The Belief-Reasoning-Based Knowledge Modal And Its Application In Game Theory

Though Game Theory has been widely used in many aspects, it can not solve all the Problems in Game, because of its limits. First, the main target of Game Theory is to find the equilibrium Point of everyone's strategy that means we have to view from an external angle, knowing everyone's information in detail. This requirement is very strict and the equilibrium can not be the best result for many cases. Second, Now the Game Theory Framework lacks the research on examples with "Uncommon Knowledge", while these samples are quite often in the real world.After an analysis on the Knowledge Modal, which is the base of Game Theory, we also found there are some limits and inconvenient in its defining. First, a "state", which is the element of knowledge Modal, includes the completely description of the world, which, though very concise, is very difficult to understand; second, it's also difficult to describe how we can get knowledge from the phenomenon of the real world. Reasoning always needs a lot of descriptions and formulas, and the language is still difficult to understand.To solve the problems above, we proposed a new knowledge modal, which, 1. Redefine the Knowledge element, make the "State" easier to understand; 2. propose the concept of "Character", which was originally mixed in "State", so the defining of knowledge becomes more reasonable, and the reasoning from "Character" to "State " is easier. 3. define a graph framework, which makes reasoning and description more clearly.Also, the new knowledge modal is applied in a Game Sample, which is famous in the history of China, describing how to find the best strategy from one's subjective belief that is a typical sample of game under "Uncommon Knowledge".