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| 12/07/2019 06:22 AM by Stefan; Potential games and potential function for three competing products |
I have been working on my thesis and am currently stuck at making the potential function that is able to track unilateral deviation within the network. Suppose there are three different products A,B,C. The utility of each product is given by
Gi(S1)=a∑i∈V12(σi−2)(σi−3)+Bi−γ
Hi(S2)=d∑i∈V−(σi−1)(σi−3)+Fi−λ
Li(n−S1−S2)=e(n−∑i∈V12(σi−2)(σi−3)−∑i∈V−(σi−1)(σi−3))+Ki−ϵ)
The payoff of an induvidul player is the following:
πi(σi,σ−i)=[Gi(S1)−γ]12(σi−2)(σi−3)+[Hi(S2)−λ]∗−(σi−1)(σi−3)+[Li(n−S1−S2)−ϵ]12(σi−1)(σi−2)
Now I am stuck on finding the potential function that can describe this system. Hopefully, someone can help me. [Manage messages]