Jürgen Eichberger

Choice under uncertainty with the best and worst in mind: Neo-additive capacities

We develop the simplest generalization of subjective expected utility that can accommodate both optimistic and pessimistic attitudes towards uncertainty-Choquet expected utility with non-extreme-outcome-additive (neo-additive) capacities. A neo-additive capacity can be expressed as the convex combination of a probability and a special capacity, we refer to as a Hurwicz capacity, that only distinguishes between whether an event is impossible, possible or certain. We show that neo-additive capacities can be readily applied in economic problems, and we provide an axiomatization in a framework of purely subjective uncertainty.

Strategic Complements, Substitutes, and Ambiguity: The Implications for Public Goods

Abstract We examine the effect of ambiguity in symmetric games with aggregate externalities. We find that ambiguity will increase/decrease the equilibrium strategy in games with strategic complements/substitutes and positive externalities. These effects are reversed in games with negative externalities. We consider some economic applications of these results to Cournot oligopoly, bargaining, macroeconomic coordination, and voluntary donations to a public good. In particular we show that ambiguity may reduce free-riding. Comparative statics analysis shows that increases in uncertainty will increase donations, to a public good. Journal of Economic Literature C72, D81, H41.

Uncertainty Aversion and Dynamic Consistency

This paper applies a proposal of M. Machina (1989) for updating nonexpected utility preferences to D. Schmeidlers (1989) nonadditive probability model. The authors discover that the updated preferences may not themselves satisfy Schmeidlers axioms. Despite this, the updates of uncertainty averse preferences are themselves uncertainty averse. Copyright 1996 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Are the treasures of game theory ambiguous

Goeree & Holt (2001) observe that, for some parameter values, Nash equilibrium provides good predictions for actual behaviour in experiments. For other payoff parameters, however, actual behaviour deviates consistently from that predicted by Nash equilibria. They attribute the robust deviations from Nash equilibrium to actual players’ considering not only marginal gains and losses but also total pay-offs. In this paper, we show that optimistic and pessimistic attitudes towards strategic ambiguity may induce such behaviour.

The α-MEU model: A comment

In [7] Ghirardato, Macheroni and Marinacci (GMM) propose a method for distinguishing between perceived ambiguity and the decision-makers reaction to it. They study a general class of preferences which they refer to as invariant biseparable. This class includes CEU and MEU. They axiomatize a subclass of a-MEU preferences. If attention is restricted to finite state spaces, we show that any a-MEU preference relation, satisfies GMMs axioms if and only if a = 0 or 1, that is, the preferences must be either maxmin or maxmax. We show by example that these axioms may be satisfied when the state space is [0,1].

CEU preferences and dynamic consistency

This paper investigates the dynamic consistency of CEU preferences. A decision maker is faced with an information structure represented by a fixed filtration. If beliefs are represented by a convex capacity, we show that a necessary and sufficient condition for dynamic consistency is that beliefs be additive over the final stage in the filtration.

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.

Case-based belief formation under ambiguity

In this paper, we consider a decision maker who tries to learn the distribution of outcomes from previously observed cases. For each observed database of cases the decision maker predicts a set of priors expressing his beliefs about the underlying probability distribution. We impose a version of the concatenation axiom introduced in Billot et al. (2005) which ensures that the sets of priors can be represented as a weighted sum of the observed frequencies of cases. The weights are the uniquely determined similarities between the observed cases and the case under investigation. The predicted probabilities, however, may vary with the number of observations. This generalization of Billot et al. (2005) allows one to model learning processes.

Ambiguity, data and preferences for information – A case-based approach

We model decision making under ambiguity based on available data. Decision makers express preferences over actions and data sets. We derive an α-max–min representation of preferences, in which beliefs combine objective characteristics of the data (number and frequency of observations) with subjective features of the decision maker (similarity of observations and perceived ambiguity). We identify the subjectively perceived ambiguity and separate it into ambiguity due to a limited number of observations and ambiguity due to data heterogeneity. The special case of no ambiguity provides a behavioral foundation for beliefs as similarity-weighted frequencies as in Billot et al. (2005) [3].

TECHNOLOGY ADOPTION AND ADAPTATION TO CLIMATE CHANGE — A CASE-BASED APPROACH

We present a model of technological adaptation in response to a change in climate conditions. The main feature of the model is that new technologies are not just risky, but also ambiguous. Pessimistic agents are thus averse to adopting a new technology. Learning is induced by optimists, who are willing to try out technologies about which there is little evidence available. We show that both optimists and pessimists are crucial for a successful adaptation. While optimists provide the public good of information which gives pessimists an incentive to innovate, pessimists choose the new technology persistently in the long-run which increases the average returns for the society. Hence, the optimal share of optimists in the society is strictly positive. When the share of optimists in the society is too low, innovation is slow and the obtained steady-state is inefficient. We discuss two policies which can potentially alleviate this inefficiency: Subsidies and provision of additional information. We show that if precise and relevant information is available, pessimists would be willing to pay for it and consequently adopt the new technology. Hence, providing information might be a more efficient policy, which is both self-financing and results in better social outcomes.