Explaining Title's Contenders behaviour by Game Theory

Legend :
C = Chelsea, L = Liverpool, MU = ManU
W = Win, L = Lose, D = Draw
Note : I am sorry for the confusion of notation (L for Liverpool and L for Lose)

This Sunday night, there will be another big match of EPL (English Premier League) between Chelsea and Liverpool. Both of them are behind Manchester United by 3 points (with the same number of games). Manchester United has a match against Everton on Sunday morning (HK Time).

Just for your information, the current standing of the league (as of Jan 31, 2009) :
1st : Manchester United (50 points)
2nd : Chelsea (48 points)
3rd : Liverpool (48 points)

In this note, I will try to explain why both Chelsea and Liverpool will try to defeat one another by using game theory approach.

As you see in the figure above,
1. If ManU win the Everton match, ManU will have 53 points. Then If Chelsea win, Chelsea will be 2 points behind (-2) and Liverpool will be 5 points behind (-5). Or If Liverpool win, the position is reversed. Or If they share a point, both will be 4 points behind (-4).
2. If ManU lose the Everton match, ManU will have 50 points.Then If Chelsea win, Chelsea will be 1 point in front (+1), and Liverpoll will be 2 points behind (-2). Or If Liverpool win, the position is reversed.Or If they share a point, both will be 1 points behind (-1).
3. If ManU vs Everton ends up with a draw, ManU will have 51 points. Then If Chelsea win, Chelsea will have same points (0) and Liverpool will be 3 points behind (-3). Or If Liverpool win, the position is reversed. Or if they share a point, both will be 2 points behind (-2).

As you see in the figure above, the best strategy for Chelsea or Liverpool is always to win the game (minimizes the point loss).

If there is no collusion activities between them, each of them will play at their best to win the game.

Collusion activity is possible to be conducted between them, because if Liverpool let Chelsea win, Chelsea has a better position to challenge ManU for the title, and vice versa (if Chelsea let Liverpool win). Both of them has same amount of points currently. In this sense, both of them joins forces to steal the title from ManU (assumed their objective is any club could win the title except ManU). I mention this only for the sake of possibility. Although, I believe that this will not happen.

Game Theory Approach of explaining behavior of Liverpool and Chelsea this coming Sunday night.