Related papers: Rational Bubbles: A Clarification
Sullivan's multi-bubble isoperimetric conjectures in $n$-dimensional Euclidean and spherical spaces assert that standard bubbles uniquely minimize total perimeter among all $q-1$ bubbles enclosing prescribed volume, for any $q \leq n+2$.…
The St. Petersburg Paradox, an important topic in probability theory, has not been solved in the last 280 years. Since Nicolaus Bernoulli proposed the St. Petersburg Paradox in 1738, many people had tried to solve it and had proposed…
As we show by using notions of equilibrium in infinite sequential games, crashes or financial escalations are rational for economic or environmental agents, who have a vision of an infinite world. This contradicts a picture of a…
The problem of investing into a cryptocurrency market requires good understanding of the processes that regulate the price of the currency. In this paper we offer a view of a cryptocurrency market as an environment for realization of a…
A rational theory is proposed to describe the large-scale motion in turbulence. The fluid element with inner orientational structures is proposed to be the building block of fluid dynamics. The variance of the orientational structures then…
The classic double bubble theorem says that the least-perimeter way to enclose and separate two prescribed volumes in $\mathbb{R}^N$ is the standard double bubble. We seek the optimal double bubble in $\mathbb{R}^N$ with density, which we…
Causality is a fundamental part of the scientific endeavour to understand the world. Unfortunately, causality is still taboo in much of psychology and social science. Motivated by a growing number of recommendations for the importance of…
Philosophical analyses of causation take many forms but one major difficulty they all aim to address is that of the spatio-temporal continuity between causes and their effects. Bertrand Russell in 1913 brought the problem to its most…
This expository paper is concerned with the rationality problems for three-dimensional algebraic varieties with a conic bundle structure. We discuss the main methods of this theory. We sketch the proofs of certain principal results, and…
It is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality. Using the physical concepts and mathematical structures of quantum mechanics, we construct an econophysics framework for…
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…
We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One…
The notion of 'slope rational connectedness' is introduced in the context of smooth orbifold pairs. The main result parallels the characterization of the rational connectedness of projective manifolds in terms of either the non-existence of…
The rationality problem of two-dimensional purely quasi-monomial actions was solved completely by Hoshi, Kang and Kitayama [HKK]. As a generalization, we solve the rationality problem of two-dimensional quasi-monomial actions under the…
The idea that the universe might be open is an old one, and the possibility of having an open universe arise form inflation is not new either. However, a concrete realization of a consistent single-bubble open inflation model is known only…
We propose a new definition of actual causes, using structural equations to model counterfactuals.We show that the definitions yield a plausible and elegant account ofcausation that handles well examples which have caused problems forother…
The paper by Mayo claims to provide a new clarification and critique of Birnbaum's argument for showing that sufficiency and conditionality principles imply the likelihood principle. However, much of the arguments go back to arguments made…
We study cautious reasoning in finite sequential games played by agents with perfect recall. Our contribution lies in formulating a definition of prudent rationalizability (Heifetz et al. 2021, BEJTE) as an iterative reduction procedure of…
This paper mainly focuses on (1) a generalized treatment of fuzzy sets of type $n$, where $n$ is an integer larger than or equal to $1$, with an example, mathematical discussions, and real-life interpretation of the given mathematical…
By combining (i) the economic theory of rational expectation bubbles, (ii) behavioral finance on imitation and herding of investors and traders and (iii) the mathematical and statistical physics of bifurcations and phase transitions, the…