3 Agent Decision Making Game - Game Theory

sharkywrecks

New member
Joined
Mar 28, 2024
Messages
1
Hi. What I am going to go through is my uni coursework for CompSci and AI. I don't want the answer but I would really appreciate an explanation and to know whether I am on the right path or not(no one else to ask for help since the uni is closing over Easter break).

Please see the context below:
1711639637490.png
The questions are as follows:
1711639813332.png
1711639834099.png

What I have done so far:
1711640274411.png
I'm assuming q1 and q2 are correct(I really don't know since the module is so poorly taught), so I will focus on q3. I've outline what I would do at the start but actually doing it is making me doubt my ability to math. Please ignore the fact that it's only worth 2 marks.
I have differentiated the expected utility for the 3rd agent in terms of x_3, ignoring when k = 3 cause I am hoping it is correct to do so. Expanding while there's still 2 strategies was rough so I simplified and took only 1 in general(i.e. strategy j) and solved. I am thinking that this will lead to where strategy j is highest and would be a best response to the other players?
 
Top