Clearly this game has no dominant strategy. If you're Player 1 you want your coin to match Player 2's which means you want to show Heads when Player 2 shows Heads and you want to show Tails when Player 2 shows Tails.

   Player 2 however always wants to show the opposite of whatever Player 1 shows. Thus for both players the best response depends on what the other player does, so there is no dominant strategy, and since this is a two strategy game there can be no dominated strategy when there is no dominant strategy.

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