rise to general aversion, therefore constitutes a key argument in explaining the origin of government.     

Subjective probability over a subjective decision tree

A state space has been assumed as a primitive for modeling uncertainty, which presumes that the analyst knows all the uncertainties a decision maker (DM) perceives. This is problematic because states are private information of the DM, and hence are not directly observable to the analyst. Dekel et al. [Representing preferences with a unique subjective state space, Econometrica 69 (2001) 891-934] derive, rather than assume, the subjective state space from preference over suitable choice objects.In a dynamic setting, a decision tree, that is, a pair consisting of a state space and a filtration, has been taken as a primitive. This assumption is also problematic—a decision tree should be derived rather than assumed as a primitive. We formulate a three-stage extension of the above literature in order to model a DM who anticipates subjective uncertainty to be resolved gradually over time. We identify also subjective beliefs on the subjective state space.     

Optimizing the shares of native tree species in forest plantations with biased financial parameters

Addressing uncertainty is a key requirement to follow the principle of precaution in sustainable ecosystem management. The maximization of worst-case outcomes according to the “maximin” decision rule, based on the two parameters mean and variance of a financial indicator, is a prominent approach to integrate uncertainty in decision-making. In forestry, the problem of selecting the optimum tree species combination for a forest plantation investment can be seen as a problem of optimal portfolio selection, to be solved according to the “maximin” decision rule. Yet, it is well known that portfolios computed from expected means and variances are highly sensitive to changes in the estimated parameters. The financial results may be poor if we rely too much on the historical data. This paper tests an extended worst-case model that considers a lower bound for the expected mean net present value (NPV) of a tree species portfolio and an upper bound for its variance. Biased expected mean NPVs, variances and correlations for the tree species Picea abies [L.] Karst. (Spruce) and Fagus sylvatica L. (Beech) were used to test the variability of the resulting tree species portfolios (27 scenarios). A comprehensive simulated data set, which was adopted from an existing study and defined as the independent reference, served to evaluate the financial performance of the tree species portfolios obtained from optimization with the biased data. Compared with the results of classical worst-case optimization instances, it was feasible to reduce the variability of tree species shares effectively when the optimization was carried out with the extended worst-case approach. Furthermore, the financial performance of this approach was better when tested with the independent data. The worst-case forest NPVs achieved with the extended approach were on average 10% (statistical confidence 0.95) or 147% (statistical confidence 0.99) greater in comparison to the results of the classical approach. The influence of the uncertainty parameter selection was tested and the results were discussed against the controversial viewpoints on the usefulness of the “information-gap decision theory”. Finally, the significance of our results for sustainable ecosystem management is pointed out.     

American hegemony after 11 September: allies,rivals and contradictions

11 September heralded and provided a pretext for a more aggressive but increasingly contradictory American hegemony. Some of the consequences are contrary to the United States' own interests. Its new doctrine of ‘preemptive strike’ against other sovereign states encourages similarly belligerent behaviour by other governments, and yet more terrorism by nonstate actors, the very threats which were to be eradicated by a re-asserted US hegemony. This essay focuses on three partly overlapping themes: different strategies towards allies – multilateral and unilateral; different forms of power – civil and military; and different ideologies of globalisation – neoliberal and neo-conservative. It argues that while US policy may oscillate between such poles, it often combines the different elements. The overall strategy of the Bush administration is best characterised as unilateral multilateralism. The main issue for US hegemonists is the ways in which their hegemony might best be exercised, maintained and strengthened vis à vis allies and rivals. But for a safer, more democratic world, the choice does not lie between one faction of US hegemonists and another: we need other alternatives such as cosmopolitan democracy and a genuine internationalist movement which would give it some much-needed substance.     

What is an ‘endogenous state space’?

Summary. In the literature on choice under unforeseen contingencies, the decision maker behaves as if she aggregates possible instances of future rankings indexed by a set S. The set S is interpreted as a subjective state space even though subsequent rankings need not conform to any one of the aggregated utilities. This paper proposes a definition for a subjective state space under unforeseen contingencies that is topologically unique, derives its existence from preference primitives as opposed to the representation of preferences, and does not commit to an interpretation in which states correspond to future realized rankings. The definition topologically concurs with and extends the identification of the essentially unique subjective state space due to Dekel, Lipman and Rustichini [4].Received: 28 October 2003, Revised: 13 October 2004, JEL Classification Numbers: D11, D81, D91.I thank Eddie Dekel, Alan Kraus, Bart Lipman, Chris Shannon, and the referee for some helpful remarks.     

