Modeling and solving multi-level games with applications to management of infectious diseases

Du Ying

Abstract

Games are traditionally represented and solved using general games trees. Recent interests in representation of games in graphical forms have lead to the development of, for example, the multi-agent influence diagrams. Although these graphical representations are more compact in form, they are normally solved by first converting them into traditional game trees as algorithms for direct solution are not well developed. In this paper, we first describe the representation of multi-level games in graphical forms using influence diagrams from decision analysis. Games represented in these forms are solved as follows: First, the relationships between the different players at multiple levels are identified from the influence diagram, and a leader-follower hierarchy for the players is established. Next, payoff relevance in the game is identified using the notion of d-separation from Bayesian Networks. Finally, a recursive procedure is used to solve the multi-level game using information from the first two steps. The proposed method described above is then applied to the management of infectious disease with the government, hospitals, and viruses as players at different levels. Data from the US Centers for Disease Control and Prevention on influenza pandemic is used in the case study to demonstrate the effectiveness of the proposed method.