There are interactive and adaptive evolution courses between the anti-terrorist measures of governments and the attack behaviors of terrorists. Moreover, for a terrorist event, governments and terrorists usually do not take the actions at the same time.
In the paper,Stackelberg game model is first built, where governments decide to defense strategies at the first and terrorists decide the attack strategies in the latter. And then, according to the above extensive-form factor game, the extensive-form evolutionary game model about the terrorism attack problem is built.
Because the equilibrium analysis of extensive-form evolutionary game model needs to consider the belief learning course at the inter-and intra-generation levels, it causes the complexity of evolutionary analysis. Although the conception of "Wright Manifold" that can be used to analyze the equilibrium solution of extensive-form evolutionary game model has been put forward, the method is difficult to understand and apply. However, if some conventional social norm are considered, the above analytical process can be simplified. Through introduceing the concept of "mental model" into evolutionary game theory, the new analytical method of evolutionary solution based mental model is proposed. For example, given terrorists take the attack strategy, the commonsensible behavior of any governmental forces should be the defense strategy. Thus, the utility functions of terrorists and governments are simplified. The replicator dynamic function of terrorists can be described as dy_i/dt=y_i·(1-y_j)·(-f-c₂)<0, where y_i is the proportion of terrorists taking attack strategy, t is the evolutionary period, and f and c₂ are the terrorists' payoffs. Similarly, the replicator dynamic function of governemnts can be described as dx_i/dt=x_i·(1-x_i)·(y_i·b-c₁), where x_i is the proportion of governments taking defense strategy, and b and c₁ are the governments' payoffs. The evolutionary solution based mental model is that terrorists take the no-attack strategy, and whether governments take the defense strategy depends on the terrorists' proportion of taking the attack strategy. Lastly, based on the 6.28 terrorism incident in Moyu County, Xinjiang, the paper compares two evolutionary solutions of Wright Manifold and Mental Model.
By introducing the universal accepted social norm into evolutionary analysis, the analytical method based on mental model does not only simplify the course of existed "Wright Manifold" evolutionary analysis method proposed by Cressman (2000), but also demonstrate the more complex and realistic evolutionary characteristics. The new evolutionary solution of mental model has the high application worth. Under the overall trend of the effective control terrorist event, the anti-terrorist measurements of government force should flexibly adjust with the proportional change of terrorists taking the attack strategy. Thus, there is no best or consistent anti-terrorist strategy (evolutionary equilibrium).