Target allocation decision of incomplete information game based on Bayesian Nash equilibrium

基于贝叶斯纳什均衡的不完全信息博弈目标分配决策

¹ School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China
² School of Electronic Engineering, Xi’an Shiyou University, Xi’an 710065, China

Received: 9 October 2021

Abstract

Aiming at the incomplete information of AUV cooperative confrontation, the incomplete information game theory is used to study the confrontation behavior of AUVs. Taking the remaining survival probability and weapon consumption as the evaluation indicators, adding the position error factor, an AUV game confrontation target allocation model for incomplete information is established. In terms of the Bayesian Nash equilibrium theory, the prior probabilities of the offensive and defensive strategy types are set by the virtual participant "Nature" in advance. Then the types of AUVs to be allocated are selected, and the judgment on the types of the target assignment strategies adopted by the other party are modified through the posterior probability. An algorithm for solving incomplete information target assignment based on the multi-target discrete particle swarms is proposed, and the Bayesian Nash equilibrium target assignment strategies of the two sides are obtained, which provides strategic choice help for the commander's combat command.

摘要

针对AUV(autonomous underwater vehicle)协同对抗过程中的信息不完全问题, 用不完全信息博弈理论研究AUV的对抗行为。以对抗双方的剩余生存概率和武器消耗量为评价指标, 加入位置误差影响因子, 建立了面向不完全信息的AUV博弈对抗目标分配模型。以贝叶斯纳什均衡理论为基础, 通过虚拟参与者"自然(Nature)", 预先设置关于攻防策略类型的先验概率, 选择出待分配的AUV类型, 然后通过后验概率不断修正关于对方采用的目标分配策略类型的判断。提出了基于多目标离散粒子群的不完全信息目标分配求解算法, 得到了博弈对抗双方的贝叶斯纳什均衡目标分配策略, 为指挥官的作战指挥提供了策略选择帮助。