States and persons—on the interpretation of some fundamental concepts in the theory of justice as fairness

In this paper we discuss the ability of persons to compare the ‘positions’ of different individuals, which is fundamental for the theory of equity and justice as fairness, through the use of a state structure involving states, persons, consequences, preferences and mappings between sets of these objects.It is shown that a type of identity axiom implies a complete identity axiom. Such a complete identity axiom will hold if properties and preferences are dependent and all persons have the same properties, or properties are part of consequences. It is argued that the latter case provides a rationale for the complete identity axiom but demands great abilities of comparison on behalf of the persons involved.     

Progressive taxation in sequential decisionmaking: Deterministic and stochastic analysis

This paper investigates the effect of progressive taxation on sequential decisionmaking. The decision is the archetypical problem of capital theory: determining the optimal cutting time for a tree that grows according to either a deterministic or stochastic process. For the deterministic model, the optimal cutting time is unaffected by proportional taxes, but decreases as taxes become more progressive. For the stochastic model, the major finding is that uncertainty can partially offset the inefficiency induced by progressive taxation; when this result holds the government benefits from increased uncertainty whereas the taxpayer is harmed. One noteworthy example of this is when the tree's growth is governed by Brownian motion.     

定性分析的工具——探索图、循环图、结构图

本文提出了复杂科学管理系统思维的定性分析工具:探索图、循环图、结构图。探索图帮助人们进行视觉思考,体现知识、信息、想象、创造结合的过程,解决未知的、难以预测的一些决策问题;循环图从环状看因果;结构图利于人们进行结构化思维。它们不仅是定性分析的工具,也体现了一种新的思维方式——视觉思考、环状看因果、结构化思维。     

Say's involvement in the 1819 French edition of Ricardo's Principles and the issue of rent

This paper focuses on Say's contribution to the first French edition of Ricardo's Principles and on the analytical consequences of his involvement on the issue of rent. Part one investigates the “story” of this edition. It stresses Say's friendship with the translator, his involvement in this publication and his attitude toward Ricardo. Part two analyses how elements from Say's thought were introduced into Ricardo's theory of rent through this edition. These elements conveyed ideas which were definitely at odds with Ricardo's theory and misrepresented Ricardo's true concept of differential rent which was central to his theory.     

The rationality and efficacy of decisions under uncertainty and the value of an experiment

Summary A decision maker faces a known prior distribution over payoff relevant states. We compare the expected utility of this individual under two scenarios. In the first, the decision maker makes a choice without further information. In the second, the decision maker has access to an experiment before choosing an action. However, the decision maker does not know the true joint distribution over states and messages. The value of the experiment as measured by the difference in the two utility levels can be negative as well as positive. We give a condition which is necessary and sufficient for the experiment to be valuable in our sense, for any decision problem.An earlier version of this paper was circulated under the title Noisy Bayes Updating and the Value of Information. We have gained from the comments of Stephen Coate, John Geanakoplos, Larry Samuelson, Timothy Van Zandt and seminar participants at Harvard Business School, Princeton, Boston University, the international conference on game theory at Stony Brook 1992 and the Winter meeting of the Econometric Society at Anaheim 1993. The first author received support for this project from NSF grant #SES-9308515 and a University of Pennsylvania Research Foundation Grant.     

Choquet Rationality

Consider a decision problem under uncertainty for a decision maker with known (utility) payoffs over prizes. We say that an act is Choquet (Shafer, Bernoulli) rational if for some capacity (belief function, probability) over the set of states, it maximizes her “expected” utility. We show that an act may be Choquet rational without being Bernoulli rational, but it is Choquet rational if and only if it is Shafer rational. Journal of Economic Literature Classification Numbers: C72, D81.     

On the Relevance of John Rawls's Theory of Justice to Welfare Economics

Mainstream microeconomic theory makes some use of John Rawls's Theory of Justicein discussing welfare economics and social welfare functionals. While various elements of his approach are usually mentioned, his basic point is generally taken to be his difference principle (maximizing the welfare of the worst off individual) applied as a decision principle for evaluating the equity of resource allocation.

To take the difference principle as the essence of Rawls's work is an error. The present paper reviews the basic argument of the Theory of Justice

compares it with the use that economists make of it, and concludes that in a number of quite specific ways Rawls's ideas are misrepresented and misused by mainstream microeconomists.     

