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Author Hochart, A.
Title Unique Ergodicity of Deterministic Zero-Sum Differential Games Type
Year 2021 Publication Dynamic Games And Applications Abbreviated Journal Dyn. Games Appl.
Volume 11 Issue Pages 109-136
Keywords Differential games; Hamilton-Jacobi equations; Viscosity solutions; Ergodicity; Limit value
Abstract We study the ergodicity of deterministic two-person zero-sum differential games. This property is defined by the uniform convergence to a constant of either the infinite-horizon discounted value as the discount factor tends to zero, or equivalently, the averaged finite-horizon value as the time goes to infinity. We provide necessary and sufficient conditions for the unique ergodicity of a game. This notion extends the classical one for dynamical systems, namely when ergodicity holds with any (suitable) perturbation of the running payoff function. Our main condition is symmetric between the two players and involve dominions, i.e., subsets of states that one player can make approximately invariant.
Address [Hochart, Antoine] Univ Adolfo Ibanez, Fac Ingn & Ciencia, Diagonal Las Torres 2640, Santiago, Chile, Email: antoine.hochart@gmail.com
Corporate Author Thesis
Publisher Springer Birkhauser Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 2153-0785 ISBN Medium
Area Expedition Conference
Notes WOS:000527444200001 Approved
Call Number UAI @ eduardo.moreno @ Serial 1148
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Author Villena, M.J.; Contreras, M.
Title Global And Local Advertising Strategies: A Dynamic Multi-Market Optimal Control Model Type
Year 2019 Publication Journal Of Industrial And Management Optimization Abbreviated Journal J. Ind. Manag. Optim.
Volume 15 Issue 3 Pages 1017-1048
Keywords Advertising strategies; multi-market oligopoly; global advertising; differential games
Abstract Differential games have been widely used to model advertising strategies of companies. Nevertheless, most of these studies have concentrated on the dynamics and market structure of the problem, neglecting their multi-market dimension. Since nowadays competition typically operates on multi-product contexts and usually in geographically separated markets, the optimal advertising strategies must take into consideration the different levels of disaggregation, especially, for example, in retail multi-product and multi-store competition contexts. In this paper, we look into the decision-making process of a multi-market company that has to decide where, when and how much money to invest in advertising. For this purpose, we develop a model that keeps the dynamic and oligopolistic nature of the traditional advertising game introducing the multi-market dimension of today's economies, while differentiating global (i.e. national TV) from local advertising strategies (i.e. a price discount promotion in a particular store). It is important to note, however, that even though this problem is real for most multi-market companies, it has not been addressed in the differential games literature. On the more technical side, we steer away from the traditional aggregated dynamics of advertising games in two aspects. Firstly, we can model different markets at once, obtaining a global instead of a local optimum, and secondly, since we are incorporating a variable that is common to markets, the resulting equations systems for every market are now coupled. In other words, one's decision in one market does not only affect one's competition in that particular market; it also affects one's decisions and one's competitors in all markets.
Address [Villena, Marcelo J.; Contreras, Mauricio] Univ Adolfo Ibanez, Fac Engn & Sci, Av Diagonal Las Torres 2640, Santiago 7941169, Chile, Email: marcelo.villena@uai.cl;
Corporate Author Thesis
Publisher Amer Inst Mathematical Sciences-Aims Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1547-5816 ISBN Medium
Area Expedition Conference
Notes WOS:000466101700002 Approved
Call Number UAI @ eduardo.moreno @ Serial 1021
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