Stability properties of value functions in terms of conjugate derivatives for dynamic bimatrix games

2021 ◽  
Author(s):  
Nikolay A. Krasovskii ◽  
Alexander M. Tarasyev
Keyword(s):  
Value Functions ◽  
Bimatrix Games ◽  
Stability Properties

scholarly journals Mechanism for shifting Nash equilibrium trajectories to cooperative Pareto solutions in dynamic bimatrix games

2020 ◽  
Vol 13 ◽  
pp. 218-243
Author(s):  
Nikolay A. Krasovskii ◽  
◽  
Alexander M. Tarasyev ◽  
◽  
Keyword(s):  
Nash Equilibrium ◽  
Viscosity Solutions ◽  
Dynamic Equilibrium ◽  
Evolutionary Game ◽  
Value Functions ◽  
Bimatrix Games ◽  
Qualitative Properties ◽  
Minimax Solutions ◽  
Jacobi Equations

In the paper, constructions of the generalized method of characteristics are applied for calculating the generalized minimax (viscosity) solutions of Hamilton-Jacobi equations in dynamic bimatrix games. The structure of the game presumes interactions of two players in the framework of the evolutionary game model. Stochastic contacts between players occur according to the dynamic process, which can be interpreted as a system of Kolmogorov's differential equations with controls instead of probability parameters. It is assumed that control parameters are not fixed and can be constructed by the feedback principle. Two types of payoff functions are considered: short-term payoffs are determined in the current moments of time, and long-term payoffs are determined as limit functionals on the infinite time horizon. The notion of dynamic Nash equilibrium in the class of controlled feedbacks is considered for the long-term payoffs. In the framework of constructions of dynamic equilibrium, the solutions are designed on the basis of maximization of guaranteed payoffs. Such guaranteeing strategies are built in the framework of the theory of minimax (viscosity) solutions of Hamilton-Jacobi equations. The analytical formulas are obtained for the value functions in the cases of different orientations for the “zigzags” (broken lines) of acceptable situations in the static game. The equilibrium trajectories generated by the minimax solutions shift the system in the direction of cooperative Pareto points. The proposed approach provides new qualitative properties of the equilibrium trajectories in the dynamic bimatrix games which guarantee better results of payoffs for both players than static Nash equilibria. As an example, interactions of two firms on the market of innovative electronic devices are examined within the proposed approach for treating dynamic bimatrix games.

Partial Activation of Purified Prothrombin: Derivation of Autoprothrombin I with Use of Autoprothrombin C

1962 ◽  
Vol 07 (02) ◽  
pp. 239-248 ◽  
Author(s):  
Walter H Seegers ◽  
Edmond R Cole ◽  
Ewa Marciniak
Keyword(s):  
Calcium Ions ◽  
Platelet Factor ◽  
Stability Properties ◽  
Partial Activation ◽  
Autoprothrombin C

SummaryActivation of purified prothrombin with autoprothrombin C in the absence of calcium ions produces autoprothrombin I activity. The solubility, and stability properties of this autoprothrombin I are different from those of autoprothrombin I when obtained by activating prothrombin with calcium ions, platelet factor 3, and Ac-globulin.

Stability properties of mean flows with turning

Tellus ◽  
1982 ◽  
Vol 34 (1) ◽  
pp. 39-49 ◽  
Author(s):  
Richard Grotjahn
Keyword(s):  
Stability Properties

The Received Wisdom

2018 ◽  
Author(s):  
Meghan Sullivan
Keyword(s):  
Temporal Discounting ◽  
Value Functions ◽  
Distant Future ◽  
Rational Planning ◽  
Future Discounting ◽  
The Future

This chapter introduces the reader to future discounting and some received wisdom. The received wisdom about rational planning tends to assume that it is irrational to have near‐biased preferences (i.e., preferences for lesser goods now compared to greater goods further in the future).Thechapter describes these preferences by introducing the reader to value functions. Value functions are then used to model different kinds of distant future temporal discounting (e.g., hyperbolic, exponential, absolute). Finally, the chapter makes a distinction between temporal discounting and risk discounting. It offers a reverse lottery test to tease apart these two kinds of discounting.

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