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>

scholarly journals Search for a moving target in a competitive environment

2021 ◽  
Author(s):  
Benoit Duvocelle ◽  
János Flesch ◽  
Hui Min Shi ◽  
Dries Vermeulen
Keyword(s):  
Markov Chain ◽  
Discrete Time ◽  
Competitive Environment ◽  
Moving Target ◽  
Time Varying ◽  
Greedy Strategy ◽  
Time Dynamic ◽  
Dynamic Search ◽  
Subgame Perfect Equilibria ◽  
Perfect Equilibria

AbstractWe consider a discrete-time dynamic search game in which a number of players compete to find an invisible object that is moving according to a time-varying Markov chain. We examine the subgame perfect equilibria of these games. The main result of the paper is that the set of subgame perfect equilibria is exactly the set of greedy strategy profiles, i.e. those strategy profiles in which the players always choose an action that maximizes their probability of immediately finding the object. We discuss various variations and extensions of the model.

Gaming in Spatial Expansion Tracks: The Case of the Swedish Brewery Industry

1992 ◽  
Vol 24 (7) ◽  
pp. 1021-1037 ◽  
Author(s):  
S Finne ◽  
R Laulajainen
Keyword(s):  
Nash Equilibrium ◽  
Population Distribution ◽  
Scale Economies ◽  
Spatial Expansion ◽  
Spatial Strategies ◽  
Market Shares ◽  
Production And Distribution ◽  
Physical Barriers ◽  
Simple Indicator

Two competitors try to maximize their respective market shares by acquiring smaller, passive companies. The heavy logistics bill and inherent scale economies in production recommend contagious expansion. This process is channeled by physical barriers and population distribution. Rationalization of production and distribution is postponed. The historical example is derived from the Swedish brewery industry. It may be seen as a game with a set of rules and some probabilistic parameters. The game is played thirty-seven times, by two persons at a time. The results span a spectrum of spatial strategies, dominated by three main types, one of which corresponds to the historical outcome. To get a firmer hold of ‘good’ strategies, the probabilistic elements are replaced by a simple indicator, the territory is abstracted into a network, and the decisionmaking sequence is analyzed deductively. The same three main types of strategy reemerge. One of them is tentatively considered to be a Nash equilibrium.

Dissipative and Generative Fractional Electric Elements in Modeling RC and RL Circuits

2021 ◽  
Author(s):  
Kristian Haška ◽  
Stevan Cvetićanin ◽  
Dušan Zorica
Keyword(s):  
Asymptotic Behavior ◽  
Steady State ◽  
Constitutive Equation ◽  
Magnetic Flux ◽  
Electromotive Force ◽  
Constitutive Models ◽  
Steady State Regime ◽  
Power Type ◽  
State Regime ◽  
Transient And Steady State

Abstract Generalized capacitor (inductor) is constitutively modeled by expressing charge (magnetic flux) in terms of voltage (current) memory as a sum of instantaneous and power type hereditary contributions and it is proved to be a dissipative electric element by thermodynamic analysis. On the contrary, generalized capacitor (inductor) as a generative electric element is modeled using the same form of the constitutive equation, but by expressing voltage (current) in terms of charge (magnetic flux) memory. These constitutive models are used in transient and steady state regime analysis of the series RC and RL circuits subject to electromotive force, as well as in the study of circuits' frequency characteristics including asymptotic behavior.

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