A ‘perfect’ Nash Equilibrium?
We have defined the concepts of ‘best response’ and ‘Nash equilibrium’ during lectures. We defined a ‘Nash equilibrium’ (NE) as a pair of strategies in whicg each player’s strategy is a best response to the other player’s strategy. We also defined a ‘best response’ in the following way: a strategy S*1 is a ‘best response’ for a player 1 to strategy S2 if P(S*1 >= S2) for all S2. Additionally, we found that some games can have more than on NE. And some of them could be unreasonable but yet, they are NE’s. For example the game below has two NE even though a ‘reasonable’ one is 10,10.
| 1 2 | L2 | R2 |
| L1 | 1,1 | 0,0 |
| R1 | 0,0 | 10,10 |
In the article: http://www.springerlink.com/content/j25028025767n682/, a new concept of equilibrium is defined to reduce the ambiguity and eliminate any kind of counter intuitive equilibrium. This one is called the ‘perfect equilibrium’. This article shows that every ‘perfect equilibrium’ is a NE but the converse is not always true.