I can't comment on "misleading" without reading, likely studying, the article you mentioned. There's a lot to game theory, e.g., one I omitted, differential ga

I can't comment on "misleading" without reading, likely studying, the article you mentioned. There's a lot to game theory, e.g., one I omitted, differential game theory as in a missile chasing an airplane. But the likely most relevant, first cut, simple view is that each of the two players, Red and Blue, has a list of moves they can make. Then there is one (von Neumann case) or two (Nash case) payoff matrices. Then each of Red and Blue picks a move or a probability distribution of moves. The broad idea is to have and use a saddle point, maybe available only by making moves probabilistically in which case each of Red and Blue finds a probability distribution over the moves they can make and then picks a move according to their distribution and independent of everything else relevant. So, just as in the classic children's game paper-scissors-rock, each player picks a move in secret, and then both players show their moves at the same time. Each player seeks to maximize their long run expected gain. As can be shown easily from linear programming and its duality theory, for paper-scissors-rock the saddle point probability distributions are that each player picks each of the three moves paper, scissors, rock with probability 1/3rd. Of course, Red and Blue pick their moves independently and in secret. The matrix for paper-scissors-rock is 3 x 3. But the theory and the linear programming solution applies the same for positive integers m and n for m moves for Red, n moves for Blue, and a matrix m x n. All the components of the matrix are >= 0 and represent, say, a gain for Red and a loss for Blue. The classic von Neumann result shows how to get a saddle point from a payoff matrix with one row for each move for Red and one column for each move for Blue. Again, we can get this result from linear programming duality theory. The Nash result is a little more general. Sion's result is really just a case of max-min in mathematical programming, i.e., optimization. Yes, convexity can play an important role, but we would need to be clear on just what is convex. Convexity is central to Sion's result. Yes, the theory gets involved with some classic fixed point results. So, for machine learning, for a start, is the game even roughly in the sense of classic von Neumann and paper-scissors-rock? If so, what are the moves and, then, the payoffs? Getting that far, are we looking for two probability distributions? Then with the distributions, how do we apply those to the machine learning calculations, iterations, optimizations, improvements, etc.? Little questions like those. So, to start to apply game theory, let's start with a problem and formulate it as a problem in some appropriate part of game theory.