780 research outputs found
Order Independence and Rationalizability
Two natural strategy elimination procedures have been studied for strategic
games. The first one involves the notion of (strict, weak, etc) dominance and
the second the notion of rationalizability. In the case of dominance the
criterion of order independence allowed us to clarify which notions and under
what circumstances are robust. In the case of rationalizability this criterion
has not been considered. In this paper we investigate the problem of order
independence for rationalizability by focusing on three naturally entailed
reduction relations on games. These reduction relations are distinguished by
the adopted reference point for the notion of a better response. Additionally,
they are parametrized by the adopted system of beliefs. We show that for one
reduction relation the outcome of its (possibly transfinite) iterations does
not depend on the order of elimination of the strategies. This result does not
hold for the other two reduction relations. However, under a natural assumption
the iterations of all three reduction relations yield the same outcome. The
obtained order independence results apply to the frameworks considered in
Bernheim 84 and Pearce 84. For finite games the iterations of all three
reduction relations coincide and the order independence holds for three natural
systems of beliefs considered in the literature.Comment: Appeared in: Proc. of the 10th conference on Theoretical Aspects of
Rationality and Knowledge (TARK X), pp. 22-38 (2005
Choice resolutions
AbstractWe describe a process to compose and decompose choice behavior, called resolution. In the forward direction, resolutions amalgamate simple choices to create a complex one. In the backward direction, resolutions detect when and how a primitive choice can be deconstructed into smaller choices. A choice is resolvable if it is the resolution of smaller choices. Rationalizability, rationalizability by a preorder, and path independence are all preserved (backward and forward) by resolutions, whereas rationalizability by a weak order (equivalently, ) is not. We characterize resolvable choices, and show that resolvability generalizes
The Many Faces of Rationalizability
The rationalizability concept was introduced in \cite{Ber84} and
\cite{Pea84} to assess what can be inferred by rational players in a
non-cooperative game in the presence of common knowledge. However, this notion
can be defined in a number of ways that differ in seemingly unimportant minor
details. We shed light on these differences, explain their impact, and clarify
for which games these definitions coincide. Then we apply the same analysis to
explain the differences and similarities between various ways the iterated
elimination of strictly dominated strategies was defined in the literature.
This allows us to clarify the results of \cite{DS02} and \cite{CLL05} and
improve upon them. We also consider the extension of these results to strict
dominance by a mixed strategy. Our approach is based on a general study of the
operators on complete lattices. We allow transfinite iterations of the
considered operators and clarify the need for them. The advantage of such a
general approach is that a number of results, including order independence for
some of the notions of rationalizability and strict dominance, come for free.Comment: 39 pages, appeared in The B.E. Journal of Theoretical Economics: Vol.
7 : Iss. 1 (Topics), Article 18. Available at:
http://www.bepress.com/bejte/vol7/iss1/art1
A characterization of sequential rationalizability
A choice function is sequentially rationalizable if there is an ordered collection of asymmetric binary relations that identifies the selected alternative in every choice problem. We propose a property, F-consistency, and show that it characterizes the notion of sequential rationalizability. F-consistency is a testable property that highlights the behavioral aspects implicit in sequentially rationalizable choice. Further, our characterization result provides a novel tool with which to study how other behavioral concepts are related to sequential rationalizability, and establish a priori unexpected implications. In particular, we show that the concept of rationalizability by game trees, which, in principle, had little to do with sequential rationalizability, is a refinement of the latter. Every choice function that is rationalizable by a game tree is also sequentially rationalizable. Finally, we show that some prominent voting mechanisms are also sequentially rationalizable.Individual rationality, Rationalizability, Consistency, Bounded rationality, Behavioral economics, Voting
Degrees of cooperation in household consumption models: a revealed preference analysis
We develop a revealed preference approach to analyze non-unitary consumption models with intrahousehold allocations deviating from the cooperative (or Pareto efficient) solution. At a theoretical level, we establish revealed preference conditions of household consumption models with varying degrees of cooperation. Using these conditions, we show independence (or non-nestedness) of the different (cooperative-noncooperative) models. At a practical level, we show that our characterization implies testable conditions for a whole spectrum of cooperative-noncooperative models that can be verified by means of mixed integer programming (MIP) methods. This MIP formulation is particularly attractive in view of empirical analysis. An application to data drawn from the Russia Longitudinal Monitoring Survey (RLMS) demonstrates the empirical relevance of consumption models that account for limited intrahousehold cooperation.household consumption, intrahousehold cooperation, revealed preferences, Generalized Axiom of Revealed Preference (GARP), mixed integer programming (MIP).
Interdependent Preferences and Strategic Distinguishability
A universal type space of interdependent expected utility preference types is constructed from higher-order preference hierarchies describing (i) an agent's (unconditional) preferences over a lottery space; (ii) the agent's preference over Anscombe-Aumann acts conditional on the unconditional preferences; and so on. Two types are said to be strategically indistinguishable if they have an equilibrium action in common in any mechanism that they play. We show that two types are strategically indistinguishable if and only if they have the same preference hierarchy. We examine how this result extends to alternative solution concepts and strategic relations between types.Interdependent preferences, Higher-order preference hierarchy, Universal type space, Strategic distinguishability
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