DOUBLE INVARIANCE: A NEW EQUILIBRIUM CONCEPT FOR TWO-PERSON DYNAMIC GAMES

2000 ◽  
Vol 02 (02n03) ◽  
pp. 193-207 ◽  
Author(s):  
P. CARAVANI
Keyword(s):  
Nash Equilibrium ◽  
Dynamic Games ◽  
Payoff Function ◽  
The State ◽  
Invariance Property ◽  
Invariant Equilibrium ◽  
Viability Theory ◽  
Necessary And Sufficient Condition ◽  
Equilibrium Concept ◽  
Necessary And Sufficient

Doubly Invariant Equilibrium is introduced as an alternative concept to Nash equilibrium in dynamic games doing away with the notion of a payoff function. A subset of the state space enjoys the invariance property if the state can be kept in it by one player, regardless of the action of the opponent. A doubly invariant equilibrium obtains when each player can make his own subset invariant. Relationships to Nash equilibrium and viability theory are discussed and a necessary and sufficient condition for the existence of a doubly invariant equilibrium is given for the class of linear discrete-time games with polyhedral constraints on the state and strategy spaces.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

scholarly journals Dinamicke igre ulaska na trziste

2005 ◽  
Vol 50 (165) ◽  
pp. 121-144
Author(s):  
Bozo Stojanovic
Keyword(s):  
Nash Equilibrium ◽  
Dynamic Games ◽  
Nash Equilibria ◽  
Dynamic Game ◽  
Backward Induction ◽  
Perfect Equilibrium ◽  
Equilibrium Concept ◽  
Reasonable Solution ◽  
Multiple Nash Equilibria ◽  
Entry Games

Market processes can be analyzed by means of dynamic games. In a number of dynamic games multiple Nash equilibria appear. These equilibria often involve no credible threats the implementation of which is not in the interests of the players making them. The concept of sub game perfect equilibrium rules out these situations by stating that a reasonable solution to a game cannot involve players believing and acting upon noncredible threats or promises. A simple way of finding the sub game perfect Nash equilibrium of a dynamic game is by using the principle of backward induction. To explain how this equilibrium concept is applied, we analyze the dynamic entry games.

A heterogeneous blocking system in a random environment

1996 ◽  
Vol 33 (01) ◽  
pp. 211-216 ◽  
Author(s):  
G. Falin
Keyword(s):  
Random Environment ◽  
Joint Distribution ◽  
Service System ◽  
External Environment ◽  
The State ◽  
Product Form ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

We obtain a necessary and sufficient condition for the interaction between a service system and an external environment under which the stationary joint distribution of the set of busy channels and the state of the external environment is given by a product-form formula.

scholarly journals DYNAMICAL STABILITY OF STRANGE QUARK STARS

2011 ◽  
Vol 20 (07) ◽  
pp. 1171-1182 ◽  
Author(s):  
P. S. NEGI
Keyword(s):  
Strange Quark ◽  
The State ◽  
Dynamical Stability ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Star Models ◽  
Quark Stars ◽  
Equilibrium Configurations ◽  
Necessary And Sufficient ◽  
R Relation

The necessary and sufficient condition for dynamical stability is worked out for the sequences of relativistic star models which correspond to the well-defined and causal values of adiabatic sound speed, [Formula: see text], at the center. On the basis of the conditions obtained in this study, we show that the mass–radius (M-R) relation corresponding to the MIT bag models of strange quark matter (SQM) and the models obtained by Dey et al. [Phys. Lett. B438 (1998) 123] does not provide the necessary and sufficient condition for dynamical stability for the equilibrium configurations. These findings will remain unaltered and can be extended to any other sequence of pure SQM. This study explicitly shows that though SQM may exist in the state of zero pressure and temperature, the models of pure strange quark "stars" cannot exist in the state of hydrostatic equilibrium. This study can affect the results which are claiming that various objects, like RX J1856.5-3754, SAX J1808.4-3658, 4U 1728-34 and PSR 0943+10, represent strange stars.

scholarly journals Finite-Time Set Reachability of Probabilistic Boolean Multiplex Control Networks

2022 ◽  
Vol 12 (2) ◽  
pp. 883
Author(s):  
Yuxin Cui ◽  
Shu Li ◽  
Yunxiao Shan ◽  
Fengqiu Liu
Keyword(s):  
Dynamical Systems ◽  
Finite Time ◽  
The State ◽  
Reconstruction Technique ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Control Networks ◽  
State Transfer ◽  
Necessary And Sufficient