Coping with ignorance: unforeseen contingencies and non-additive uncertainty

Summary. In real-life decision problems, decision makers are never provided with the necessary background structure: the set of states of the world, the outcome space, the set of actions. They have to devise all these by themselves. I model the (static) choice problem of a decision maker (DM) who is aware that her perception of the decision problem is too coarse, as for instance when there might be unforeseen contingencies. I make a “bounded rationality' assumption on the way the DM deals with this difficulty, and then I show that imposing standard subjective expected utility axioms on her preferences only implies that they can be represented by a (generalized) expectation with respect to a non-additive measure, called a belief function. However, the axioms do have strong implications for how the DM copes with the type of ignorance described above. Finally, I show that some decision rules that have been studied in the literature can be obtained as a special case of the model presented here (though they have to be interpreted differently). Received: December 16, 1999; revised version: March 22, 2000     

Risk, ambiguity, and state-preference theory

The state-preference framework for modeling choice under uncertainty, in which objects of choice are allocations of wealth or commodities across states of the world, is a natural one for modeling ??smooth?? ambiguity-averse preferences. It does not require reference to objective probabilities, personalistic consequences, or counterfactual acts, and it allows for state dependence of utility and unobservable background risk. The decision maker??s local revealed beliefs are encoded in her risk-neutral probabilities (her relative marginal rates of substitution between states) and her local risk preferences are encoded in the matrix of derivatives of the risk-neutral probabilities. This matrix plays a central but generally unappreciated role in the modeling of risk attitudes in the state-preference framework. It can be computed by inverting a bordered Slutsky matrix and vice versa, it generalizes the Arrow?CPratt measure for approximating local risk premia, and its structure reveals whether the decision maker??s risk preferences are ambiguity averse as well as risk-averse. Two versions of the smooth ambiguity model are analyzed??the source-dependent risk aversion model and the second-order uncertainty (KMM) model??and it is shown that in both cases, the overall premium for local uncertainty can be decomposed as the sum of a risk premium and an ambiguity premium.     

The UK and the Eurozone

The article reviews the case for the UK to join the Eurozoneby way of presenting a review of HM Treasury's widely well-regarded"Euro Report" (2003). The review provides an opportunity torehearse and update the elements of optimum currency area (OCA)theory. In particular, the study draws attention to fresh estimatesof the trade effect of the UK's adhesion to the Eurozone, thesmall size of which sharply contrasts with earlier estimates.They substantially remove a challenge to the Report's negativeconclusion. The study sets the review in the perspective ofpublic opinion surveys and HM Government's decisions. (JEL codes:E42, F0, F15)     

Left-side Relatively Weak Increases in Risk and Their Comparative Statics

This paper proposes a new concept, a left-side relatively weak increase in risk (L-RWIR) order, that extends the definition of a relatively weak increase in risk (RWIR) order. We show that, for the class of linear payoffs, one can obtain an appealing comparative statics result for L-RWIR shifts imposing additional restrictions on risk preferences of a risk-averse decision maker.JEL classification: D81.revised version received October 10, 2003Acknowledgements The authors would like to thank an anonymous referee for insightful comments and useful suggestions.     

A model to analyse financial fragility

Summary. This paper sets out a tractable model which illuminates problems relating to individual bank behaviour, to possible contagious inter-relationships between banks, and to the appropriate design of prudential requirements and incentives to limit ‘excessive’ risk-taking. Our model is rich enough to include heterogeneous agents, endogenous default, and multiple commodity, and credit and deposit markets. Yet, it is simple enough to be effectively computable and can therefore be used as a practical framework to analyse financial fragility. Financial fragility in our model emerges naturally as an equilibrium phenomenon. Among other results, a non-trivial quantity theory of money is derived, liquidity and default premia co-determine interest rates, and both regulatory and monetary policies have non-neutral effects. The model also indicates how monetary policy may affect financial fragility, thus highlighting the trade-off between financial stability and economic efficiency.Received: 6 November 2003, Revised: 6 October 2004 JEL Classification Numbers: D52, E4, E5, G11, G21.C.A.E. Goodhart, P. Sunirand, D.P. Tsomocos: We are grateful to T.F. Bewley, S. Bhattacharya, F. Hahn, C. Mayer, H.S. Shin and seminar participants at the Bank of Austria, Bank of England, Bank of Norway, Bank for International Settlements, Brown University, the 7th Annual Macroeconomic Conference, Crete, EcoMod-IIOA International Conference, Brussels, the 2nd Oxford Finance Summer Symposium and Nuffield, Oxford, the Hong Kong Institute for Monetary Research, Purdue University, the University of Birmingham, the VI SAET Conference, Rhodes, Yale University, and especially an anonymous referee and H.M. Polemarchakis for helpful comments. The views expressed are those of the authors and do not necessarily reflect those of the Bank of England. Correspondence to: D.P. Tsomocos