Consistency of beliefs and epistemic conditions for Nash and correlated equilibria

A consistency condition (action-consistency) on the interim beliefs of players in a game is introduced. Action-consistency is weaker than common priors and, unlike common priors, is characterized by a “no-bets” condition on verifiable events. Using action-consistency, we provide epistemic conditions to Nash and correlated equilibria weakening the common knowledge restrictions in Aumann and Brandenburger [Aumann, R., Brandenburger, A., 1995. Epistemic conditions for Nash equilibrium. Econometrica 63, 1161–1180] and Aumann [Aumann, R., 1987. Correlated equilibrium as an expression of Bayesian rationality. Econometrica 55, 1–18].     

Allowing disagreement in evaluations of social welfare

There is no consensus on how to measure interpersonally comparable, cardinal utility. Despite of this, people repeatedly make welfare evaluations in their everyday lives. However, people do not always agree on such evaluations, and this is one important reason for political disagreements. Thus, to keep in control of the normative premises, decision makers may prefer information which can be used as input to an arbitrary social welfare function to information which is the output from a social welfare function specified by the analyst. In this paper we try to identify and simplify sufficient welfare indicators; information which enables decision makers to arrive at welfare evaluations of social states or projects, according to their own ethical beliefs. Our conclusion is that providing factual information about different population groups, their social state, size, and characteristics, may be better for this purpose than the more traditional approach of focusing on ordinal utility information.     

Agreement theorem for neo-additive beliefs

In this paper, we extend Aumann’s (Ann Stat 4:1236–1239, 1976) probabilistic agreement theorem to situations in which agents’ prior beliefs are represented by a common neo-additive capacity. In particular, we characterize the family of updating rules for neo-additive capacities, which are necessary and sufficient for the impossibility of “agreeing to disagree” on the values of posterior capacities as well as on the values of posterior Choquet expectations for binary acts. Furthermore, we show that generalizations of this result to more general acts are impossible.     

Epistemic Conditions for Equilibrium in Beliefs without Independence

Aumann and Brandenburger [Econometrica63(1995), 1161–1180.] provide sufficient conditions on the knowledge of the players in a game for their beliefs to constitute a Nash equilibrium. They assume, among other things, mutual knowledge of rationality. By rationality of a player, it is meant that the action chosen by him maximizes his expected utility, given his beliefs. There is, however, no need to restrict the notion of rationality to expected utility maximization. This paper shows that their result can be generalized to the case where players' preferences over uncertain outcomes belong to a large class of non-expected utility preferences.Journal of Economic LiteratureClassification Numbers: C72, D81.     

Self-Serving Cheap Talk: A Test Of Aumann's Conjecture

The effectiveness of pre-play communication in achieving efficient outcomes has long been a subject of controversy. Aumann conjectures that, in a variant of the Stag Hunt game, “an agreement to play [the efficient outcome] conveys no information about what the players will do” and thus should not affect behavior. Farrell and Rabin suspect that cheap talk will achieve efficiency. Results show impressive coordination when the sender first chooses a signal and then an action. Without communication, efforts to achieve efficiency are largely unsuccessful. As Farrell suggests, reversing the order of the action and signal appears to change players' behavior. Journal of Economic Literature Classification Numbers: A13, C72, C91, D82, D84.     

APPARENT BIAS: WHAT DOES ATTITUDE POLARIZATION SHOW?

Many, though not all, experiments have found that exposing groups of subjects who disagree to the same evidence may cause their initial attitudes to strengthen and move further apart, or polarize. Some have concluded that findings of attitude polarization show that people process information in a biased manner so as to support their initial views. We argue that, on the contrary, polarization is often what we should expect to find in an unbiased Bayesian population, in the context of experiments that find polarization.     

Second-order ambiguous beliefs

This paper axiomatizes models of second-order ambiguous beliefs in the original domain of preferences of Anscombe and Aumann (Ann Math Stat 34:199–205, 1963) by weakening the first-stage independence postulate. The models we propose include the second-order subjective expected utility (SOSEU) of Seo (Econometrica 77:1575–1605, 2009) as a particular case. We characterize the intersection of our models of second-order ambiguity with the canonical models of (first-order) ambiguity aversion and provide a further generalization of SOSEU by relaxing the completeness axiom.     

