A dynamic solution concept for abstract games

1980 ◽  
Vol 32 (2) ◽  
pp. 151-169 ◽  
Author(s):  
P. P. Shenoy
Keyword(s):  
Solution Concept ◽  
Dynamic Solution ◽  
Abstract Games

scholarly journals The stabilization of equilibria in evolutionary game dynamics through mutation: mutation limits in evolutionary games

2019 ◽  
Vol 475 (2231) ◽  
pp. 20190355 ◽  
Author(s):  
Johann Bauer ◽  
Mark Broom ◽  
Eduardo Alonso
Keyword(s):  
Nash Equilibrium ◽  
Replicator Dynamics ◽  
Evolutionary Game ◽  
Solution Concept ◽  
Evolutionary Games ◽  
Dynamic Approach ◽  
Q Learning ◽  
Interior Equilibrium ◽  
Dynamic Solution ◽  
Multi Agent

The multi-population replicator dynamics is a dynamic approach to coevolving populations and multi-player games and is related to Cross learning. In general, not every equilibrium is a Nash equilibrium of the underlying game, and the convergence is not guaranteed. In particular, no interior equilibrium can be asymptotically stable in the multi-population replicator dynamics, e.g. resulting in cyclic orbits around a single interior Nash equilibrium. We introduce a new notion of equilibria of replicator dynamics, called mutation limits, based on a naturally arising, simple form of mutation, which is invariant under the specific choice of mutation parameters. We prove the existence of mutation limits for a large class of games, and consider a particularly interesting subclass called attracting mutation limits. Attracting mutation limits are approximated in every (mutation-)perturbed replicator dynamics, hence they offer an approximate dynamic solution to the underlying game even if the original dynamic is not convergent. Thus, mutation stabilizes the system in certain cases and makes attracting mutation limits near attainable. Hence, attracting mutation limits are relevant as a dynamic solution concept of games. We observe that they have some similarity to Q-learning in multi-agent reinforcement learning. Attracting mutation limits do not exist in all games, however, raising the question of their characterization.

Problems on the Gravitational Wave and the Repulsive Gravitation

2016 ◽  
pp. 4422-4429
Author(s):  
C. Y. Lo
Keyword(s):  
Black Holes ◽  
Gravitational Wave ◽  
Einstein Equation ◽  
Wave Solution ◽  
Dynamic Solution ◽  
Pure Mathematics ◽  
Non Linear

It is exciting that the gravitational wave has been confirmed, according to the announcement of LIGO. This would be the time to fix the Einstein equation for the gravitational wave and the nonexistence of the dynamic solution. As a first step, theorists should improve their pure mathematics on non-linear mathematics and related physical considerations beyond Einstein. Then, it is time to rectify the Einstein equation that has no gravitational wave solution which Einstein has recognized, and no dynamic solution that Einstein failed to see. A problem is that physicists in LIGO did not know their shortcomings. Also, in view of the far distance of the sources, it is very questionable that the physicists can determine they are from black holes. Moreover, since the repulsive gravitation can also generate a gravitational wave, the problem of gravitational wave is actually far more complicated than we have known. A useful feature of the gravitational wave based on repulsive gravitation is that it can be easily generated on earth. Thus this can be a new tool for communication because it can penetrate any medium.

scholarly journals High Molar Mass Polycarbonate via Dynamic Solution Transcarbonation Using Bis(methyl salicyl) Carbonate, an Activated Carbonate

2021 ◽  
pp. 2100186
Author(s):  
Annelore Aerts ◽  
Camiel Kroonen ◽  
Jan Henk Kamps ◽  
Rint P. Sijbesma ◽  
Johan P. A. Heuts
Keyword(s):  
Molar Mass ◽  
High Molar Mass ◽  
Dynamic Solution

scholarly journals Conditional Entropy: A Potential Digital Marker for Stress

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 286
Author(s):  
Soheil Keshmiri
Keyword(s):  
Resting State ◽  
Nearest Neighbor ◽  
Brain Activity ◽  
Solution Concept ◽  
Conditional Entropy ◽  
K Nearest Neighbor ◽  
Brain Response ◽  
Substantial Progress ◽  
Eeg Recordings ◽  
The Brain

Recent decades have witnessed a substantial progress in the utilization of brain activity for the identification of stress digital markers. In particular, the success of entropic measures for this purpose is very appealing, considering (1) their suitability for capturing both linear and non-linear characteristics of brain activity recordings and (2) their direct association with the brain signal variability. These findings rely on external stimuli to induce the brain stress response. On the other hand, research suggests that the use of different types of experimentally induced psychological and physical stressors could potentially yield differential impacts on the brain response to stress and therefore should be dissociated from more general patterns. The present study takes a step toward addressing this issue by introducing conditional entropy (CE) as a potential electroencephalography (EEG)-based resting-state digital marker of stress. For this purpose, we use the resting-state multi-channel EEG recordings of 20 individuals whose responses to stress-related questionnaires show significantly higher and lower level of stress. Through the application of representational similarity analysis (RSA) and K-nearest-neighbor (KNN) classification, we verify the potential that the use of CE can offer to the solution concept of finding an effective digital marker for stress.

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.

Economies with complex property rights

2021 ◽  
Vol 19 (1) ◽  
pp. 30-44
Author(s):  
Ivan Balbuzanov ◽  
Maciej H. Kotowski
Keyword(s):  
Property Rights ◽  
Solution Concept ◽  
Object Allocation ◽  
Top Trading Cycles ◽  
The Right ◽  
Shared Ownership

We discuss the exclusion core, a solution concept for object-allocation and object-exchange problems. The exclusion core is based on the right of exclusion and is especially useful for the analysis of economies with complicated property arrangements, such as those with shared ownership. The exclusion core coincides with the (strong) core in classic settings, and is closely related to the celebrated Top Trading Cycles algorithm.

Structures and Dynamic Solution Behavior of Cationic, Two-Coordinate Gold(I)-π-Allene Complexes

2012 ◽  
Vol 18 (22) ◽  
pp. 6959-6971 ◽  
Author(s):  
Timothy J. Brown ◽  
Atsushi Sugie ◽  
Marina G. D. Leed ◽  
Ross A. Widenhoefer
Keyword(s):  
Solution Behavior ◽  
Dynamic Solution
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