动态博弈在应急决策中的应用

【摘 要】本文将动态博弈应用于应急决策的制定过程，将“突发事件”与“决策者”假设为博弈的双方，综合考虑事件阶段、事件类型，根据事件进展中阶段结果和信息变化，利用贝叶斯法则修正先验概率的动态决策过程，该方法充分考虑了应急管理决策过程中信息的变化及决策的动态调整，对应急决策实践有一定的借鉴作用。

【关键词】动态博弈；先验概率；后验概率；应急管理

[Abstract] The task at one stage varies with the previous action and the reaction in Emergency management. Dynamic game theory extends project management process from static to dynamic. It’s suitable to suppose that decision-making process is a dynamic game process between the two players of “decision maker” and “emergency” itself. Decision maker could update prior probability consistently along with the increasing information and previous activities. Based on Bayesian rule， we raise a dynamic game model to help choose optimal strategy and take actions. Finally， a case study is given to illustrate the application of above decision method.

[Key words] Dynamic game；Prior probability；Posterior probability；Emergency management

1. Introduction

Various kinds of incidents occurred more frequently in recent years. The 911 incident happened in 2001 was one of the social security incidents made by human beings while “SARS” appeared in 2003 was one of the public health incidents triggered by bacteria. There were other kinds of emergency which had made great tragedy on human beings such as the power blackouts in August 2003 in North America and tsunami natural disasters on Indian Ocean in 2005[1]. Although the probability of all these incidents is very small， negative influence is no negligible.

It’s necessary for us to study emergency management because it can help us control disaster and reduce uncertainty. There has been much research on emergency management recently， some on emergency laws， regulations， standards and organizations[2]， some on location and distribution of resources[3][4]， some on information management system for the emergency management[5][6]， and still others on classification of emergency in incidents management[7].

Although these systems have played an important role on information sharing and cooperation， there is much limit on decision. In emergency situation， decision makers usually make decisions by their own experience and knowledge under uncertainty since incidents occurred suddenly and unexpectedly. In fact， decision makers must modify his decisions along with the increasing information and previous activities， in other words， the decision process in emergency management must be a dynamic game process. The decisions should be adjusted on time according to the results and new information from previous activities of the emergency.

For example， when the “SARS” broke out initially， decision makers made judgment and forecast under the general knowledge of infectious disease. However the people who suffer from SARS was much more than the forecast later， so decision makers need to modify his decisions according to new information and current condition.

Based on Bayesian rule， we raise a dynamic game model with Graphical Evaluation and Review Technique to help choose optimal strategy and take actions in following stage. To apply the incomplete and incremental information effectively and make decision dynamically， prior probability should be updated consistently during the dynamical decision-making process.

2. Dynamic Game Analysis

Emergency management is similar to project management in many characters thus we can use dynamic game theory to analyze emergency management. However， compared with traditional project management， emergency management has the following characteristics. The task at one stage varies with the previous action and the reaction is also a dynamic game process， which is one of the most major and difficult problems in emergency management[8].It’s suitable to suppose that decision-making process is a dynamic game process between the two players of “decision maker” and “emergency” itself.

As a new method， the dynamic game network is for the decision maker to choose the optimal decisions using game model with incomplete information， based on environmental changes and additional information. The detailed application process of dynamic game theory in emergency management is following： in dynamic game process with incomplete information [9]， “nature” firstly decides the type of players， and then the players take actions subsequently. The latter-player can only observe the action of former-player， but the knowledge of types may be shown by the actions. The latter-player can adjust his prior probability after observing the former-player and choose his optimal actions. On the other hand， the former-player know that his actions are useful to the latter， he will try to hide favorable information for the aim of competition. For both players， the game includes selecting action and updating their prior belief. The basic equilibrium for dynamic game under incomplete information is refined perfect Bayesian equilibrium， in which the strategies of participants are optimal in every stage assuming other players’ belief of types and actions is given. In other words， refined perfect Bayesian equilibrium is strategy and belief equilibrium at the same time.

3. Bayesian rule-based Dynamic Game of Emergency Management

Suppose that the emergency has n game stages and 3 type levels and decision maker has k actions in dynamic game analysis.

Firstly emergency chooses his type in n levels randomly， Decision maker then judges the prior probability that emergency in type i. Because of bounded rationality and incomplete information of human， the decision maker need to update his prior probability by getting more information from historical resource or expert judgments. After the update， decision maker takes optimal action out of k actions for the first stage. At the end of stage 1， assessment of previous results is made and new information is collected by decision maker to update his prior belief for the second stage. So reassessment and recollection are repeated for the next stage … The process repeat until the incident is controlled completely. “Emergency” takes action first by choosing his type in n levels randomly， Decision maker then judges the prior probability ti and update his prior probability. Initially the decision maker assigned prior belief p（?） according to his knowledge about the incidents. As new information D is available， the prior belief p（?） is updated by p（?|D） using Bayesian rule.

Stage 1： After the update， then decision maker takes optimal action out of k actions according to the expected utility theory. The posterior probability will be used as the new prior probability for stage 2.

Stage 2： After the first stage， “emergency” chooses his type in n levels according to decision maker’s action in stage 1， then assessment of previous results is made and new information about the type of emergency is collected to update prior probability. Decision maker takes optimal action out of k actions for stage 2.

……

Stage m： “emergency” chooses his type responding to decision maker’s action in the （n-1）th stage， then decision maker assesses previous results and collects new information about the type of emergency. As new information D becomes available， the prior belief is updated using Bayesian rule to choose optimal action in k actions for the nth stage. Finally emergency is controlled.

References：

[1] Ji Lei， Chi Hong， Chen An etc. Emergency Management[J] . Higher Education Press. 2006.3， 93-94（in Chinese）.

[2] Li Jie. Public Crisis Administration Institution for Public Crisis [J]. Journal of Harbin University of Commerce： Social Science Edition.2005，1.（in Chinese）.

[3] C. S. ReVelle， H. A. Eiselt. Location Analysis： A Synthesis and Survey [J]. European Journal of Operational Research . 2005， 165（1）：1-19. [3]

[4] Jia Chuanliang， Chi Hong， Ji Lei. The Allocation Model of Fire Resource Based on Multistage Fire Protection Process[J]. Systems Engineering， 2005， 23（9）：12-15（in Chinese）.

[5] Eleftherios Iakovou， Christos Douligeris. An information management system for the emergency management of hurricane disasters [J]. International Journal of Emergency Management， 2001， 2 （3/4）：243-262.

[6] Jean Luc Wybo， Harriet Lonka. Emergency Management and the information Society： how to improve the synergy？ [J] International Journal of Emergency Management，2002，1（2）：183-190

[7] Yang Jing， Chen Jianming and Zhao Hong. The Classification of Emergency in Incidents Management. Management Review. 2005，4： 37-41（in Chinese）.

[8] Yao Jie， Ji Lei and Chi Hong. Dynamic Game Analysis of Emergency Management [J]. Management Review， 2005， 17（3）：46-50（in Chinese）.

[9] Zhang Weiying. Game Theory and Information Economics [M]. Shanghai People’s publishing House， 1996（in Chinese）.

作者简介：

赵淑红，1979.09，女，河南大学国际教育学院；教师，讲师，硕士。