A weakened asymptotic monogeny condition

Functions of one complex variable that satisfy a weakened asymptotic monogeny condition are proved to be holomorphic. Translated fromMatematicheskie Zametki, Vol. 60, No. 6, pp. 902–911, December, 1996. The author thanks Proffessor Dolzhenko for discussing the results of the paper. The research was supported by the Russian Foundation for Basic Research under grant No. 93-01-00236.     

Information patterns and Nash equilibria in extensive games: 1

In this paper we explore the relation between information patterns and Nash Equilibria in extensive games. By information we mean what players know about moves made by others, as well as by chance. For the most part we confine ourselves to pure strategies. But in Section 2 behavioral strategies are also examined. It turns out that they can be modeled as pure strategies of an appropriately enlarged game. Our results, applied to the enlarged game, can then be reinterpreted in terms of the behavioral strategies of the original game.     

关于Menger定理的推广的注

本文给出了一个图为Ｍｅｎｇｅｒ型的一个充分必要条件，利用这个条件，我们拓广了已知的Ｍｅｎｇｅｒ型图的类。     

A proof of the normal form theorem for the closed terms of Girard's system F by means of computability

In this paper a proof of the normal form theorem for the closed terms of Girard's system F is given by using a computability method à la Tait. It is worth noting that most of the standard consequences of the normal form theorem can be obtained using this version of the theorem as well. From the proof-theoretical point of view the interest of the proof is that the definition of computable derivation here used does not seem to be well founded. MSC: 03F05, 03B15.     

Lattice Approach to Wigner-Type Theorems

The Wigner's Theorem states that a bijective transformation of the set of all one-dimensional linear subspaces of a complex Hilbert space which preserves orthogonality is induced by either a unitary or an anti-unitary operator. There exist many Wigner-type theorems, in particular in indefinite metric spaces, von Neumanns algebras and Banach spaces and we try to find a common origin of all these results by using properties of the lattice subspaces of certain topological vector spaces. We prove a Wigner-type theorem for a pair of dual spaces which allows us to obtain, as particular cases, the usual Wigner's Theorem and some of its generalizations. PACS: 02.40.Dr, 03.65.Fd,03.65.Ta AMS Subject Classification (1991): 06C15, 46A20, 81P10.     

General sampling theorem using contour integral

We present the sampling theorem with sampling functions of general form for entire functions satisfying one of the growth conditions

     

The reproducible properties of correct forecasts

Each period, one outcome out of finitely many possibilities is observed. Each period, a forecaster announces some probability for the future outcomes based on the available data. An outsider wants to know if the forecaster has some knowledge of the data generating process. Let a test be an arbitrary function from sequences of forecasts and outcomes to {0,1}. When the test returns a 0 the test is said to reject the forecasts based on the outcome sequence. When the test resturns a 1 the test is said to not reject the forecasts based on the outcome sequence. Consider any test that does not reject the truth, i.e. it does not reject when the announced forecasts are the conditional probabilities of the data generating process. Based on Fans (1953) Minimax theorem, I show that it is possible to produce forecasts that will not be rejected on any sequence of outcomes. Journal of Economic Literature Classification Number:D83 LearningI thankfully acknowledge financial support from the National Science Foundation grant SES 0109650. I also thank a referee for useful comments. All errors are mine.