Preference for safety under the Choquet model: in search of a characterization

Victor prefers safety more than Ursula if whenever Ursula prefers a constant to an uncertain act, so does Victor. This paradigm, whose expected utility (EU) version is Arrow and Pratt’s more risk aversion concept, will be studied in the Choquet expected utility (CEU) model. Necessary condition Pointwise inequality between a function of the utility functions and another of the capacities is necessary and sufficient for the preference by Victor of safety over a dichotomous act whenever such is the preference of Ursula. However, increased preference for safety versus dichotomous acts does not imply preference by Victor of safety over a general act whenever such is the preference of Ursula. A counterexample will be provided, via the casino theory of Dubins and Savage. Sufficient condition Separation of the two functions by some convex function is sufficient for Victor to prefer safety more than Ursula, over general acts. Furthermore, a condition on the capacities will be presented for simplicity seeking, the preference by Victor over any act for some dichotomous act that leaves Ursula indifferent. This condition is met in particular if Victor’s capacity is a convex function of Ursula’s capacity. For these cases, the pointwise inequality (necessary) condition is a characterization of greater preference for safety, extending the Arrow–Pratt notion from EU to CEU and rank-dependent utility (RDU). These inequalities preserve the flavor of the “more pessimism than greediness” characterization of monotone risk aversion by Chateauneuf, Cohen and Meilijson in the RDU model and its extension by Grant and Quiggin to CEU. Preferences between safety and dichotomous acts are at the core of the biseparable preferences model of Ghirardato and Marinacci.     

Stochastic dominance and behavior towards risk: The market for Internet stocks

Internet stocks registered large gains in the late 1990s, followed by large losses from early 2000. Using stochastic dominance theory, we infer how investor risk preferences have changed over this cycle, and relate our findings to utility theory and behavioral finance. Our major findings are as follows. First, risk averters and risk seekers show a distinct difference in preference for Internet versus “old economy” stocks. This difference is most evident during the bull market period (1998–2000) where Internet stocks stochastically dominate old economy stocks for risk seekers but not risk averters. In the bear market, risk averters show an increased preference for old economy stocks, while risk seekers show a reduced preference for Internet stocks. These results are inconsistent with prospect theory and indicate that investors exhibit reverse S-shaped utility functions.     

Ambiguity aversion and trade

What is the effect of ambiguity aversion on trade? Although in a Bewley??s model, ambiguity aversion always leads to less trade; in other models, this is not always true. However, we show that if the endowments are unambiguous, then more ambiguity aversion implies less trade for a very general class of preferences. The reduction in trade caused by ambiguity aversion can be as severe as to lead to no trade. In an economy with MEU decision makers, we show that if the aggregate endowment is unanimously unambiguous, then every Pareto optima allocation is also unambiguous. We also characterize the situation in which every unanimously unambiguous allocation is Pareto optimal. Finally, we show how our results can be used to explain the home-bias effect. As a useful result for our methods, we also obtain an additivity theorem for CEU and MEU decision makers that does not require comonotonicity.     

Knightian uncertainty and poverty trap in a model of economic growth

This paper explores how Knightian uncertainty affects dynamic properties in an economic growth model. The decision-making theory employed in the analysis is the theory of expected utility under a non-additive probability measure, i.e., the Choquet expected utility model of preference. We apply this decision-making theory to an overlapping generations model where producers face “uncertainty” in their technologies. When the producer is averse to uncertainty, the firm's profit function may not be differentiable. Therefore, the firm's decision to invest and hire labor becomes rigid for a certain measurable range of real interest rates. In dynamic equilibrium, the existence of firm-level rigidity causes discontinuity in the wage function; this makes multiple equilibria the more likely outcomes under the log utility and Cobb–Douglas production functions. In this paper, we show that even if aversion to uncertainty is small, the “poverty trap” can arise for a wide range of parameter values.     

