If an agent (weakly) prefers early resolution of uncertainty then the recursive forms of both the most commonly used non-expected utility models, betweenness and rank dependence, almost reduce to Kreps & Porteus's (1978) recursive expected utility.
Suppose, following Kreps & Porteus (1978), that an agent values information not only to make contingent plans but also for itself; that is, intrinsically. What, then, is the relationship between an agent's attitude towards information and her attitude towards risk? If an agent always prefers more information, does this imply that she obeys the independence axiom? We generalize the recursive expected utility model, dropping both recursivity and expected utility. Exploiting the geometric analogy between risk and information, we characterize intrinsic information loving, for general preferences, in terms of a substitution property analogous to multivariate risk loving; and, for smooth preferences, in terms of the convexity of the Gateaux derivatives. Even with recursivity, preference for information does not imply expected utility: we provide an example. We examine, for all recursive preferences, the connection between information loving and comparative risk aversion for early versus late resolving risks.
We give sufficient conditions for an agent to always prefer more informative signals. As neither recursivity nor reduction are needed, the agent need not conform to expected utility. We argue, however, that if an agent desires information, for example, to relieve anxiety then there are reasons to expect her to be dynamically inconsistent.
A number of papers have shown that a strict Nash equilibrium action profile of a game may never be played if there is a small amount of incomplete information (see, for example, Carlsson and van Damme). We present a general approach to analyzing the robustness of equilibria to a small amount of incomplete information. A Nash equilibrium of a complete information game is said to be robust to incomplete information if every incomplete information game with payoffs almost always given by the complete information game has an equilibrium which generates behavior close to the Nash equilibrium. We show that many games with strict equilibria have no robust equilibrium and examine why we get such different results from existing refinements. If a game has a unique correlated equilibrium, it is robust. A natural many-player many-action generalization of risk dominance is a sufficient condition for robustness.
In this paper we provide an axiomatization for a representation of preferences over lotteries that is only one parameter richer than expected utility. Our model is a special case of Rank Dependent Expected Utility. Moreover, we show that the same restriction on this parameter is required for: risk aversion; intuitive comparative static results for a reasonably general class of economically interesting choice problems; and accommodating some of the most well-known violations of Expected Utility Theory.
Sunspots do not matter when there is a complete set of sunspot contingent assets. We consider the case where only option contracts written on a real asset are available. So state contingent contracts are possible only indirectly. We show that when the exercise price is in units of real numeraire, for a generic set of economies parameterized by utility functions, sunspots do not matter. Since options do not span sunspot states, this role of options is different from the spanning role. To establish this result, we show the generic regularity of economies with two sunspot states and one asset, which is of independent interest.
This paper studies the regularity of competitive equilibria in a two period exchange economy where a sunspot signal is observed in the beginning of the second period. It is shown that an equilibrium which does not depend on sunspots is regular if and only if it is sequentially regular as an equilibrium of the economy without sunspots. As an application, we show that a sequential regular equilibrium is robust against any sunspot structure, which may be endogenously generated.
This paper establishes the generic existence of sunspot equilibria in a standard two period exchange economy with real assets. We show that for a generic choice of utility functions and endowments, there exists an open set of real asset structures whose payoffs are independent of sunspots such that the economy with this asset structure has a regular sunspot equilibrium. Since an economy with a unique regular non-sunspot equilibrium is robust, this result shows that the multiplicity of non-sunspot equilibria is not necessary for the existence of sunspot equilibria. Our technique is general and can be applied to other frameworks.
We provide a multi-agent extension of the Rubinstein-Safra-Thomson (ordinal) bargaining theory where bargainers are described by their risk preferences. The ordinal Nash solution for this multi-agent bargaining problem corresponds to an outcome that is "immune'' against any agent seeking a concession from any one other agent. A geometric characterization of this ordinal Nash solution allows us to define a class of preference relations that are compatible with well-known experimental violations of expected utility and for which the ordinal Nash solution is well-defined. If preferences are assumed to be "smooth'' then an ordinal Nash solution is also equally marginally bold , where a bargainer's marginal boldness measures his or her willingness to risk disagreement in return for a marginal improvement in his or her position.
Refinements and Higher Order Beliefs: A Unified Survey
This paper presents a simple framework that allows us to survey and relate some different strands of the game theory literature. We describe a "canonical'' way of adding incomplete information to a complete information game. This framework allows us to give a simple "complete theory'' interpretation (Kreps 1990) of standard normal form refinements such as perfection, and to relate refinements both to the "higher order beliefs literature'' (Rubinstein 1989; Monderer and Samet 1989; Morris, Rob and Shin 1995; Kajii and Morris 1995) and the "payoff uncertainty approach'' (Fudenberg, Kreps and Levine 1988; Dekel and Fudenberg 1990).
Rubinstein's Similarity Consistent Preferences: A Complete Characterization,
This paper provides a complete characterization of utility functions that are consistent with similarity relations considered in Rubinstein (1988).
Weakening the Sure-Thing Principle: Decomposable Choice under Uncertainty
Savage motivated his Sure Thing Principle by arguing that, whenever an act would be preferred if an event obtains and preferred if that event did not obtain, then it should be preferred overall. The idea that it should be possible to decompose and recompose decision problems in this way has normative appeal. We show, however, that it does not require the full separability across events implicit in Savage's axiom. We formulate a weaker axiom that suffices for decomposability, and show that this implies an implicit additive representation. Our decomposability property makes local necessary conditions for optimality, globally sufficient. Thus, it is useful in computing optimal acts. None of these results rely on probabilistic sophistication; indeed, our axiom is consistent with the Ellsberg paradox. If we assume probabilistic sophistication, however, then the axiom holds if and only if the agent's induced preferences over lotteries satisfy betweenness. Thus, the weak sure thing principle forms part if an axiomatization of subjective betweenness theory, just as its stronger ancestor did for subjective expected utility.
Bargaining and Boldness
We study a multi-person bargaining problem with general risk preferences through the use of Shaked's game of cycling offers with exogenous breakdown. If preferences are assumed to be "smooth'' then in the limit as the risk of breakdown vanishes, our approach leads to an outcome in which bargainers are equally marginally bold , where a bargainer's marginal boldness measures his willingness to risk disagreement in return for a marginal improvement in his or her position. A unique equally marginally bold outcome exists in natural cases, in particular when the preferences are of the Gul's disappointment averse and the rank dependent expected utility types. Thus, behavior consistent with the Allais Ratio Paradox is compatible with the existence of the equally marginally bold solution.