General economics question, help needed please.

[Georgelamb]

Dear all,

 

I am a pharmacist taking a MSc in Health Economics.

I am stuck trying to solve a problem on game theory.

 

Question:

Consider the following two player iE(1,2) symmetric game. The payoff function of each player is ui(si,sj)=(2si-sj+1)(si-2sj)+12, where j is different from i. Each player's strategy space is defined as Si=(1,2,3).

Represent this interaction as a game in strategic form (a bi-matrix).

 

I would really appreciate your help.

 

Thanks!!

[fatsho]

Basically, draw a 3x3 box, where the columns are j's strategy and the rows are i's strategies. so the first box will be where i plays 1 and j plays 1, so inside the box you can write the payoffs by substituting si=1 and sj=1 in each player's payoff function. Do this exercise for all boxes i.e the 9 combinations.

[Georgelamb]

Thank you for your reply,

Could I ask you:

I have replaced si and sj by 1 and 1, 2 and 1, 3 and 1... in the utility function given.

Are the values that I obtained the payoffs for player i?

What do I need to do differently to obtain player j's payoffs?

 

 

Thank you for your help!

[fatsho]

since, it's a symmetric game the payoffs should be same for both for different combinations for eg. when i play si=1 and j plays sj=2, the payoff to i should be the same as payoff to j when si=2 and sj=1.

 

More generally, substituting the values in ui gives you i's payoff for a particular combination of strategies and substituting them in uj gives you j's payoff.

 

You might wanna check out some of yale ocw videos for game theory.

[Georgelamb]

I got it now.

Thank you so much for your help!

[fatsho]

Don't mention. :)

 

Glad you're sorted.