 

M matrix  Bird 2  
Cooperate  Defect  
Bird  Cooperate 


1  Defect  
 
P matrix  Bird 2  
Cooperate  Defect  
Bird  Cooperate 


1  Defect  
 

The first number in each cell represents the payoff to bird 1, the second number the payoff to bird 2.
In the M (byproduct mutualism) matrix, there is no temptation to defect, as cooperating always fared better than defecting (4 > 1, 1 > 0).
The P (prisoner's dilemma) matrix should also encourage reciprocity, provided the birds follow a strategy such as titfortat.