Abstract
In a large system, there are many controllers, each having different imperfect information on the state of the system. The interplay of information and control is very interesting. Here the design of information pattern is considered on the ground of analysis.
There are two factors in designing the information pattern. By the space factor, the information network displaying the transmission among controllers is determined. The memory and the information delay fall under the category of the time factor.
Here is considered how to design the information pattern by connection the transmission or communication lines among contollers. The information patterns generated by information transmission form a non-modular lattice, while ones generated by communication form a modular lattice. The relation between the information pattern and the number of transmission lines is discussed.
The necessary and sufficient conditions for complete communication are derived for each design using transmission lines and communication lines. The lattice of the information patterns is homomorphic to the totally ordered sets of the payoff and the information cost for each information pattern.
When an information delay exists, not every controller could obtain the same information even under a complete communication. The information patterns constituted by transmission and communication with information delay form a modular lattice. The minimum time problem to transmit the information from one player to the other is solved. Moreover the relation between the number of transmission lines and the transmission time for the complete communication is discussed.
