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Session Overview
Session
TA 08: Optimal Control Applications
Time:
Thursday, 05/Sept/2024:
8:30am - 10:00am

Session Chair: Gustav Feichtinger
Location: Wirtschaftswissenschaften Z538
Room Location at NavigaTUM


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Presentations

Analyzing the Impact of Advertising on Manufacturer-Retailer Business Model Choice in Bilateral Monopoly

Sigué Simon1, Gromova Ekaterina2

1Athabasca University; 2Transport and Telecommunication Institute (TSI)

This study explores how advertising influences manufacturers' and retailers' decisions between reselling and agency selling in bilateral monopolies. Three analytical models examine under what conditions each strategy is admissible. The Stackelberg equilibrium is analytically derived for all models, delivering the optimal solution, and explaining the structure of strategic interactions. Managerially, the importance of considering advertising's impact on consumer demand when selecting a business model is highlighted.

In this research, we mostly have focused on vertical pricing and advertising interactions in a context where a manufacturer sells a single product to a retailer or to consumers via a retailer-owned platform. Additionally, preliminary findings will be presented on using different channel structures, including horizontal competition.

References

Sigue, S. and Gromova, E. (2024), The role of advertising in the choice between reselling and agency selling. Intl. Trans. in Op. Res.. https://doi.org/10.1111/itor.13351



Optimal Paths to Demographic Equilibria

Stefan Wrzaczek1, Thomas Fent2, Gustav Feichtinger3, Andreas J. NOVAK4

1IIASA; 2Austrian Academy of Sciences; 3Vienna University of Technology; 4University of Vienna

The principle goal of the presentation is to establish a firm fundament of population policy. It is shown how intertemporal optimisation theory can be used to fulfill this important task. In particular this will be illustrated by calculating the optimal trade-off between the further growth (or shrinking) of a population and the fluctuations of its age-structure generated by the decline (or increase ) of the fertility.

While the system dynamics of the age-structured optimal control model considered in this paper is described by the McKendrick-von Foerster partial differential equation, its objective functional is given by the discounted stream of the adaptation costs of the net reproduction rate (NRR) and the afore-mentioned trade-off. Numerical simulations for a stylized population structure show how the change of the NRR carries over to the total population and age groups along time.



How to control Mexican cartels in an optimal way?

Gustav Feichtinger1, Gian Maria Campedelli2, Jonathan P. Caulkins3, Dieter Grass1, Rafael Prieto-Curiel4, Gernot Tragler1, Stefan Wrzaczek5

1TU Wien, Austria; 2Fondazione Bruno Kessler, Italy; 3H. John Heinz III School of Public Policy & Management, Carnegie Mellon University, USA; 4Complexity Science Hub, Austria; 5Economic Frontiers, Institute for Applied Systems Analysis (IIASA), Austria

Violence is today one of the most serious issues in most Latin American countries. State forces in Mexico invest considerable resources to reduce homicides. Essentially, two instruments are available to control the power of cartels, namely incapacitation of its members and reducing recruitment.

In a remarkable recent paper (Prieto-Curiel et al., Science 381, 1312–1316, 2023), two of the above authors have shown that ‘reducing cartel recruitment is the preferred way to lower violence in Mexico’. It seems to be natural to ask additionally how the control instruments should be varied optimally over time. To answer this question we have to quantify the impact of incarceration and recruitment reduction on the dynamics of the cartel sizes. Or, to put in another way, one has to specify the costs of the controls restricted by the available budget of the Mexican government. In that context the validation of the proposed control model is a crucial step to obtain not only interesting insights into the structure of efficient incapacitation and recruitment policies but (hopefully) also policy recommendations.

Preliminary calculations for two interacting cartels show that for realistic parameter constellations multiple long-run optimal equilibria do exist. Their basins of attraction are separated by Skiba-curves implying history-dependence of the optimal solutions.