A counterexample on overtaking optimality

1999 ◽  
Vol 49 (3) ◽  
pp. 435-439 ◽  
Author(s):  
Andrzej S. Nowak ◽  
Oscar Vega-Amaya
Keyword(s):  
Overtaking Optimality

Overtaking optimality for controlled Markov-modulated diffusions

Optimization ◽  
2012 ◽  
Vol 61 (12) ◽  
pp. 1405-1426
Author(s):  
Beatris Adriana Escobedo-Trujillo ◽  
Onésimo Hernández-Lerma
Keyword(s):  
Overtaking Optimality ◽  
Markov Modulated

VARIATIONAL PROBLEMS ON UNBOUNDED TWO-DIMENSIONAL DOMAINS

1992 ◽  
Vol 02 (02) ◽  
pp. 183-201
Author(s):  
ARIE LEIZAROWITZ
Keyword(s):  
Control Theory ◽  
Large Class ◽  
Optimality Criterion ◽  
Variational Problems ◽  
Two Dimensional ◽  
Minimal Energy ◽  
Chemical Systems ◽  
Overtaking Optimality ◽  
Special Case ◽  
Class Of Functions

We consider the functional IΩ(u) = ∫Ω [ψ (u(x,y)) + ½K (∇ u)]dxdy defined for real valued functions u on ℝ2 and study its minimization over a certain class of functions u(·, ·). We look for a minimizer u⋆ which is universal in the sense that IΩ(u⋆)≤IΩ(u) for every bounded domain (in a certain class) and for every u(·, ·) which satisfies u|∂Ω=u⋆|∂Ω. This optimality notion is an extension to a multivariable situation of the overtaking optimality criterion used in control theory, and the minimal-energy-configuration concept employed in the study of certain chemical systems. The existence of such universal minimizers is established for a large class of variational problems. In the special case were K(∇ u) = ½ |∇ u|2 these minimizers are characterized as the functions u⋆(x, y)=ϕ(ax+by+c) for some explicitly computable ϕ:ℝ1→ℝ1 and constants a, b and c.

scholarly journals Overtaking optimality in a discrete-time advertising game

2021 ◽  
Vol 7 (1) ◽  
pp. 552-568
Author(s):  
Jewaidu Rilwan ◽  
◽  
Poom Kumam ◽  
Idris Ahmed ◽  
◽  
...  
Keyword(s):  
Asymptotic Behavior ◽  
Steady State ◽  
Nash Equilibrium ◽  
Discrete Time ◽  
Dynamic Game ◽  
Present Value ◽  
Time Dynamic ◽  
Overtaking Optimality ◽  
Advertising Strategy ◽  
Market Shares

<abstract><p>In this paper, advertising competition among $ m $ firms is studied in a discrete-time dynamic game framework. Firms maximize the present value of their profits which depends on their advertising strategy and their market share. The evolution of market shares is determined by the firms' advertising activities. By employing the concept of the discrete-time potential games of González-Sánchez and Hernández-Lerma (2013), we derived an explicit formula for the Nash equilibrium (NE) of the game and obtained conditions for which the NE is an overtaking optimal. Moreover, we analyze the asymptotic behavior of the overtaking NE where the convergence towards a unique steady state (turnpike) is established.</p></abstract>

Overtaking Optimality for Markov Decision Chains

1979 ◽  
Vol 4 (2) ◽  
pp. 144-152 ◽  
Author(s):  
Eric V. Denardo ◽  
Uriel G. Rothblum
Keyword(s):  
Overtaking Optimality ◽  
Markov Decision
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