American Institute of Mathematical Sciences

July  2019, 6(3): 195-209. doi: 10.3934/jdg.2019014

Cooperative dynamic advertising via state-dependent payoff weights

Received  November 2018 Revised  April 2019 Published  May 2019

Fund Project: This work was partially supported by the German Research Foundation (DFG) within the Collaborative Research Center "On-The-Fly Computing" (SFB 901) under the project number 160364472-SFB901

We consider an infinite horizon cooperative advertising differential game with nontransferable utility (NTU). The values of each firm are parametrized by a common discount rate and advertising costs. First we characterize the set of efficient solutions with a constant payoff weight. We show that there does not exist a constant weight that supports an agreeable cooperative solution. Then we consider a linear state-dependent payoff weight and derive an agreeable cooperative solution for a restricted parameter space.

Citation: Simon Hoof. Cooperative dynamic advertising via state-dependent payoff weights. Journal of Dynamics & Games, 2019, 6 (3) : 195-209. doi: 10.3934/jdg.2019014
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Plot of $h(\kappa) - 1 + \ln(2)$ for $\kappa \in (0, \overline \kappa]$
(Non) cooperative strategies and values
Note: For $x \in [0, 1]$ and $\mathit{\boldsymbol{\rho}} = (\frac{3}{4}, 1)$ the figure illustrates the noncooperative $\phi_i(x)$ and cooperative strategies $\sigma_i(x)$ (top panels) as well as noncooperative $D_i(x)$ and cooperative values $A_i(x)$ (bottom panels).
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