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# Nash equilibrium

| 🗖 nosplit | ↑ parent "Game theory" | words: 142 | descendant words: 154 | descendants: 3
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Yes, you can think about the prisoner's dilemma, but that's boring, a much more interesting example is choosing a deck of a TCG competition: Magic: The Gathering meta-based deck choice is a bimatrix game
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The key idea is that:
• imagine that the game will be played many times between two players
• if one player always chooses one deck, the other player will adapt by choosing the anti-deck
• therefore, the best strategy for both players, is to pick decks randomly, each with a certain probability. This type of probabilistic approach is called a mixed strategy
• if any player deviates from the equilibrium probability, then the other player can add more of the anti-deck to the deck that the other player deviated, and gain an edge
Therefore, using equilibrium probabilities is the optimal way to play
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