Self-referential thinking and equilibrium as states of mind in games: fMRI evidence

Sixteen subjects' brain activity were scanned using fMRI as they made choices, expressed beliefs, and expressed iterated 2nd-order beliefs (what they think others believe they will do) in eight games. Cingulate cortex and prefrontal areas (active in “theory of mind” and social reasoning) are differentially activated in making choices versus expressing beliefs. Forming self-referential 2nd-order beliefs about what others think you will do seems to be a mixture of processes used to make choices and form beliefs. In equilibrium, there is little difference in neural activity across choice and belief tasks; there is a purely neural definition of equilibrium as a “state of mind.” “Strategic IQ,” actual earnings from choices and accurate beliefs, is negatively correlated with activity in the insula, suggesting poor strategic thinkers are too self-focused, and is positively correlated with ventral striatal activity (suggesting that high IQ subjects are spending more mental energy predicting rewards).     

Consensus and common knowledge of an aggregate of decisions

McKelvey and Page [McKelvey, R., Page, T., 1986. Common knowledge, consensus and aggregate information. Econometrica 54, 109–127] generalized Aumann's [Aumann, R.J., 1976. Agreeing to disagree. Ann. Statist. 4, 1236–1239] agreement theorem to the case where agents have common knowledge of a statistic of their posterior probabilities of some event. They showed that if individuals have the same prior, and if the statistic satisfies a stochastic regularity condition, then common knowledge of it implies equality of all posteriors. We show a similar result in a more general setting where agents have common knowledge of a statistic of their individual decisions. Decisions can be posteriors as well as discrete actions such as buy or sell. We show that if the decision rule followed by individuals is balanced union consistent, and if the statistic of individual decisions is exhaustive, then common knowledge of it implies equality of all decisions. We give an example showing that neither Cave's [Cave, J., 1983. Learning to agree. Econ. Letters 12, 147–152] union consistency condition nor Parikh and Krasucki's [Parikh, R., Krasucki, P., 1990. Communication, consensus and knowledge. J. Econ. Theory 52, 178–189] convexity condition is sufficient to guarantee the result.     

On redundant types and Bayesian formulation of incomplete information

A type structure is non-redundant if no two types of a player represent the same hierarchy of beliefs over the given set of basic uncertainties, and it is redundant otherwise. Under a mild necessary and sufficient condition termed separativity, we show that any redundant structure can be identified with a non-redundant structure with an extended space of basic uncertainties. The belief hierarchies induced by the latter structure, when “marginalized,” coincide with those induced by the former. We argue that redundant structures can provide different Bayesian equilibrium predictions only because they reflect a richer set of uncertainties entertained by players but unspecified by the analyst. The analyst shall make use of a non-redundant structure, unless he believes that he misspecified the players' space of basic uncertainties. We also consider bounding the extra uncertainties by the action space for Bayesian equilibrium predictions.     

Hierarchies of ambiguous beliefs

We present a theory of interactive beliefs analogous to Mertens and Zamir [Formulation of Bayesian analysis for games with incomplete information, Int. J. Game Theory 14 (1985) 1-29] and Brandenburger and Dekel [Hierarchies of beliefs and common knowledge, J. Econ. Theory 59 (1993) 189-198] that allows for hierarchies of ambiguity. Each agent is allowed a compact set of beliefs at each level, rather than just a single belief as in the standard model. We propose appropriate definitions of coherency and common knowledge for our types. Common knowledge of coherency closes the model, in the sense that each type homeomorphically encodes a compact set of beliefs over the others’ types. This space universally embeds every implicit type space of ambiguous beliefs in a beliefs-preserving manner. An extension to ambiguous conditional probability systems [P. Battigalli, M. Siniscalchi, Hierarchies of conditional beliefs and interactive epistemology in dynamic games, J. Econ. Theory 88 (1999) 188-230] is presented. The standard universal type space and the universal space of compact continuous possibility structures are epistemically identified as subsets.     

