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Overtaking optimality in a discrete-time advertising game. (English) Zbl 1485.90059

Summary: 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 D. González-Sánchez and O. Hernández-Lerma [Discrete-time stochastic control and dynamic potential games. The Euler-equation approach. New York, NY: Springer (2013; Zbl 1344.93001)], 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.

MSC:

90B60 Marketing, advertising
91A50 Discrete-time games
91A80 Applications of game theory

Citations:

Zbl 1344.93001
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References:

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