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


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:

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


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