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I am solving a bargaining problem in which I have two players $player_1 $ and $ player_2 $. Both of them have a service (represented as $ z_1 ,z_2 $) that they can provide . Moreover they will charge some price(cost) ($ \lambda_1, \lambda_2 $ ) for providing that service.

The utility function are based on benefit-cost function.

Player 1 provide a service to the player 2 and charges some price for it.

The utility of $player_2$ can be represented as : $U_{player_2} =f(z_2)- \lambda_2z_2$

Player 2 provide a service to the player 1 and charges some price for it. $U_{player_1} =f(z_1)- \lambda_1z_1$.

$z_2$ is the decision variable of player 1 and $z_1$ is the decision variable of player 2 .

How can I model it using a bargaining game , can I use any other cooperative game approach.

I have tried some thing like this :

$log(f(z_2)- \lambda_2z_2+\lambda_1z_1)+(log(f(z_1)+\lambda_2z_2-\lambda_1z_1 )$

Is this correct?

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  • $\begingroup$ Player 1 is providing service to player 2 and vice versa; if I omit the price factor for both players and model this as a service exchange only (without price ) than this can be modeled as a bargaining game; but I wanted to know if I include the price, than can I modeled it using a bargaining game. $\endgroup$ – user9919909 Jun 15 '18 at 11:56
  • $\begingroup$ Also your 'attempt' is rather vague. $\endgroup$ – Giskard Jun 15 '18 at 12:19
  • $\begingroup$ Yes this is right . $\endgroup$ – user9919909 Jun 15 '18 at 12:27
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    $\begingroup$ If you're primarily interested in a bargaining outcome, then you're going to need to refine the problem a bit by defining what properties you want your solution to satisfy. Almost any outcome can be justified by some set of beliefs and properties, the trick is figuring out which set makes the most sense for your application. Even among the classical examples of bargaining solutions, they all satisfy slightly different requirements (axioms). $\endgroup$ – AndrewC Jun 15 '18 at 14:10

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