This study focuses on the finite-time set reachability of probabilistic Boolean multiplex control networks (PBMCNs). Firstly, based on the state transfer graph (STG) reconstruction technique, the PBMCNs are extended to random logic dynamical systems. Then, a necessary and sufficient condition for the finite-time set reachability of PBMCNs is obtained. Finally, the obtained results are effectively illustrated by an example.

scholarly journals Forward Euler Solutions and Weakly Invariant Time-Delayed Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Norma L. Ortiz-Robinson ◽  
Vinicio R. Ríos
Keyword(s):  
Approximation Scheme ◽  
Invariance Property ◽  
Necessary And Sufficient Condition ◽  
Discontinuous Differential Equations ◽  
Delayed Systems ◽  
Euler Approximation ◽  
Weak Invariance ◽  
Delayed System ◽  
Necessary And Sufficient ◽  
Forward Euler

This paper presents a necessary and sufficient condition for the weak invariance property of a time-delayed system parametrized by a differential inclusion. The aforementioned condition generalizes the well-known Hamilton-Jacobi inequality that characterizes weakly invariant systems in the nondelay setting. The forward Euler approximation scheme used in the theory of discontinuous differential equations is extended to the time-delayed context by incorporating the delay and tail functions featuring the dynamics. Accordingly, an existence theorem of weakly invariant trajectories is established under the extended forward Euler approach.

scholarly journals Controllability of generalised dynamical systems with constrained control

1988 ◽  
Vol 30 (1) ◽  
pp. 69-78
Author(s):  
Chen Zhaolin ◽  
Hong Huimin ◽  
Zhang Jifeng
Keyword(s):  
Dynamical Systems ◽  
Control Function ◽  
The State ◽  
Sufficient Condition ◽  
Constrained Control ◽  
Sense Of Control ◽  
Necessary And Sufficient Condition ◽  
Impulsive Behaviour ◽  
Necessary And Sufficient

AbstractThe state controllability for generalised dynamical systems with constrained control is discussed in this paper. The main results of the paper are the following:(1) a necessary and sufficient condition of the state controllability in the sense of control energy or amplitude constrained for generalised dynamical systems is obtained;(2) a control function u(t) is constructed such thata) u(t) satisfies constrained energy or amplitude condition,b) the state driven by u(t) moves from an arbitrary x(0−) = x0 to x(T(x0)) = 0,c) the trajectory driven by u(t) has no impulsive behaviour within (0, T(x0)].

A Necessary and Sufficient Condition for Partial Monotonicity of Noncooperative Games

2020 ◽  
pp. 2050006
Author(s):  
Naoki Matsumoto
Keyword(s):  
Nash Equilibrium ◽  
Pure Strategy ◽  
Noncooperative Games ◽  
Noncooperative Game ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Partial Monotonicity ◽  
Person Game ◽  
Necessary And Sufficient ◽  
Strategy Nash Equilibrium

It is a classical and interesting problem to find a Nash equilibrium of noncooperative games in the strategic form. It is well known that the game always has a mixed-strategy Nash equilibrium, but it does not necessarily have a pure-strategy Nash equilibrium. Takeshita and Kawasaki proved that every noncooperative partially monotone game has a pure-strategy Nash equilibrium, that is, the partial monotonicity is a sufficient condition for a noncooperative game to have a pure-strategy Nash equilibrium. In this paper, we prove the necessary and sufficient condition for a noncooperative [Formula: see text]-person game with [Formula: see text] to be partially monotone. This result is an improvement of Takeshita and Kawasaki’s result.

A heterogeneous blocking system in a random environment

1996 ◽  
Vol 33 (1) ◽  
pp. 211-216 ◽  
Author(s):  
G. Falin
Keyword(s):  
Random Environment ◽  
Joint Distribution ◽  
Service System ◽  
External Environment ◽  
The State ◽  
Product Form ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

We obtain a necessary and sufficient condition for the interaction between a service system and an external environment under which the stationary joint distribution of the set of busy channels and the state of the external environment is given by a product-form formula.

scholarly journals On rational solution of the state equation of a finite automaton

1988 ◽  
Vol 11 (2) ◽  
pp. 355-364
Author(s):  
R. Chaudhuri ◽  
H. Höft
Keyword(s):  
Finite Automaton ◽  
Rational Solution ◽  
State Equation ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

We prove that the necessary and sufficient condition for the state equation of a finite automatonMto have a rational solution is that the lexicographical Gödel numbers of the strings belonging to each of the end-sets ofMform an ultimately periodic set. A method of determining the existence of a rational solution of the state equation is also given.

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