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I understand the notion of Dominant Strategy Incentive Compatibility in auctions. I am wondering whether this concept can be extended to all games.

For example, the game "Rock Paper Scissors" does not have a dominant strategy (at least in pure strategies), but consider the game "Rock Beats All," which is identical to the former game, except that Rock wins against Paper (as well as Scissors; Scissors still wins against paper). In Rock Beats All, Rock is a dominant strategy. Is it meaningful to ask whether this game is Dominant Strategy Incentive Compatibility? If so, how would the incentive compatibility question be answered? There is no valuation as in the auction game; there is only a player's assessment of which strategy is most likely to win.

Do mechanism design concepts such as this apply to all games, or only a certain subset?

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DSIC is a possible property of a direct mechanism, not of an arbitrary game. A direct mechanism starts by players reporting their private information (i.e., types), so it is a very special kind of game. The mechanism is DSIC if reporting one's type truthfully is a dominant strategy. Your "Rock Beats All" is a complete information game and therefore has no types to report. So asking whether it is DSIC doesn't make a lot of sense.

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