5.3 Fictitious-Play-Based Algorithms 135 MS1\MS2 BS1 log 2 1 + BS1 N 0 +p 2 |h 2 | 2 p 2 |h 2 | 2 N 0 +p 1 |h 1 | 2 p 1 |h 1 | 2 N 0 p 2 |h 2 | 2 N 0 p 1 |h 1 | 2 BS2 , log 2 1 + log 2 1 + log 2 1 + log 2 1 + p 1 |h 1 | 2 N 0 p 2 |h 2 | 2 N 0 , log 2 1 + BS2 log 2 1 + log 2 1 + , p 1 |h 1 | 2 N 0 +p 2 |h 2 | 2 p 2 |h 2 | 2 N 0 +p 1 |h 1 | 2 , · By applying the fictitious play algorithm with the initial belief point (0, 1), one gets a cycling behavior between the two worst configurations. Since the two alternating cycling configurations lead to the worst utilities, the Cesaro-limit util- ity obtained under the fictitious play algorithm is worse than the worst Nash equilibrium 1 utility. Now, if the initial belief point is fixed to 1 , 2 , then the outcome of the fictitious 2 play algorithm is the completely mixed Nash equilibrium. 1 ¯ 1+ ¯ , 1+¯ , ¯