scholarly journals ANALYSIS OF TREMBLING HAND PERFECT EQUILIBRIA IN QUANTUM GAMES

2008 ◽  
Vol 08 (01) ◽  
pp. L23-L30 ◽  
Author(s):  
IRENEUSZ PAKUŁA
Keyword(s):  
Game Theory ◽  
Probability Distribution ◽  
Distribution Functions ◽  
Quantum Game ◽  
Quantum Games ◽  
Probability Distribution Functions ◽  
Perfect Equilibria ◽  
Quantum Strategies

We analyse Selten' concept of trembling hand perfect equilibria in the context of quantum game theory. We define trembles as mixed quantum strategies by replacing discrete probabilities with probability distribution functions. Explicit examples of analysis are given.

scholarly journals Quantum Mean-Field Games with the Observations of Counting Type

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 7
Author(s):  
Vassili N. Kolokoltsov
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Open Problem ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Mean Field ◽  
Mean Field Games ◽  
Quantum Game ◽  
Quantum Games ◽  
Interesting Open Problem

Quantum games and mean-field games (MFG) represent two important new branches of game theory. In a recent paper the author developed quantum MFGs merging these two branches. These quantum MFGs were based on the theory of continuous quantum observations and filtering of diffusive type. In the present paper we develop the analogous quantum MFG theory based on continuous quantum observations and filtering of counting type. However, proving existence and uniqueness of the solutions for resulting limiting forward-backward system based on jump-type processes on manifolds seems to be more complicated than for diffusions. In this paper we only prove that if a solution exists, then it gives an ϵ-Nash equilibrium for the corresponding N-player quantum game. The existence of solutions is suggested as an interesting open problem.

Probability Distribution Functions for the Random Forced Burgers Equation

1997 ◽  
Vol 78 (10) ◽  
pp. 1904-1907 ◽  
Author(s):  
Weinan E ◽  
Konstantin Khanin ◽  
Alexandre Mazel ◽  
Yakov Sinai
Keyword(s):  
Probability Distribution ◽  
Burgers Equation ◽  
Distribution Functions ◽  
Probability Distribution Functions

Exploring probability distribution functions best-fitting the kinetic energy of coarse particles at above threshold flow conditions

2021 ◽  
Author(s):  
Hamed Farhadi ◽  
Manousos Valyrakis
Keyword(s):  
Probability Distribution ◽  
Kinetic Energy ◽  
Test Section ◽  
Particle Transport ◽  
River Flow ◽  
Distribution Functions ◽  
Transport Processes ◽  
Flow Conditions ◽  
Probability Distribution Functions ◽  
Transport Regime

<p>Applying an instrumented particle [1-3], the probability density functions of kinetic energy of a coarse particle (at different solid densities) mobilised over a range of above threshold flow conditions conditions corresponding to the intermittent transport regime, were explored. The experiments were conducted in the Water Engineering Lab at the University of Glasgow on a tilting recirculating flume with 800 (length) × 90 (width) cm dimension. Twelve different flow conditions corresponding to intermittent transport regime for the range of particle densities examined herein, have been implemented in this research. Ensuring fully developed flow conditions, the start of the test section was located at 3.2 meters upstream of the flume outlet. The bed surface of the flume is flat and made up of well-packed glass beads of 16.2 mm diameter, offering a uniform roughness over which the instrumented particle is transported. MEMS sensors are embedded within the instrumented particle with 3-axis gyroscope and 3-axis accelerometer. At the beginning of each experimental run, instrumented particle is placed at the upstream of the test section, fully exposed to the free stream flow. Its motion is recorded with top and side cameras to enable a deeper understanding of particle transport processes. Using results from sets of instrumented particle transport experiments with varying flow rates and particle densities, the probability distribution functions (PDFs) of the instrumented particles kinetic energy, were generated. The best-fitted PDFs were selected by applying the Kolmogorov-Smirnov test and the results were discussed considering the light of the recent literature of the particle velocity distributions.</p><p>[1] Valyrakis, M.; Alexakis, A. Development of a “smart-pebble” for tracking sediment transport. In Proceedings of the International Conference on Fluvial Hydraulics (River Flow 2016), St. Louis, MO, USA, 12–15 July 2016.</p><p>[2] Al-Obaidi, K., Xu, Y. & Valyrakis, M. 2020, The Design and Calibration of Instrumented Particles for Assessing Water Infrastructure Hazards, Journal of Sensors and Actuator Networks, vol. 9, no. 3, 36.</p><p>[3] Al-Obaidi, K. & Valyrakis, M. 2020, Asensory instrumented particle for environmental monitoring applications: development and calibration, IEEE sensors journal (accepted).</p>

Design for Project Change Management: Part 2 — Attribute Design

2004 ◽  
Author(s):  
D. Xue ◽  
S. Y. Cheing ◽  
P. Gu
Keyword(s):  
Optimal Design ◽  
Probability Distribution ◽  
Taguchi Method ◽  
Systematic Approach ◽  
Distribution Functions ◽  
Probability Distribution Functions ◽  
Construction Tasks ◽  
Design Attribute ◽  
Value Changes ◽  
Design Aspect

This research introduces a new systematic approach to identify the optimal design configuration and attributes to minimize the potential construction project changes. The second part of this paper focuses on the attribute design aspect. In this research, the potential changes of design attribute values are modeled by probability distribution functions. Attribute values of the design whose construction tasks are least sensitive to the changes of these attribute values are identified based upon Taguchi Method. In addition, estimation of the potential project change cost due to the potential design attribute value changes is also discussed. Case studies in pipeline engineering design and construction have been conducted to show the effectiveness of the introduced approach.

scholarly journals Using Percentiles to Communicate Snowfall Uncertainty

2014 ◽  
Vol 29 (5) ◽  
pp. 1259-1265 ◽  
Author(s):  
David R. Novak ◽  
Keith F. Brill ◽  
Wallace A. Hogsett
Keyword(s):  
Probability Distribution ◽  
False Alarm ◽  
Weather Prediction ◽  
Winter Precipitation ◽  
Risk Tolerance ◽  
Distribution Functions ◽  
Precipitation Forecast ◽  
Ensemble Forecasts ◽  
False Alarm Ratio ◽  
Probability Distribution Functions

Abstract An objective technique to determine forecast snowfall ranges consistent with the risk tolerance of users is demonstrated. The forecast snowfall ranges are based on percentiles from probability distribution functions that are assumed to be perfectly calibrated. A key feature of the technique is that the snowfall range varies dynamically, with the resultant ranges varying based on the spread of ensemble forecasts at a given forecast projection, for a particular case, for a particular location. Furthermore, this technique allows users to choose their risk tolerance, quantified in terms of the expected false alarm ratio for forecasts of snowfall range. The technique is applied to the 4–7 March 2013 snowstorm at two different locations (Chicago, Illinois, and Washington, D.C.) to illustrate its use in different locations with different forecast uncertainties. The snowfall range derived from the Weather Prediction Center Probabilistic Winter Precipitation Forecast suite is found to be statistically reliable for the day 1 forecast during the 2013/14 season, providing confidence in the practical applicability of the technique.

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