Government spending, capital accumulation and the optimal policy rule: The role of public service capital

In this paper, we modify the Djajić [Djajić, S., 1987. “Government Spending and the Optimal Rates of Consumption and Capital Accumulation,” Canadian Journal of Economics 20, 544–554.] model in such a way that government consumption expenditure provides utility to households via the total stock of government services rather than the government consumption flow alone. By using such a framework, we show that the optimality condition for the public service capital stock is the marginal rate of substitution between public service capital and consumption that equals the intertemporal marginal rate of transformation between the two goods. In addition, we show that the relationship between private consumption and public service capital in a household's utility plays an important role in determining the transitional behavior of relevant variables. We also examine the second-best government consumption expenditure policy. By contrast, in the standard flow specification, e.g., Turnovsky and Brock [Turnovsky, S.J. and Brock, W.A., 1980. “Time Consistency and Optimal Government Policies in Perfect Foresight Equilibrium,” Journal of Public Economics 13, 183–212.], Ihori [Ihori, T., 1990. “Government Spending and Private Consumption,” Canadian Journal of Economics 23, 60–69.], and Turnovsky and Fisher [Turnovsky, S.J. and Fisher, W.H., 1995. “The Composition of Government Expenditure and its Consequences for Macroeconomic Performance,” Journal of Economic Dynamics and Control 19, 747–786.], the second-best government consumption expenditure is decided on the basis that the marginal utility of consumption is equal to the discounted sum of the marginal utility of the government's flow spending.     

The impossibility of compromise: some uniqueness properties of expected utility preferences

Summary. We focus on the following uniqueness property of expected utility preferences: Agreement of two preferences on one interior indifference class implies their equality. We show that, besides expected utility preferences under (objective) risk, this uniqueness property holds for subjective expected utility preferences in Anscombe-Aumann's (partially subjective) and Savage's (fully subjective) settings, while it does not hold for subjective expected utility preferences in settings without rich state spaces. Indeed, when it holds the uniqueness property is even stronger than described above, as it needs only agreement on binary acts. The extension of the uniqueness property to the subjective case is possible because beliefs in the mentioned settings are shown to satisfy an analogous property: If two decision makers agree on a likelihood indifference class, they must have identical beliefs. Received: November 15, 1999; revised version: December 29, 1999     

Theories of choice under risk: Insights from financial markets

To date, the plausibility of theories of choice under risk hinges are mainly on experimental evidence. This paper devises and implements an approach amenable of assessing the performance of three families of models (expected utility, rank-dependent expected utility, and the cumulative prospect theory) using information from financial asset markets. Our findings unequivocally support reference-point dependence, diminishing marginal sensitivity, loss aversion, and nonlinear weighting of (gain and loss) physical probabilities. The empirical observations are found to be robust to, inter alia, the parameterization of the utility and probability weighting functions, “day-of-the-week effects”, the choice of a reference point, and the introduction of possible, low-probability market crashes (peso component).     

An introduction to nanotechnology policy: Opportunities and constraints for emerging and established economies

Nanotechnology has captured wide attention all over the world and excited the imagination of young and old alike. Interest in the subject has increased remarkably during the last few years because of potential technological applications, and commercial interest has skyrocketed. The promise of nanotechnology as an economic engine that can redefine the wellbeing of regions and nations is pervasive; yet the imprecise language, and overuse of the term nanotechnology, has made that term fuzzier, broader, and trendier than many imagined possible. This is especially evident in nanotechnology market projections, which rose dramatically over the past five years as more traditional “product families” were engulfed by the expanding use of the term. Government policy regarding nanotechnology has often resembled an embrace of imagination rather than a systematic use of what Sun Tzu and others have taught about strategic decision making. Further, if nanotechnology is truly the next wave of technology product paradigms, how will we provide an educated workforce to support it? Moreover, in company with these societal benefits come increased societal risks. This paper is intended to provide policy makers and strategists with observations that might limit actions such as those that led to the “over-hype” of nanotechnology and to the fear (or discounting) of societal risks. In the latter case we might learn from the experiences of policy makers connected with other emerging enabling-technology bases, such as nuclear energy and, to a lesser extent, the “dot-com” boom.     

On the value of human resources

One challenge for planners is to discover conditions under which a society has a positive and growing “net worth” in terms of its human resources and to bring about and maintain those conditions. We discuss the utility and validity of the concept of people as “assets” or “liabilities”, the structure and cultural contexts for a proposed model of the dynamics of value that account for opportunity costs; and links between information technologies and human resources management, including planned development of these resources.