不完备偏好下广义强Berge均衡的存在性

Fixed Point Theorems and Its Application to Theory of Strong Berge Equilibrium under Incomplete Preferences

本文基于不完备偏好集中元素对应的等价类集是一个偏序集,把不完备偏好问题转化为偏序问题,得到了不完备偏好下的不动点定理,提供一种新的方法证明局中人的决策偏好不满足完备性时,n人非合作博弈中广义强Berge均衡的存在性.

Based on the equivalence class set corresponding the incomplete prefer- ences set is a partial order set, this paper translates the incomplete preferences problem into the partial order problem. Using the famous Zorn＇s lemma, we get the fixed point theorems in incomplete preference sets. By this technique, it is strictly proven that the existence of generalized strong Berge equilibrium in the noncooperative game under incomplete preferences.