scholarly journals A formula for the value of a stochastic game

2019 ◽  
Vol 116 (52) ◽  
pp. 26435-26443 ◽  
Author(s):  
Luc Attia ◽  
Miquel Oliu-Barton
Keyword(s):  
Dynamic Model ◽  
Discount Rate ◽  
Stochastic Games ◽  
Stochastic Game ◽  
Solution Concept ◽  
Robust Solution ◽  
General Dynamic

In 1953, Lloyd Shapley defined the model of stochastic games, which were the first general dynamic model of a game to be defined, and proved that competitive stochastic games have a discounted value. In 1982, Jean-François Mertens and Abraham Neyman proved that competitive stochastic games admit a robust solution concept, the value, which is equal to the limit of the discounted values as the discount rate goes to 0. Both contributions were published in PNAS. In the present paper, we provide a tractable formula for the value of competitive stochastic games.

scholarly journals Stochastic games

2015 ◽  
Vol 112 (45) ◽  
pp. 13743-13746 ◽  
Author(s):  
Eilon Solan ◽  
Nicolas Vieille
Keyword(s):  
Dynamic Model ◽  
Stochastic Games ◽  
Historical Context ◽  
Stationary Equilibrium ◽  
The Impact ◽  
General Dynamic

In 1953, Lloyd Shapley contributed his paper “Stochastic games” to PNAS. In this paper, he defined the model of stochastic games, which were the first general dynamic model of a game to be defined, and proved that it admits a stationary equilibrium. In this Perspective, we summarize the historical context and the impact of Shapley’s contribution.

General dynamic model verification procedure for Space Station truss segments

2000 ◽  
Author(s):  
Y. Chung ◽  
B. Foist ◽  
E. Grau ◽  
M. Sernaker
Keyword(s):  
Dynamic Model ◽  
Space Station ◽  
Model Verification ◽  
General Dynamic

scholarly journals Cooperative Stochastic Games with Mean-Variance Preferences

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 230
Author(s):  
Elena Parilina ◽  
Stepan Akimochkin
Keyword(s):  
Standard Deviation ◽  
Stochastic Games ◽  
Stochastic Game ◽  
Stochastic Variable ◽  
Expected Payoff ◽  
The Core ◽  
Risk Sensitive ◽  
Payoff Functions ◽  
Cooperative Solutions ◽  
Mean Variance

In stochastic games, the player’s payoff is a stochastic variable. In most papers, expected payoff is considered as a payoff, which means the risk neutrality of the players. However, there may exist risk-sensitive players who would take into account “risk” measuring their stochastic payoffs. In the paper, we propose a model of stochastic games with mean-variance payoff functions, which is the sum of expectation and standard deviation multiplied by a coefficient characterizing a player’s attention to risk. We construct a cooperative version of a stochastic game with mean-variance preferences by defining characteristic function using a maxmin approach. The imputation in a cooperative stochastic game with mean-variance preferences is supposed to be a random vector. We construct the core of a cooperative stochastic game with mean-variance preferences. The paper extends existing models of discrete-time stochastic games and approaches to find cooperative solutions in these games.

Modeling and Grasp Stability Analysis for Object Manipulation by Soft Rolling Fingertips

2014 ◽  
Vol 11 (03) ◽  
pp. 1450020 ◽  
Author(s):  
John Fasoulas ◽  
Michael Sfakiotakis
Keyword(s):  
Stability Analysis ◽  
Dynamic Model ◽  
Object Manipulation ◽  
Kinematics And Dynamics ◽  
Control Law ◽  
Two Dimensional ◽  
Orientation Control ◽  
Grasp Stability ◽  
Different Types ◽  
General Dynamic

This paper presents a general dynamic model that describes the two-dimensional grasp by two robotic fingers with soft fingertips. We derive the system's kinematics and dynamics by incorporating rolling constraints that depend on the deformation and on the rolling distance characteristics of the fingertips' material. We analyze the grasp stability at equilibrium, and conclude that the rolling properties of the fingertips can play an important role in grasp stability, especially when the width of the grasped object is small compared to the radius of the tips. Subsequently, a controller, which is based on the fingertips' rolling properties, is proposed for stable grasping concurrent with object orientation control. We evaluate the dynamic model under the proposed control law by simulations and experiments that make use of two different types of soft fingertip materials, through which it is confirmed that the dynamic model can successfully capture the effect of the fingertips' deformation and their rolling distance characteristics. Finally, we use the dynamic model to demonstrate by simulations the significance of the fingertips' rolling properties in grasping thin objects.

Snails on oceanic islands: testing the general dynamic model of oceanic island biogeography using linear mixed effect models

2012 ◽  
Vol 40 (1) ◽  
pp. 117-130 ◽  
Author(s):  
Robert A. D. Cameron ◽  
Kostas A. Triantis ◽  
Christine E. Parent ◽  
François Guilhaumon ◽  
María R. Alonso ◽  
...  
Keyword(s):  
Dynamic Model ◽  
Island Biogeography ◽  
Oceanic Islands ◽  
Oceanic Island ◽  
Mixed Effect ◽  
Linear Mixed Effect ◽  
Mixed Effect Models ◽  
Linear Mixed Effect Models ◽  
General Dynamic

scholarly journals Oceanic island biogeography through the lens of the general dynamic model: assessment and prospect

2016 ◽  
Vol 92 (2) ◽  
pp. 830-853 ◽  
Author(s):  
Michael K. Borregaard ◽  
Isabel R. Amorim ◽  
Paulo A. V. Borges ◽  
Juliano S. Cabral ◽  
José M. Fernández-Palacios ◽  
...  
Keyword(s):  
Dynamic Model ◽  
Island Biogeography ◽  
Oceanic Island ◽  
Model Assessment ◽  
General Dynamic

scholarly journals Transferring and implementing the general dynamic model of oceanic island biogeography at the scale of island fragments: the roles of geological age and topography in plant diversification in the Canaries

2016 ◽  
Vol 43 (5) ◽  
pp. 911-922 ◽  
Author(s):  
Rüdiger Otto ◽  
Robert J. Whittaker ◽  
Markus von Gaisberg ◽  
Christian Stierstorfer ◽  
Agustín Naranjo-Cigala ◽  
...  
Keyword(s):  
Dynamic Model ◽  
Island Biogeography ◽  
Oceanic Island ◽  
Geological Age ◽  
General Dynamic ◽  
Plant Diversification
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