Abstract
In this paper, we analyze a game in which a retailer adjusts her advertising efforts according to the type of defects (failures) that consumers experience, which depends on a manufacturer’s conformance quality investments. Negligible failures are associated with an increase of the advertising expenditures, while catastrophic failures are followed by a decrease in the advertising efforts. Moreover, we take into consideration the bounded rationality of both retailer and manufacturer that do not know the shape of their objective functions. Taking all the relevant factors into account is quite demanding, and the assumption of perfect knowledge of the market appears unrealistic. In our model, the firms adopt the heuristic of adjusting their advertising and quality in the direction indicated by the respective marginal profits. We show that firms can optimize their profits when the defect is negligible and the speed of reaction to the marginal profit signals is not excessive, while a catastrophic failure leads to unstable solutions due to its operational and managerial complexity.
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Notes
- 1.
Actually it is technically possible that by using extremely high values of λ q , the conformance quality level exits the feasible range \(\left [ 0,1\right ] \). In the following, we avoid using such values ensuring the feasibility of the conformance quality level.
- 2.
We only consider cases in which the steady states are feasible, i.e., a ∗ > 0 and 0 ≤ q ∗≤ 1.
- 3.
It is the locus of points in a parameter plane when the Jacobian matrix calculated at the steady state has two complex and conjugated eigenvalues whose modulus is equal to 1 (see [16]).
- 4.
Figures 5 and 6 are both obtained by keeping fixed the parameters h = 1, k = 0.42, θ = 1.15, γ = 0.2, π = 0.9, c p = 0.045, and c d = 0.062. In Figure 5, we see that λ q = 0.3 and λ a varies, while in Figure 6, λ a is fixed at a value of 2 and λ q varies. These scenarios are qualitatively similar to what can be obtained with any other parameters’ combinations.
- 5.
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Giovanni, P.D., Tramontana, F. (2017). A Discrete Model of Conformance Quality and Advertising in Supply Chains. In: Apaloo, J., Viscolani, B. (eds) Advances in Dynamic and Mean Field Games. ISDG 2016. Annals of the International Society of Dynamic Games, vol 15. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-70619-1_9
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