Ask HN: Does game theory work if all participants are using it in zero sum game?

Yes.

https://link.springer.com/chapter/10.1007/978-1-4612-1654-4_...

John von Neumann’s Game Theory

László Mérő

The fundamental theorem of John von Neumann’s game theory states that in a broad category of games it is always possible to find an equilibrium from which neither player should deviate unilaterally. Such equilibria exist in every two-person game that satisfies the following criteria:

    1. The game is finite both in that the number of options at each move is finite and in that the game always ends in a finite number of moves.

    2. It is a zero-sum game: One player’s gain is exactly the other’s loss.

    3. The game is one of complete information: Each player knows precisely all the options available to him and to his opponent, the value of each possible outcome of the game, and his own and his opponent’s scales of values. (If the game is zero-sum, these two values are the same. There exist non-zero-sum games with complete information content, but von Neumann’s theorem does not encompass them.)

Game theory, if you boil down to its jist, is nothing but instilling fear in all the participants. Even if one of the participants comes all gun blazing to the party, then all hell breaks loose. The theory fails.

Yes, in fact the most common way to use it assumes that all players are completely rational and making perfect moves to maximize their goals.