The non-existence of a universal topological type space

The concept of types was introduced by Harsányi[8]. In the literature there are two approaches for formalizing types, type spaces: the purely measurable and the topological models. In the former framework Heifetz and Samet [11] showed that the universal type space exists and later Meier[13] proved that it is complete. In this paper we examine the topological approach and conclude that there is no universal topological type space in the category of topological type spaces

Adoption and Aspiration: The Uniform Adoption Act, the Deboer-Schmidt Case, and the American Quest for the Ideal Family

When the state must designate a child\u27s legal parentage, should the goal be to protect the biological parents\u27 opportunity interests to raise their child or to protect the child\u27s established relationships with the individuals who have actually functioned as her parents? What characteristics render an adult an appropriate parent? These questions, long in the background of disputes over adoption, have been raised with new intensity in the early 1990s in two distinctive settings. The first is the debate about these questions waged in the courts and the media. The second is the effort of the National Conference of Commissioners on Uniform State Laws (NCCUSL) to create a Uniform Adoption Act. The fate of the child called Jessica by her would-be adopters in Michigan and Anna by her birth parents in Iowa was a matter of agitated public debate before, during, and after it was decided by a legal system slow to resolve the conflicting claims of the adoptive and birth parents and even slower to recognize the young child\u27s interest in a quick decision. 1 Similarly, the law\u27s inability to resolve the competing claims of entitlement with respect to other young children--Richard Doe in Illinois, Emily W. in Florida, Michael S. in California--generates yet more media attention to the questions of where do children belong? and to whom do children belong? 2 As American culture\u27s internal conflicts over the ideal family are projected onto the various individuals, relationships, and households involved in each case, images of the conflicting ..

Derivation of the Local-Mean Stochastic Quantum Force

We regard the non-relativistic Schrodinger equation as an ensemble mean representation of the stochastic motion of a single particle in a vacuum, subject to an undefined stochastic quantum force. The local mean of the quantum force is found to be proportional to the third spatial derivative of the probability density function, while its associated pressure is proportional to the second spatial derivative. The latter arises from the single particle diluted gas pressure, and this observation allows to interpret the quantum Bohm potential as the energy required to put a particle in a bath of fluctuating vacuum at constant entropy and volume. The stochastic force expectation value is zero and is uncorrelated with the particle location, thus does not perform work on average. Nonetheless it is anti-correlated with volume and this anti-correlation leads to an uncertainty relation. We analyze the dynamic Gaussian solution to the Schrodinger equation as a simple example for exploring the mean properties of this quantum force. We conclude with a few possible interpretations as to the origins of quantum stochasticity.Comment: Accepted to Fluctuation and Noise Letters. This manuscript supersedes arXiv:1607.0284

Common Knowledge of Rationality and Market Clearing in Economies with Asymmetric Information

Consider an exchange economy with asymmetric information. What is the set of outcomes that are consistent with common knowledge of rationality and market clearing? To address this question we define an epistemic model for the economy that provides a complete description not only of the beliefs of each agent on the relationship between states of nature and prices but also of the whole system of interactive beliefs. The main result, theorem 1, provides a characterization of outcomes that are consistent with common knowledge of rationality and market clearing (henceforth, CKRMC outcomes) in terms of a solution notion - Ex - Post Rationalizability - that is defined directly in terms of the parameters that define the economy. We then apply theorem 1 to characterize the set of CKRMC outcomes in a general class of economies with two commodities. CKRMC manifests several intuitive properties that stand in contrast to the full revelation property of Rational Expectations Equilibrium: In particular, we obtain that for a robust class of economies: (1) there is a continuum of prices that are consistent with CKRMC in every state of nature, and hence these prices do not reveal the true state, (2) the range of CKRMC outcomes is monotonically decreasing as agents become more informed about the economic fundamentals, and (3) trade is consistent with common knowledge of rationality and market clearing even when there is common knowledge that there are no mutual gains from trade.common knowledge, rationality, rationalizability, rationalizable expectations

On entropy production in the Madelung fluid and the role of Bohm's potential in classical diffusion

The Madelung equations map the non-relativistic time-dependent Schrodinger equation into hydrodynamic equations of a virtual fluid. Here we show that an increase of the Boltzmann entropy of this Madelung fluid is proportional to the expectation value of its velocity divergence. Hence, entropy growth is accompanied by expansion resulting from the ability of the Madelung fluid to be compressible. The compressibility itself reflects superposition of solutions of the Schrodinger equation. Thus, in unitary processes where the Madelung fluid expands and then shrinks, the Boltzmann entropy may, correspondingly, grow and then decrease. The notion of entropy growth due to expansion is common in diffusive processes, however in the latter the process is irreversible. Much unlike the Boltzmann entropy, the von Neumann entropy, does not vary with time. To elucidate the physical underpinning of the Boltzmann entropy, we examine several specific examples. We demonstrate that, for classical diffusive processes, the "force" accelerating diffusion has the form of the positive gradient of the quantum Bohm potential. In the Madelung fluid, the advective and the diffusive velocities correspond respectively to the the real and imaginary parts of the complex momentum. We find that the diffusion coefficient provides a lower bound of Heisenberg uncertainty type product between the gas mean free path and the Brownian momentum.Comment: 9 pages. The second version contains more examples and explanation

Dynamic unawareness and rationalizable behavior

We define generalized extensive-form games which allow for mutual unawareness of actions. We extend Pearce's (1984) notion of extensive-form (correlated) rationalizability to this setting, explore its properties and prove existence.Unawareness, extensive-form games, extensive-form rationalizability