基于博弈论的道路交叉口信号灯设置标准

Game Analysis of Standards for Setting Traffic Signal Lights at Road Intersection

摘要:

交叉口相互冲突交通流之间的关系实质是各方争夺有限的时空资源的博弈关系,因此,可利用博弈论研究交叉口信号灯的设置标准.分两人对称博弈和两人非对称博弈分别提出了无信号交叉口相互冲突机动车之间、机动车与行人或非机动车之间的斗鸡博弈模型,提出各自的混合策略纳什均衡解,并证明混合策略纳什均衡解的整体效率不如纯策略纳什均衡,说明了引入信号灯轮换均衡机制的必要性.采用现实性很强的有限理性进化博弈的大群体成员随机配对复制动态分析方法,得到了斗鸡博弈模型的进化稳定策略,说明了混合策略纳什均衡解的合理性.从斗鸡博弈模型混合策略纳什均衡解得到的交叉口博弈交通冲突率及由此换算来的年交通事故数可作为信号灯的设置标准.以上海市为算例,得到了本地化的交叉口信号灯设置标准.最后分析了交叉口斗鸡博弈模型参数变化的影响,阐述了相应的现实意义及对我国道路交通安全管理立法的意义.

Abstract:

The relationship between conflicting traffic streams at road intersection is essentially a game,thus game theory is applicable in analysis of standards for setting traffic signal lights at road intersection.The competitions between auto streams,and that between auto stream and pedestrian stream were modeled respectively as twoparty symmetrical and twoparty asymmetrical chicken games.Mixed strategies Nash equilibrium for the chicken games were deducted and proved to be lower in social efficiency than that of pure strategy Nash equilibrium,signifying the necessity for introduction of traffic signal lights.Replicator dynamics in rationally bounded evolutionary game was applied to deducing the evolutional stable strategies (ESS) for the chicken games.The ESS analysis proved reasonableness of the mixed strategies of the games.The accident rates and their corresponding annual accident numbers from the games may be used as standards for setting traffic signal lights.A case study was conducted on standards for setting traffic signal lights in Shanghai.Finally,practical significance of parameters change of the chicken games was investigated.