Central Concepts

2020 ◽  
pp. 13-26
Author(s):  
John M. McNamara ◽  
Olof Leimar
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Stability Condition ◽  
Performance Measure ◽  
Evolutionary Stability ◽  
Necessary Condition ◽  
Invasion Fitness ◽  
Mean Lifetime ◽  
Lifetime Number ◽  
The Mean

The chapter defines and discusses some of the central concepts in biological game theory. Strategies, which are rules for choosing actions as a function of state, play a pivotal role. It is explained how the theory operates at the level of strategies rather than attempting to follow the details of the underlying genetics that code for them. This is referred to as 'the phenotypic gambit', which is discussed and illustrated. The concept of the invasion fitness of a mutant strategy in a population that adopts another resident strategy is also central. This performance measure is used to give a necessary condition for evolutionary stability, formulated as the Nash equilibrium condition. It is explained how this stability condition can be reformulated in terms of simpler fitness proxies such as the mean lifetime number of offspring or the net rate of energy gain.

Temperature Dependences in the O + OH → O2 + H Reaction. Quasiclassical Trajectory Calculation

1993 ◽  
Vol 58 (2) ◽  
pp. 234-243 ◽  
Author(s):  
Viliam Klimo ◽  
Martina Bittererová ◽  
Stanislav Biskupič ◽  
Ján Urban ◽  
Miroslav Micov
Keyword(s):  
Temperature Dependence ◽  
Energy Surface ◽  
Analytical Form ◽  
Mean Values ◽  
Quantum Numbers ◽  
Mean Lifetime ◽  
Temperature Dependences ◽  
Quasiclassical Trajectory Calculation ◽  
The Mean ◽  
Combustion Processes

The reaction O + OH → O2 + H in conditions of combustion of hydrocarbons and polymers was modelled by using the method of quasiclassical trajectories. The potential energy surface was determined by the multiconfiguration interaction method and fitted with the analytical form of the extended LEPS function. Attention was paid to the mean values of the vibrational and rotational quantum numbers of O2 molecules and their temperature dependence. The temperature dependence of the mean lifetime of the OOH collision complex was also examined. The calculated rate constants were analyzed and compared with the experimental data over the temperature region of the combustion processes.

scholarly journals A Type of Time-Symmetric Stochastic System and Related Games

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 118
Author(s):  
Qingfeng Zhu ◽  
Yufeng Shi ◽  
Jiaqiang Wen ◽  
Hui Zhang
Keyword(s):  
Nash Equilibrium ◽  
Time Delay ◽  
Differential Equations ◽  
Equilibrium Point ◽  
Stochastic Differential Equations ◽  
Stochastic System ◽  
Stochastic Systems ◽  
Necessary Condition ◽  
Nash Equilibrium Point ◽  
Doubly Stochastic

This paper is concerned with a type of time-symmetric stochastic system, namely the so-called forward–backward doubly stochastic differential equations (FBDSDEs), in which the forward equations are delayed doubly stochastic differential equations (SDEs) and the backward equations are anticipated backward doubly SDEs. Under some monotonicity assumptions, the existence and uniqueness of measurable solutions to FBDSDEs are obtained. The future development of many processes depends on both their current state and historical state, and these processes can usually be represented by stochastic differential systems with time delay. Therefore, a class of nonzero sum differential game for doubly stochastic systems with time delay is studied in this paper. A necessary condition for the open-loop Nash equilibrium point of the Pontriagin-type maximum principle are established, and a sufficient condition for the Nash equilibrium point is obtained. Furthermore, the above results are applied to the study of nonzero sum differential games for linear quadratic backward doubly stochastic systems with delay. Based on the solution of FBDSDEs, an explicit expression of Nash equilibrium points for such game problems is established.

scholarly journals Holding a group together: non-game-theory vs. game-theory

2021 ◽  
Author(s):  
Michael Richter ◽  
Ariel Rubinstein
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Competitive Equilibrium ◽  
Solution Concept ◽  
Equilibrium Concept

Abstract Each member of a group chooses a position and has preferences regarding his chosen position. The group’s harmony depends on the profile of chosen positions meeting a specific condition. We analyse a solution concept (Richter and Rubinstein, 2020) based on a permissible set of individual positions, which plays a role analogous to that of prices in competitive equilibrium. Given the permissible set, members choose their most preferred position. The set is tightened if the chosen positions are inharmonious and relaxed if the restrictions are unnecessary. This new equilibrium concept yields more attractive outcomes than does Nash equilibrium in the corresponding game.

scholarly journals Effectiveness of Home-Based Occupational Therapy on COPM Performance and Satisfaction Scores in Patients with COPD

2020 ◽  
pp. 000841742097112
Author(s):  
Eleonore H. Koolen ◽  
Martijn A. Spruit ◽  
Marianne de Man ◽  
Jeanine C. Antons ◽  
Elieke Nijhuis ◽  
...  
Keyword(s):  
Occupational Therapy ◽  
Integrated Management ◽  
Performance Measure ◽  
Occupational Performance ◽  
Post Intervention ◽  
Canadian Occupational Performance Measure ◽  
Home Based ◽  
Copd Patients ◽  
The Mean ◽  
Mean Differences

