Zero sum game in game theory & economics | Convex Optimization Application # 4

📚About
In game theory and economic theory, a zero-sum game is a mathematical representation of a situation in which each participant's gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants. If the total gains of the participants are added up and the total losses are subtracted, they will sum to zero. We will regard the zero-sum game from a convex optimization perspective, that is each player is solving a convex optimization problem. Well, are they related ? Watch the whole lecture to know. This lecture is outlined as follows:

⏲Outline⏲
00:00 Intro
02:08 What is the Zero-sum Game ?
03:18 The Payoff Matrix
04:00 Randomized - Mixed strategies
07:55 What is Player 2 trying to do ?
09:49 What is Player 1 trying to do ?
11:37 Reformulating (P1) as a linear program
14:42 Solving for Player's 1 optimal strategy on MATLAB
17:33 Solving for Player's 2 optimal strategy on MATLAB
18:41 Solving both strategies for any Zero-sum Game
23:41 The influence of the Payoff matrix
25:45 Outro

🔴 Subscribe for more videos on Game Theory Applications
👍 Smash that like button, in case you find this tutorial useful.
👁‍🗨 Speak up and comment, I am all ears.

#Game #GameTheory #Convex

[fooxmoody]

Ahmad Bazzi is John Forbes Nash reincarnated !!

[jerrydaboss]

According to Matlab docs, linprob solves for Gx <= h in this case given the variables you called the function on. Verifying, we evaluate G * x (using Matlab, after running the script you wrote), and find it to be [[0], [0], [-10]]. However, in you written notes/work, you write that we want to solve for Gx >= h. Fixing the script, and calling linprog(f, -G, h, A, b, lb, ub), we get that u = [[0], [0.5], [0.5]] and G * x = [[10], [5], [0]]. I think this should be the correct solution.

Further proof 3/7 and 4/7 is incorrect:
We want to maximize the minimum. If player 2 chooses 1 or 2, player 1 will get expected 50/7 (90/7-40/7 and -30/7+80/7), but if player 2 chooses 3, then player 1 gets expected -20/7 (60/7-80/7), so the solution was not optimal.
In the .5 and .5 case, worse case is player 2 chooses move 3, in which case you get expected 0.

Idk mb I'm wrong. Please do correct me if I am.

[vargalaszlo]

Please make a video on stock prediction prices : )

[furkannighlost]

I have an exam in financial statistics tomorrow and this was helpful. Thank you Ahmad

[kyzruh]

Man, I wish that I had found this channel much sooner. But, better late than never. Great vid.

[theatre]

Problems are opportunities. Right now there are a lot of problems.

[Vinay]

How is in 9:35 the set equal to min of u^TP over all entries ? Thank you

[deedrastrunk]

Prisoner’s i don’t understand this topic

[عادلابراهيم-كب]

The internet really is great isn't it ? Once you get beyond all gaming, memes and anime, you realise you can educate yourself to a high level and pay nothing