28-2-2020

A New Game Theory Paradigm from HKSYU

20-01-2020
Professor David Yeung

Professor David Yeung

By: Lubanski Lam, Aloysius Lui and Cynthia Zhang

Photo: Courtesy of SRS Consortium

Professor David Yeung and Professor Leon Petrosyan of the SRS Consortium of Advanced Study in Dynamic Cooperative Games have developed a novel game theory paradigm – Cooperative Dynamic Games with Durable Controls*. In existing dynamic game theory, the controls do not have durable effects. However, durable controls that have effects lasting over a certain period of time are prevalent in real-life situations. Revenue generating investments, toxic waste disposal, durable goods, emission of pollutants, regulatory measures, coalition agreements, diffusion of knowledge, advertisement and investments to build up physical capital are vivid examples of durable controls.

Professor David Yeung is currently Head of Department of Business Administration, Hong Kong Shue Yan University (HKSYU), and Executive Director of SRS Consortium of Advanced Study in Dynamic Cooperative Games; and Professor Leon Petrosyan is an internationally renowned game theorist, Professor of the Faculty of Applied Mathematics and Control Process of St. Petersburg State University and Co-director of SRS Consortium for Advanced Study in Dynamic Cooperative Games.

From left to right: Professor David Yeung, Nobel Laureate John F. Nash Jr. and Professor Leon Petrosyan

From left to right: Professor David Yeung, Nobel Laureate John F. Nash Jr. and Professor Leon Petrosyan

The “Petrosyan-Yeung Cooperative Dynamic Games with Durable Controls” presents a novel game theory framework in which durable controls of different lag durations affecting both the players’ payoffs and the state dynamics exist. The definitive contributions of this new game theory paradigm include:

(1) Theoretically, cooperative dynamic games with durable controls provided a novel and realistic game paradigm. Subgame consistent cooperative solutions are given to ensure that no participants will choose to opt out the scheme.

(2) Mathematically, a novel dynamic optimization theorem involving durable controls is developed. The derived dynamic optimization technique predominates the classic dynamic programming by providing a more comprehensive solution mechanism.

(3) Application-wise, given that durable controls would be involved in most real-life situations, the game paradigm yields a wide scope of applications. These applications include many practical scenarios, such as: public goods provision under technology diffusion, long-lasting pollution-generating effects in global environmental management, advertising race with lagged effects, oligopoly competition with investments requiring several stages to be converted into productive physical capital, dynamic games involving payment by instalments. In addition, the paradigm also sheds lights on the analyses of current cooperation schemes like Brexit, the Paris climate agreements, cyber security and trade negotiations where durable controls prevail.

(4) In addition, cooperative dynamic games with durable controls produces crucial novel results which cannot be generated by any of the existing analytical frameworks and techniques. For an illustrative application given in the paper, the emission of environmentally damaging industrial waste (like toxic and chemical wastes and deforestation) could continue for many years, hence it is possible that pollution would persist or exacerbate even after the operation stops completely.

In sum, cooperative dynamic games with durable controls represents a significant advancement in the field of game theory. Its profound contributions include a milestone prototype for the future development of dynamic games, a novel solution mechanism and original mathematical techniques. Scholars having this kind of seminal contributions in game theory include Nobel laureates John F. Nash Jr., Lloyd Shapley and Robert Aumann. Last but not least, it signifies the pioneering role of HKSYU research in this area of study.

From left to right: Nobel Laureate Lloyd Shapley and Professor David Yeung

From left to right: Nobel Laureate Lloyd Shapley and Professor David Yeung

From left to right: Professor David Yeung and Nobel laureate Robert Aumann

From left to right: Professor David Yeung and Nobel laureate Robert Aumann

* L.A. Petrosyan and D.W.K. Yeung: Cooperative Dynamic Games with Durable Controls: Theory and Application, forthcoming in Dynamic Games and Applications, 2020.

Source: December 2019/January 2020 Combined Issue

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