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Help with shared constraints (game theory)

  1. Dec 22, 2013 #1
    I've been struggling with shared constraints problems for a while now. I have a game between two players with a shared constraint. For example, player 1 is trying to maximize f(x,y) by choosing x, and player 2 is trying to maximize g(x,y) by choosing y. The players are competing in a non-cooperative game.
    There is a shared constraint such that x+y<= a.

    If I understand the source below correctly (p. 18 onward), what I should do is form a Lagrangian: L1 = f(x,y)+λ(a-x-y) and L2=g(x,y)+λ(a-x-y)? (i.e., λ for player 1 is the same as for player 2) and then solve the FOC? Is this the right way to approach this?

    Reference: http://www.dis.uniroma1.it/~facchinei/didattica/giochi/Lettura_3.pdf
  2. jcsd
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