Background. Occupational therapy (OT) may be an important intervention in patients with COPD, but studies show conflicting results. Purpose. To evaluate the effectiveness of home-based monodisciplinary OT in COPD patients Method. We conducted an observational clinical study. Main outcomes were the mean differences in the Canadian Occupational Performance Measure (COPM) performance and satisfaction scores, pre and post intervention. Findings. Pre- and postintervention data were obtained from 41 patients. Statistically significant increases were observed in COPM performance (5.0 ± 1.1 versus 6.9 ± 0.9; P<0.001) and satisfaction (4.6 ± 1.3 versus 6.9 ± 1.0; P<0.001). The most frequently reported occupational performance problems were found in the domains of productivity (47%) and mobility (40%), fewer in self-care (10%) and the least in leisure (3%). Implications. Home-based monodisciplinary OT can contribute significantly to the improvement of daily functioning of patients with COPD. OT should therefore be considered more often as part of the integrated management of these patients.

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.

scholarly journals On strongly nonlinear gravity waves in a vertically sheared atmosphere

2020 ◽  
Vol 6 (1) ◽  
pp. 63-74
Author(s):  
Mark Schlutow ◽  
Georg S. Voelker
Keyword(s):  
Gravity Waves ◽  
Lower Layer ◽  
Vertical Shear ◽  
Horizontal Wind ◽  
Necessary Condition ◽  
Mean Flow ◽  
Individual Layer ◽  
Strongly Nonlinear ◽  
The Mean ◽  
The Stability

Abstract We investigate strongly nonlinear stationary gravity waves which experience refraction due to a thin vertical shear layer of horizontal background wind. The velocity amplitude of the waves is of the same order of magnitude as the background flow and hence the self-induced mean flow alters the modulation properties to leading order. In this theoretical study, we show that the stability of such a refracted wave depends on the classical modulation stability criterion for each individual layer, above and below the shearing. Additionally, the stability is conditioned by novel instability criteria providing bounds on the mean-flow horizontal wind and the amplitude of the wave. A necessary condition for instability is that the mean-flow horizontal wind in the upper layer is stronger than the wind in the lower layer.

A-136 The Transfer of Cognitive Training to Real-World Functioning: Results of our First Six Pilot Subjects at Six-Month Follow-Up

2021 ◽  
Vol 36 (6) ◽  
pp. 1187-1188
Author(s):  
Jason A Blake ◽  
Brandon Mitchell ◽  
Staci McKay ◽  
Gitendra Uswatte ◽  
Edward Taub
Keyword(s):  
Cognitive Training ◽  
Real World ◽  
Cognitive Task ◽  
Case Series ◽  
Performance Measure ◽  
The Real ◽  
Cognitive Activities ◽  
The Mean ◽  
Laboratory Measures

Abstract Objective Currently, the majority of cognitive training research measures treatment efficacy using in-laboratory measures, with minimal focus on real-world treatment changes. This case series demonstrates the feasibility of transferring cognitive improvements from the laboratory into the everyday life setting. Method This case series includes 6 chronic post-stroke participants; mild to moderate cognitive impairment. The intervention combines cognitive training with behavioral techniques, known as the Transfer Package (TP). The TP involves components that target functionality on IADLs in the real-world. Performance on cognitively-based IADLs in the real world are measured pre-treatment, post, and 6-month follow-up. Measures of real-world ability are the: Canadian Occupational Performance Measure (COPM), Cognitive Task Activity Log (CTAL) and Inventory of Improved and New Abilities (INCA). In-laboratory measures included the D-KEFS and Timed IADL assessments. Results The real-world outcome measures used in this study were the COPM and two measures developed for this study, the CTAL and INCA. The mean change from pre to post on the COPM Performance Scale was 2.18 (SD = 1.33) and the mean change on the COPM Satisfaction Scale was 2.70 (SD = 1.27). The mean change on the CTAL was 1.96 (SD = 0.93). On the INCA, the mean number of improved real-world cognitive activities was 11.8 (SD = 4.9) and the mean number of new cognitive activities was 7.6 (SD = 3.9). Follow-up reported near-perfect retention on CTAL and continued improvement on the INCA. There were minimal changes on in-laboratory measures. Conclusions This case series provides a framework for achieving the transfer of cognitive training treatment effects in the real-world life situation by overcoming behavioral barriers to functioning.

scholarly journals On the Absoluteness of Time

2017 ◽  
Vol 9 (3) ◽  
pp. 46
Author(s):  
Carmine Cataldo
Keyword(s):  
Analytical Solutions ◽  
Relativistic Corrections ◽  
Mean Lifetime ◽  
The Mean

This paper aims to qualitatively summarize the results up until now obtained in investigating the compatibility between the absoluteness of time and several well-known phenomena, such as the alleged increase of the mean lifetime of muons and the so-called relativistic corrections for GPS, whose explanation is commonly provided by resorting to Einstein’s Relativity. To make the discussion more flowing, we have herein preferred to completely avoid the writing of equations. All the analytical solutions, as well as several explicative figures, can be found in the first six articles cited in the references, drafted by the same author of this manuscript.

A Formula for the Mean Lifetime of Metapopulations in Heterogeneous Landscapes

2002 ◽  
Vol 159 (5) ◽  
pp. 530-552 ◽  
Author(s):  
Karin Frank ◽  
Christian Wissel
Keyword(s):  
Heterogeneous Landscapes ◽  
Mean Lifetime ◽  
The Mean
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