Existence of a value for a general zero-sum mixt game

2005 ◽  
pp. 688-695
Author(s):  
J. P. Lepeltier
Keyword(s):  
A Value ◽  
Zero Sum

scholarly journals Solving Partially Observable Stochastic Games with Public Observations

2019 ◽  
Vol 33 ◽  
pp. 2029-2036
Author(s):  
Karel Horák ◽  
Branislav Bošanský
Keyword(s):  
Stochastic Games ◽  
Partial Information ◽  
General Setting ◽  
Value Functions ◽  
Value Of The Game ◽  
A Value ◽  
Stochastic Events ◽  
Zero Sum ◽  
Partially Observable ◽  
Practical Demonstration

In many real-world problems, there is a dynamic interaction between competitive agents. Partially observable stochastic games (POSGs) are among the most general formal models that capture such dynamic scenarios. The model captures stochastic events, partial information of players about the environment, and the scenario does not have a fixed horizon. Solving POSGs in the most general setting is intractable.Therefore, the research has been focused on subclasses of POSGs that have a value of the game and admit designing (approximate) optimal algorithms. We propose such a subclass for two-player zero-sum games with discounted-sum objective function—POSGs with public observations (POPOSGs)—where each player is able to reconstruct beliefs of the other player over the unobserved states. Our results include: (1) theoretical analysis of PO-POSGs and their value functions showing convexity (concavity) in beliefs of maximizing (minimizing) player, (2) a novel algorithm for approximating the value of the game, and (3) a practical demonstration of scalability of our algorithm. Experimental results show that our algorithm can closely approximate the value of non-trivial games with hundreds of states.

scholarly journals Certain Infinite Zero-Sum Two-Person Games

1956 ◽  
Vol 8 ◽  
pp. 412-416 ◽  
Author(s):  
A. L. Dulmage ◽  
J. E. L. Peck
Keyword(s):  
Infinite Games ◽  
Von Neumann ◽  
A Value ◽  
The Matrix ◽  
Pure Strategies ◽  
Person Game ◽  
Zero Sum

1. Introduction. The theorem of von Neumann, that every finite, zero-sum two-person game has a value, has been extended in various ways to infinite games. In particular Wald (6) has shown that any bounded game in which one player has finitely many pure strategies, has a value. Our interest was aroused by the infinite analogue of the game of “hide and seek” as described by von Neumann (5), which does not appear to fit any of the known cases, unless the matrix is bounded.

scholarly journals A probabilistic verification theorem for the finite horizon two-player zero-sum optimal switching game in continuous time

2019 ◽  
Vol 51 (2) ◽  
pp. 425-442
Author(s):  
S. Hamadène ◽  
R. Martyr ◽  
J. Moriarty
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Continuous Time ◽  
Backward Stochastic Differential Equations ◽  
Finite Horizon ◽  
Optimal Switching ◽  
Verification Theorem ◽  
A Value ◽  
Zero Sum ◽  
Switching Game

AbstractIn this paper we study continuous-time two-player zero-sum optimal switching games on a finite horizon. Using the theory of doubly reflected backward stochastic differential equations with interconnected barriers, we show that this game has a value and an equilibrium in the players’ switching controls.

scholarly journals Replicating and stress-testing behavioural profiles following feedback: Assessing the interpretation of neutral outcomes

2020 ◽  
Author(s):  
Rimsa Dahal ◽  
Kelsey MacLellan ◽  
Danielle Vavrek ◽  
Ben Dyson
Keyword(s):  
Stress Testing ◽  
Mixed Strategy ◽  
Reaction Times ◽  
Optimal Performance ◽  
Negative Results ◽  
A Value ◽  
Behavioural Profile ◽  
Strategy Performance ◽  
The Difference ◽  
Zero Sum

Previous data point to neutral outcomes (draws) being subjectively assigned negative rather than positive value. The combined observations of faster rather than slower reaction times, subsequent actions defined by shift rather than stay behaviour, reduced flexibility, and, larger rather than smaller deviations from optimal performance all align with consequences of explicitly negative outcomes such as losses. We further tested the negative interpretation of draws via a value manipulation by assigning draws in a zero-sum game to +1, 0 or -1. If draws are inherently negative then the difference in behavioural profile comparisons should be greater when draw values are changed to a positive (+1) rather than negative (-1) value. Despite the observations of post-draw speeding and bias towards draw-shift behaviour, the degree of shift behaviour was equivalent between draw values of 0 and +1 and approached an approximation of optimal mixed-strategy performance. This was in contrast to draw values of -1 significantly increasing the degree of shift behaviour. This modification of draw behaviour was weaker when the same value modifications were applied to win or lose trials. Rather than viewing draws as neutral and valence-free outcomes, the processing cascade generated by stalemate produces a complex behavioural profile containing elements found in response to both explicitly positive and explicitly negative results.

