scholarly journals Mathematical Theory of Zero-Sum Two-Person Games with a Finite Number or a Continuum of Strategies

10.7249/r115 ◽  
1948 ◽  
Author(s):  
H. Bohnenblust ◽  
Melvin Dresher ◽  
M. Girshick ◽  
Theodore Harris ◽  
Olaf Helmer-Hirschberg ◽  
...  
Keyword(s):  
Finite Number ◽  
Mathematical Theory ◽  
Zero Sum

scholarly journals STATIONARY STRATEGIES IN ZERO-SUM STOCHASTIC GAMES

2001 ◽  
Vol 03 (04) ◽  
pp. 283-290
Author(s):  
J. FLESCH ◽  
F. THUIJSMAN ◽  
O. J. VRIEZE
Keyword(s):  
Finite Number ◽  
Stochastic Games ◽  
Stationary Strategies ◽  
Pure Strategies ◽  
Zero Sum

We deal with zero-sum stochastic games. We demonstrate the importance of stationary strategies by showing that stationary strategies are better (in terms of the rewards they guarantee for a player, against any strategy of his opponent) than (1) pure strategies (even history-dependent ones), (2) strategies which may use only a finite number of different mixed actions in any state, and (3) strategies with finite recall. Examples are given to clarify the issues.

The null set of the join of paths

2019 ◽  
Vol 12 (04) ◽  
pp. 1950060
Author(s):  
Arnold A. Eniego ◽  
I. J. L. Garces
Keyword(s):  
Abelian Group ◽  
Positive Integer ◽  
Finite Number ◽  
Sum Formula ◽  
Zero Sum ◽  
Null Set

For positive integer [Formula: see text], a graph [Formula: see text] is said to be [Formula: see text]-magic if the edges of [Formula: see text] can be labeled with the nonzero elements of Abelian group [Formula: see text], where [Formula: see text] (the set of integers) and [Formula: see text] is the group of integers mod [Formula: see text], so that the sum of the labels of the edges incident to any vertex of [Formula: see text] is the same. When this constant sum is [Formula: see text], we say that [Formula: see text] is a zero-sum [Formula: see text]-magic graph. The set of all [Formula: see text] for which [Formula: see text] is a zero-sum [Formula: see text]-magic graph is the null set of [Formula: see text]. In this paper, we will completely determine the null set of the join of a finite number of paths.

scholarly journals Cumulative Subtraction Games

10.37236/7904 ◽  
2019 ◽  
Vol 26 (4) ◽  
Author(s):  
Gal Cohensius ◽  
Urban Larsson ◽  
Reshef Meir ◽  
David Wahlstedt
Keyword(s):  
Finite Number ◽  
Explicit Description ◽  
Zero Sum ◽  
Outcome Function

We study a variation of Nim-type subtraction games, called Cumulative Subtraction (CS). Two players alternate in removing pebbles out of a joint pile, and their actions add or remove points to a common score. We prove that the zero-sum outcome in optimal play of a CS with a finite number of possible actions is eventually periodic, with period $2s$, where $s$ is the size of the largest available action. This settles a conjecture by Stewart in his Ph.D. thesis (2011). Specifically, we find a quadratic bound, in the size of $s$, on when the outcome function must have become periodic. In case of exactly two possible actions, we give an explicit description of optimal play.

Why do people believe in a zero-sum economy?

2018 ◽  
Vol 41 ◽  
Author(s):  
Samuel G. B. Johnson
Keyword(s):  
Perspective Taking ◽  
Evolutionary Model ◽  
Everyday Experience ◽  
Coalitional Psychology ◽  
The Face ◽  
Zero Sum

AbstractZero-sum thinking and aversion to trade pervade our society, yet fly in the face of everyday experience and the consensus of economists. Boyer & Petersen's (B&P's) evolutionary model invokes coalitional psychology to explain these puzzling intuitions. I raise several empirical challenges to this explanation, proposing two alternative mechanisms – intuitive mercantilism (assigning value to money rather than goods) and errors in perspective-taking.

Criteria and Methods for Reliable Three-Dimensional Image Reconstruction

1974 ◽  
Vol 32 ◽  
pp. 330-331
Author(s):  
R. A. Crowther
Keyword(s):  
Image Reconstruction ◽  
Finite Number ◽  
Density Distribution ◽  
Electron Micrographs ◽  
Mathematical Problem ◽  
Three Dimensional ◽  
Ideal Case ◽  
Dimensional Image ◽  
General Object ◽  
The Ideal

The reconstruction of a three-dimensional image of a specimen from a set of electron micrographs reduces, under certain assumptions about the imaging process in the microscope, to the mathematical problem of reconstructing a density distribution from a set of its plane projections.In the absence of noise we can formulate a purely geometrical criterion, which, for a general object, fixes the resolution attainable from a given finite number of views in terms of the size of the object. For simplicity we take the ideal case of projections collected by a series of m equally spaced tilts about a single axis.

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