Game Theory of Yale University Open Courses (18-19)-Information Set and Optimal Subgame
Theory and Concept
In the eighteenth lecture, the relevant content of the global Nash equilibrium is introduced, which is mainly to transform the traditional simultaneous game into a sequential game problem by introducing the concept of information set, so as to use reverse reasoning to solve the simultaneous game problem. For example, the well-known simultaneous game-Prisoner's Dilemma: If it is assumed that they make sequential decisions, but no matter which party answers first, the other party cannot obtain the other party's decision information, then the final effect is equivalent to simultaneous decision-making. But this can apply the most important tool of game theory-reverse reasoning to the problem of simultaneous games. The teacher here also emphasizes again: The most important thing in game theory is not time, but information.
There is also a more complicated example in the video.
The dotted line in the red box in the figure indicates that he does not know whether he is currently on the upper or lower node when making the 3 decision. In the example, if we directly use the Nash equilibrium to judge, then (A, U, r) will be a Nash equilibrium point, because first, if 1 chooses B, then his income will change from 1 of (A, U, r) to ( B, U, r) is 0, and 2, 3, no matter what choice is made, the return will be (0, 0). But if we assume that 1 has chosen B, then according to the Nash equilibrium, the Nash equilibrium point of 2, 3 should be (D, r). So out