# What is Mathematical Game Theory (#3) 精选

So far our discussions have been mostly on two person nonzero sum game theory (TPNZSG).

Before we leave the subject, we ought to mention a couple more of ideas associated with the topic.

First of all, there is nothing to prevent a game having more than one Nash equilibrium (NE). When that happens, a player can force the other player to play the NE of his/her choice by announcing FIRST which one s/he has chosen and committed to it. This has led to the famous simple 2x2 game so-called “battle of the sexes” game which illustrates this issue (note to reader, if you are interested in the explanation of this game, you should do a little research on your own rather than having me explain it here). This idea of leading the other player to follow your dictate produced further the idea of Stackelberg solutions of a two person non-cooperative game. We can illustrate this again using our basic figure 4 in my first article on the subject (http://www.sciencenet.cn/blog/user_content.aspx?id=17894)

Let us look at this from the viewpoint of player or decision maker 1. So long as DM1 can choose first AND s/he knows that DM2 will respond in DM2’s own interest according to the response curve R2. Then clearly DM1 should choose the point on R2 which touches the highest J1 contours (we are maximizing) and not the NE point which is the intersection of R2 with R1. This is called the Stackelberg solution of TPNZSG. In practice, this may illustrate a commercial market in which there is one dominant firm who may be able to dictate market prices. He is called the leader and other small firms are followers. See fig.8 below

https://blog.sciencenet.cn/blog-1565-21210.html

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