Georgelamb Posted July 23, 2014 Share Posted July 23, 2014 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!! Quote Link to comment Share on other sites More sharing options...
fatsho Posted July 23, 2014 Share Posted July 23, 2014 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. Quote Link to comment Share on other sites More sharing options...
Georgelamb Posted July 23, 2014 Author Share Posted July 23, 2014 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! Quote Link to comment Share on other sites More sharing options...
fatsho Posted July 23, 2014 Share Posted July 23, 2014 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. Quote Link to comment Share on other sites More sharing options...
Georgelamb Posted July 23, 2014 Author Share Posted July 23, 2014 I got it now. Thank you so much for your help! Quote Link to comment Share on other sites More sharing options...
fatsho Posted July 23, 2014 Share Posted July 23, 2014 Don't mention. :) Glad you're sorted. Quote Link to comment Share on other sites More sharing options...
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