Strategic Advantages and Equilibrium Structure in Sequential and Multiplayer Colonel Blotto Games
数学学科创建110周年系列报告
报告题目(Title)：Strategic Advantages and Equilibrium Structure in Sequential and Multiplayer Colonel Blotto Games
报告人(Speaker)：Jie Zhang (University of Bath, UK)
地点(Place)：后主楼1223
时间(Time)：2026年1月2日（周五）16:00-17:00
邀请人(Inviter)：刘君
报告摘要
This talk brings together two strands of work on resource competition within the Colonel Blotto family of games. I begin with a sequential version of the Lottery Colonel Blotto game, modelled as a Stackelberg competition in which the leader commits to a strategy before the follower reacts. I show how this problem can be written as a bi-level optimisation programme and present a constructive reduction method that computes the leader’s optimal commitment strategy in polynomial time. I also discuss when the Stackelberg and Nash equilibria coincide, and explain how the budget ratio threshold that determines this equivalence can be derived in closed form. In several cases, early commitment generates utility improvements for both players, and in extreme cases the leader’s gain can become unbounded.
The second part focuses on the multiplayer General Lotto game played across multiple contests. I outline the existence of Nash equilibrium in the general asymmetric setting and explain how this follows from a fixed-point argument. I then describe the structure of equilibrium strategies in a single contest, including shared upper support endpoints and the inverse link between budgets and minimum support values. In the multi-contest setting, I present results on participation bounds, show examples where equilibrium is not unique, and conclude with the symmetric setting where a closed form equilibrium can be obtained.
主讲人简介
Dr Jie Zhang is an Associate Professor in the Department of Computer Science at the University of Bath. His research focuses on algorithmic game theory, network economics, blockchain protocols, and multi-agent systems. He has served as the sole principal investigator on research projects funded by the UK Engineering and Physical Sciences Research Council (EPSRC) and The Leverhulme Trust.
