On the non-existence of a rationality definition for extensive games

Standard solution concepts, like subgame perfection, implicitly require that players will continue to assume everybody is rational even if this has been revealed to be false by virtue of having reached a node that could not have been reached had all players behaved rationally. Several attempts have been made in the literature to solve this problem. The present paper shows that the problem is insoluble.     

Eine Approximation der Binomialverteilung durch die Normalverteilung der Ordnung 1/n

Summary The class (1) of transformations of a binomial variablek is studied. The famous De Moivre-Laplace local and integral limit theorems are generalized for the asymptotically standardized transformations (2). The transformation (4) respectively (3) is singled out as the only one with an error of order 1/n. Besides it is shown, that the error term of ordern ^–1/2 of the identical transformation, the angular transformation, and the logarithmic transformation are in proportion to 1/6, –1/12, and –1/3. Results on the influence of a correction of unbiasedness are mentioned in the last section. Such corrections allow a slight improvement of our new transformation.     

Some undecidable determined games

Computing machines using algorithms play games and even learn to play games. However, the inherent finiteness properties of algorithms impose limitations on the game playing abilities of machines. M. Rabin illustrated this limitation in 1957 by constructing a two-person win-lose game with decidable rules but no computable winning strategies. Rabin's game was of the type where two players take turns choosing integers to satisfy some decidable but very complicated winning condition. In the present paper we obtain similar theorems of this type but the winning conditions are extremely simple relations (polynomial equations). Specific examples are given.     

Nichtlineare Schwingungen und kinetische Instabilität bei Saiten und Stäben

Ohne Zusammenfassung     

Value on a class of non-differentiable market games

We prove the existence of a (unique) Aumann-Shapley value on the space on non-atomic gamesQ ⁿ generated byn-handed glove games. (These are the minima ofn non-atomic mutually singular probability measures.) It is also shown that this value can be extended to a value on the smallest space containingQ ⁿ andpNA.     

The weak capacity of averaged channels

Summary Coding theorem and weak converse of the coding theorem are proved for averaged semicontinuous stationary channels and for almost periodic discrete channels, whose phases are statistically known. Explicit formulas for the capacities are given. The strong converses of the coding theorems do not hold.     

Sur les suites de Toeplitz

Summary The spectral properties and strict ergodicity property of the Toeplitz sequences which have been introduced in [1] are also consequences of an isomorphism of the dynamical systems associated to these sequences with translations on certain abelian compact groups.