Optimism and Pessimism in Games.

This paper considers the impact of ambiguity in strategic situations. It extends the earlier literature by allowing for optimistic responses to ambiguity. Ambiguity is modelled by CEU preferences. We study comparative statics of changes in ambiguity-attitude in games with strategic complements or substitutes. This gives a precise statement of the impact of ambiguity on economic behaviour. We also the possibility that players may be overconfident in the sense of over-estimating the probability of favourable outcomes. This has a similar effect of increasing equilibrium strategies in games of strategic complements, Finally we consider RDEU preferences.Ambiguity in games, overcon?fidence, strategic complementarity, optimism, RDEU.

Optimism and Pessimism in Games

This paper considers the impact of ambiguity in strategic situations. It extends the earlier literature by allowing for optimistic responses to ambiguity. Ambiguity is modelled by CEU preferences. We propose a new solution concept for players who may express ambiguity- preference. Then we study comparative statics of changes in ambiguity-attitude in games with strategic complements. This gives a precise statement of the impact of ambiguity on economic behaviour.Ambiguity in games, support, strategic complementarity, optimism, multiple equilibria.

Multiple Priors as Similarity Weighted Frequencies

In this paper, we consider a decision-maker who tries to learn the distribution of outcomes from previously observed cases. For each observed sequence of cases, the decision-maker entertains a set of priors expressing his hypotheses about the underlying probability distribution. The set of probability distributions shrinks when new information confirms old data. We impose a version of the concatenation axiom introduced in BILLOT, GILBOA, SAMET AND SCHMEIDLER (2005) which insures 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.

Updating Choquet Beliefs.

We apply Pires’s coherence property between unconditional and conditional preferences that admit a CEU representation. In conjunction with consequentialism (only those outcomes on states which are still possible can matter for conditional preference) this implies that the conditional preference may be obtained from the unconditional preference by taking the Full Bayesian Update of the capacity. Attitudes towards sequential versus simultaneous resolution of uncertainty for a simple bet are analyzed. We show that for a class of recursive CEU preferences which exhibit both optimism and pessimism, a 'good-news' signal is preferred to no signal which is preferred to a 'bad-news' signal.updating ambiguous beliefs, Full Bayesian Updating, Choquet Expected Utility, optimism, pessimism, recursive preferences.

Differentiating Ambiguity: A Comment.

In Ghirardato, Macheroni and MArcinaccri (GMM) propose a method for distinguishing between percieved ambiguity and the decision-maker's reaction to it. They study a general class of preferences which includes CEU and a-MEU and axiomatise a subclass of a-MEU preferences. We show that for Hurwicz preferences the proposed measure of ambiguity depends on parameters which intuitively reflect ambiguity-attitude. Furthermore, any a-MEU preferences which satisfy the CEU axioms, satisfy GMM's axioms if and only if a = 0 or 1, that is, the capacity must be convex or concave.Ambiguity, multiple priors, Hurwicz, Choquet expected utility.

Ambiguity and Social Interaction

We present a non-technical account of ambiguity in strategic games and show how it may be applied to economics and social sciences. Optimistic and pessimistic responses to ambiguity are formally modelled. We show that pessimism has the e?ect of increasing (decreasing) equilibrium prices under Cournot (Bertrand) competition. In addition the e?ects of ambiguity on peace-making are examined. It is shown that ambiguity may select equilibria in coordination games with multiple equilibria. Some comparative statics results are derived for the impact of ambiguity in games with strategic complements.Ambiguity, Optimism, Oligopoly, Peace-making, Choquet expected utility

The a-MEU Model: A Comment

In [7] Ghirardato, Macheroni and Marinacci (GMM) propose a method for distinguishing between perceived ambiguity and the decision-maker's 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 GMM's 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].Ambiguity, multiple priors, invariant biseparable, Clarke derivative, ambiguity-preference.

A Simple Axiomatization and Constructive Representation Proof for Choquet Expected Utility

We provide a simple and intuitive set of axioms that allow for a direct and constructive proof of the Choquet Expected Utility representation for decision making under uncertainty.