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I have been struggling at solving what I think is a system of 1st order PDEs. Here is what I have:

[tex]\frac{dy1}{dt1}[/tex] = y1*F1(t1,t2) + F2(t1,t2)

[tex]\frac{dy2}{dt2}[/tex] = y2*F1(t2,t1) + F2(t2,t1)

These equations have been obtained after modeling a problem using the game theory. More specifically, I want the Nash equilibrium to equal the Pareto optima by giving the players additional money if they cooperate (and thus achieving Pareto).

Any tips on how to solve this system of PDE ?

Note : the number of equations equals the number of players. For now, I limit the model to 2 players, but in the future, N players should be considered.