481 research outputs found
A Dynamic Ellsberg Urn Experiment
Two rationality arguments are used to justify the link between conditional and unconditional preferences in decision theory: dynamic consistency and consequentialism. Dynamic consistency requires that ex ante contingent choices are respected by updated preferences. Consequentialism states that only those outcomes which are still possible can matter for updated preferences. We test the descriptive validity of these rationality arguments with a dynamic version of Ellsberg's three color experiment and find that subjects act more often in line with consequentialism than with dynamic consistency
Decision theory under uncertainty
We review recent advances in the field of decision making under uncertainty or ambiguity.Ambiguity ; ambiguity aversion ; uncertainty ; decision
Ellsberg Paradox and Second-order Preference Theories on Ambiguity: Some New Experimental Evidence
We study the two-color problem by Ellsberg (1961) with the modification that the decision maker draws twice with replacement and a different color wins in each draw. The 50-50 risky urn turns out to have the highest risk conceivable among all prospects including the ambiguous one, while all feasible color distributions are mean-preserving spreads to one another. We show that the well-known second-order sophisticated theories like MEU, CEU, and REU as well as Savage’s first-order theory of SEU share the same predictions in our design, for any first-order risk attitude. Yet, we observe that substantial numbers of subjects violate the theory predictions even in this simple design
Identifying Quantum Structures in the Ellsberg Paradox
Empirical evidence has confirmed that quantum effects occur frequently also
outside the microscopic domain, while quantum structures satisfactorily model
various situations in several areas of science, including biological, cognitive
and social processes. In this paper, we elaborate a quantum mechanical model
which faithfully describes the 'Ellsberg paradox' in economics, showing that
the mathematical formalism of quantum mechanics is capable to represent the
'ambiguity' present in this kind of situations, because of the presence of
'contextuality'. Then, we analyze the data collected in a concrete experiment
we performed on the Ellsberg paradox and work out a complete representation of
them in complex Hilbert space. We prove that the presence of quantum structure
is genuine, that is, 'interference' and 'superposition' in a complex Hilbert
space are really necessary to describe the conceptual situation presented by
Ellsberg. Moreover, our approach sheds light on 'ambiguity laden' decision
processes in economics and decision theory, and allows to deal with different
Ellsberg-type generalizations, e.g., the 'Machina paradox'.Comment: 16 pages, no figures. arXiv admin note: substantial text overlap with
arXiv:1208.235
Beliefs and Dynamic Consistency,
In this chapter, we adopt the decision theoretic approach to the representation and updating of beliefs. We take up this issue and propose a reconsideration of Hammond's argument. After reviewing the argument more formally, we propose a weaker notion of dynamic consistency. We observe that this notion does not imply the full fledged sure thing principle thus leaving some room for models that are not based on expected utility maximization. However, these models still do not account for ''imprecision averse" behavior such as the one exhibited in Ellsberg experiment and that is captured by non-Bayesian models such as the multiple prior model. We therefore go on with the argument and establish that such non-Bayesian models possess the weak form of dynamic consistency when the information considered consists of a reduction in imprecision (in the Ellsberg example, some information about the proportion of Black and Yellow balls)R. Arena and A. Festré
Optimal learning under robustness and time-consistency
We model learning in a continuous-time Brownian setting where there is prior ambiguity. The associated model of preference values robustness and is time-consistent. It is applied to study optimal learning when the choice between actions can be postponed, at a per-unit-time cost, in order to observe a signal that provides information about an unknown parameter. The corresponding optimal stopping problem is solved in closed form, with a focus on two specific settings: Ellsberg’s two-urn thought experiment expanded to allow learning before the choice of bets, and a robust version of the classical problem of sequential testing of two simple hypotheses about the unknown drift of a Wiener process. In both cases, the link between robustness and the demand for learning is studied.Accepted manuscrip
Ellsberg Paradox and Second-order Preference Theories on Ambiguity: Some New Experimental Evidence
We study the two-color problem by Ellsberg (1961) with the modification that the decision maker draws twice with replacement and a different color wins in each draw. The 50-50 risky urn turns out to have the highest risk conceivable among all prospects including the ambiguous one, while all feasible color distributions are mean-preserving spreads to one another. We show that the well-known second-order sophisticated theories like MEU, CEU, and REU as well as Savage’s first-order theory of SEU share the same predictions in our design, for any first-order risk attitude. Yet, we observe that substantial numbers of subjects violate the theory predictions even in this simple design.Ellsberg paradox, Ambiguity, Second-order risk, Second-order preference theory, Experiment
Elicitation of ambiguous beliefs with mixing bets
I consider the elicitation of ambiguous beliefs about an event and show how
to identify the interval of relevant probabilities (representing ambiguity
perception) for several classes of ambiguity averse preferences. The agent
reveals her preference for mixing binarized bets on the uncertain event and its
complement under varying betting odds. Under ambiguity aversion, mixing is
informative about the interval of beliefs. In particular, the mechanism allows
to distinguish ambiguous beliefs from point beliefs, and identifies the belief
interval for maxmin preferences. For ambiguity averse smooth second order and
variational preferences, the mechanism reveals inner bounds for the belief
interval, which are sharp under additional assumptions. In an experimental
study, participants perceive almost as much ambiguity for natural events
(generated by the stock exchange and by a prisoners dilemma game) as for the
Ellsberg Urn, indicating that ambiguity may play a role in real-world decision
making
Benevolent and Malevolent Ellsberg Games
Traditionally, real experiments testing subjective expected utility theory take for granted that subjects view the Ellsberg task as a one-person decision problem. We challenge this view: Instead of seeing the Ellsberg task as a one-person decision problem, it can be perceived as a two-player game. One player chooses among the bets. The second player determines the distribution of balls in the Ellsberg urn. The Nash equilibrium predictions of this game depend on the payoff of the second player, with the game ranging from a zero-sum one to a coordination game. Meanwhile, the predictions by ambiguity aversion models remain unchanged. Both situations are implemented experimentally and yield different results, in line with the game-theoretic prediction. Additionally, the standard scenario (without explicit mention of how the distribution is determined) leads to results similar to the zero-sum game, suggesting that subjects view the standard Ellsberg experiment as a game against the experimenter
- …