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.

Observations of the Thermal Decomposition of Brucite

1968 ◽  
Vol 26 ◽  
pp. 446-447
Author(s):  
P. L. Burnett ◽  
W. R. Mitchell ◽  
C. L. Houck
Keyword(s):  
Thermal Decomposition ◽  
Magnesium Oxide ◽  
Basal Plane ◽  
Magnesium Ions ◽  
A Value ◽  
Reaction Proceeds

Natural Brucite (Mg(OH)2) decomposes on heating to form magnesium oxide (MgO) having its cubic ﹛110﹜ and ﹛111﹜ planes respectively parallel to the prism and basal planes of the hexagonal brucite lattice. Although the crystal-lographic relation between the parent brucite crystal and the resulting mag-nesium oxide crystallites is well known, the exact mechanism by which the reaction proceeds is still a matter of controversy. Goodman described the decomposition as an initial shrinkage in the brucite basal plane allowing magnesium ions to shift their original sites to the required magnesium oxide positions followed by a collapse of the planes along the original <0001> direction of the brucite crystal. He noted that the (110) diffraction spots of brucite immediately shifted to the positions required for the (220) reflections of magnesium oxide. Gordon observed separate diffraction spots for the (110) brucite and (220) magnesium oxide planes. The positions of the (110) and (100) brucite never changed but only diminished in intensity while the (220) planes of magnesium shifted from a value larger than the listed ASTM d spacing to the predicted value as the decomposition progressed.

Field-assisted ionization theory for microscopists

1994 ◽  
Vol 52 ◽  
pp. 820-821
Author(s):  
Patrick P. Camus
Keyword(s):  
Electric Field ◽  
Electron Tunneling ◽  
Ionization Probability ◽  
Critical Distance ◽  
Tunneling Probability ◽  
Field Ionization ◽  
Radius Of Curvature ◽  
Field Evaporation ◽  
A Value ◽  
Ion Emission

The theory of field ion emission is the study of electron tunneling probability enhanced by the application of a high electric field. At subnanometer distances and kilovolt potentials, the probability of tunneling of electrons increases markedly. Field ionization of gas atoms produce atomic resolution images of the surface of the specimen, while field evaporation of surface atoms sections the specimen. Details of emission theory may be found in monographs.Field ionization (FI) is the phenomena whereby an electric field assists in the ionization of gas atoms via tunneling. The tunneling probability is a maximum at a critical distance above the surface,xc, Fig. 1. Energy is required to ionize the gas atom at xc, I, but at a value reduced by the appliedelectric field, xcFe, while energy is recovered by placing the electron in the specimen, φ. The highest ionization probability occurs for those regions on the specimen that have the highest local electric field. Those atoms which protrude from the average surfacehave the smallest radius of curvature, the highest field and therefore produce the highest ionizationprobability and brightest spots on the imaging screen, Fig. 2. This technique is called field ion microscopy (FIM).

Vitamin A Value of Plant Food Provitamin A - Evaluated by the Stable Isotope Technologies

2014 ◽  
Vol 84 (Supplement 1) ◽  
pp. 25-29 ◽  
Author(s):  
Guangwen Tang
Keyword(s):  
Stable Isotope ◽  
Vitamin A ◽  
Provitamin A ◽  
Animal Origin ◽  
Plant Food ◽  
Plant Foods ◽  
A Value ◽  
Provitamin A Carotenoids ◽  
Β Carotene

Humans need vitamin A and obtain essential vitamin A by conversion of plant foods rich in provitamin A and/or absorption of preformed vitamin A from foods of animal origin. The determination of the vitamin A value of plant foods rich in provitamin A is important but has challenges. The aim of this paper is to review the progress over last 80 years following the discovery on the conversion of β-carotene to vitamin A and the various techniques including stable isotope technologies that have been developed to determine vitamin A values of plant provitamin A (mainly β-carotene). These include applications from using radioactive β-carotene and vitamin A, depletion-repletion with vitamin A and β-carotene, and measuring postprandial chylomicron fractions after feeding a β-carotene rich diet, to using stable isotopes as tracers to follow the absorption and conversion of plant food provitamin A carotenoids (mainly β-carotene) in humans. These approaches have greatly promoted our understanding of the absorption and conversion of β-carotene to vitamin A. Stable isotope labeled plant foods are useful for determining the overall bioavailability of provitamin A carotenoids from specific foods. Locally obtained plant foods can provide vitamin A and prevent deficiency of vitamin A, a remaining worldwide concern.

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