Topologies on types

We define and analyze a "strategic topology'' on types in the Harsanyi-Mertens-Zamir universal type space, where two types are close if their strategic behavior is similar in all strategic situations. For a fixed game and action define the distance between a pair of types as the difference between the smallest epsilon for which the action is epsilon interim correlated rationalizable. We define a strategic topology in which a sequence of types converges if and only if this distance tends to zero for any action and game. Thus a sequence of types converges in the strategic topology if that smallest epsilon does not jump either up or down in the limit. As applied to sequences, the upper-semicontinuity property is equivalent to convergence in the product topology, but the lower-semicontinuity property is a strictly stronger requirement, as shown by the electronic mail game. In the strategic topology, the set of "finite types'' (types describable by finite type spaces) is dense but the set of finite common-prior types is not.Rationalizability, incomplete information, common knowledge, universal type space, strategic topology

Interim Rationalizability

This paper proposes the solution concept of interim rationalizability, and shows that all type spaces that have the same hierarchies of beliefs have the same set of interim rationalizable outcomes. This solution concept characterizes common knowledge of rationality in the universal type space.

Interim correlated rationalizability

This paper proposes the solution concept of interim correlated rationalizability, and shows that all types that have the same hierarchies of beliefs have the same set of interim-correlated-rationalizable outcomes. This solution concept characterizes common certainty of rationality in the universal type space.Rationalizability, incomplete information, common certainty, common knowledge, universal type space

Topologies on Types

We define and analyze "strategic topologies" on types, under which two types are close if their strategic behavior will be similar in all strategic situations. To oper- ationalize this idea, we adopt interim rationalizability as our solution concept, and define a metric topology on types in the Harsanyi-Mertens-Zamir universal type space. This topology is the coarsest metric topology generating upper and lower hemiconti- nuity of rationalizable outcomes. While upper strategic convergence is equivalent to convergence in the product topology, lower strategic convergence is a strictly stronger requirement, as shown by the electronic mail game. Nonetheless, we show that the set of "finite types" (types describable by finite type spaces) are dense in the lower strategic topology.

Approaches to Development and Extension of Capture Technologies for Developing Small Scale Fisheries

Over half the world\u27s supply of fish for human consumption is produced by small scale fisheries. In recent years, increasing attention has been focused on improvement of small scale fisheries in developing countries. In spite of substantial investments, and the arduous labor of many competent, well-intentioned people, the success rates of small scale fisheries development projects have not been encouraging. This paper will discuss two types of project approaches which have been used in small scale fisheries development, with examples of the challenges and problems they have encountered. A description of the Appropriate Technology Adaptive Research, Development, and Extension (ATARDE) approach for small scale fisheries will follow, with comments on its potential, and challenges it will have to address

Uniform approximation of barrier penetration in phase space

A method to approximate transmission probabilities for a nonseparable multidimensional barrier is applied to a waveguide model. The method uses complex barrier-crossing orbits to represent reaction probabilities in phase space and is uniform in the sense that it applies at and above a threshold energy at which classical reaction switches on. Above this threshold the geometry of the classically reacting region of phase space is clearly reflected in the quantum representation. Two versions of the approximation are applied. A harmonic version which uses dynamics linearised around an instanton orbit is valid only near threshold but is easy to use. A more accurate and more widely applicable version using nonlinear dynamics is also described