Solving Structured Hierarchical Games Using Differential Backward Induction


Zun Li, Feiran Jia, Aditya Mate, Shahin Jabbari, Mithun Chakraborty, Milind Tambe, and Yevgeniy Vorobeychik. 8/2022. “Solving Structured Hierarchical Games Using Differential Backward Induction.” In Conference on Uncertainty in Artificial Intelligence (UAI). Eindhoven, Netherlands.


From large-scale organizations to decentralized political systems, hierarchical strategic decision making is commonplace. We introduce a novel class of structured hierarchical games (SHGs) that formally capture such hierarchical strategic interactions. In an SHG, each player is a node in a tree, and strategic choices of players are sequenced from root to leaves, with root moving first, followed by its children, then followed by their children, and so on until the leaves. A player’s utility in an SHG depends on its own decision, and on the choices of its parent and all the tree leaves. SHGs thus generalize simultaneous-move games, as well as Stackelberg games with many followers. We leverage the structure of both the sequence of player moves as well as payoff dependence to develop a gradientbased back propagation-style algorithm, which we call Differential Backward Induction (DBI), for approximating equilibria of SHGs. We provide a sufficient condition for convergence of DBI and demonstrate its efficacy in finding approximate equilibrium solutions to several SHG models of hierarchical policy-making problems.
See also: 2022