Author: Xin Zheng

After study with Game theory, there are more expanding concepts of relative game theories that is waiting for us to dig it up. Dynamic Games with Incomplete information is one of a form of Non-cooperative Game. As we have been introduced so far in lecture, Static Games represents two players are making their choices simultaneously, or playing with a unknown sequence of actions. However, In the Dynamic Games, participants play with a sequence of action, under the condition of incomplete information, each participant in the game knows which types of the other participants and the probability of occurrence of each type, unluckily participant has no idea which type of their components belong to.

According to the condition described above, Dynamic Games with Incomplete Information demonstrates that the latter players can obtain information about the previous players by observing the behavior of the previous player, thereby making his turn with the possible outcome he gets from the previous player.

Specifically, at the beginning of the incomplete information dynamic game, a participant establishes his own preliminary judgment based on the different types of other participants and the probability distribution of their respective types. When the game begins, the participant can correct his initial judgment based on the actual actions of other participants he observes. And based on this ever-changing judgment, choose his own strategy.

New equilibrium concept: Prefect Bayesian equilibrum

-Belief: The new term defined in PBE, the belief of a player in a given information set decides which node they are playing at, represented by a probability distribution over the nodes in the information-set. The strategies and beliefs must satisfy Sequence rationality and Consistency.

https://en.wikipedia.org/wiki/Perfect_Bayesian_equilibrium

https://economics.stackexchange.com/questions/25634/perfect-bayesian-equilibria

As the rapid development of social media especially in the mobile platform, various homogenous social application has been developed and widely being used(Instagram, Twitter, Facebook, e-mail). Users can share information on the web anytime, anywhere, resulting in large amount of user data. Social network actually have a lot of practical value under the era of big data. Therefore, the data in many fields can be detected by the special instruments such as police departments.

The classic drama PERSON OF INTEREST tells a story that using a backdoor of a “machine” to detect the possibility of the happening of crime, and figure out who might be the potential victim or criminal. The mechanism beneath the “machine” is the analysis of the big data comes from social network of the victim or criminal, for example, if a married man has a mistress, they will try to text each other, the information of their communication will express what are they thinking and planning, so the wife of the married man might become a potential victim.

The big data from personal social network can be used to:

• To reveal hidden relationships, detect any criminal patterns, and prevent security threats.
• Link personal real-time social account to discover unusual user behaviour and suspicious transactions to expose fraud base on the his historical account activities.
• Test new sources of information and various data as evidence of criminal activity, such as the Internet, mobile devices, transaction processing, email, and social media.

In 2010, LAPD (Los Angles Police Department ) become the first employ data technology and information about past crimes to predict future unlawful activity. The technologies they were using are designed to predict where and when the crimes are likely to occur in next 12hours by examining the 10 years of data.

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