Yomi vs. Nash Equilibria
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Games: David Sirlin, game design, math, yomi
I was rereading David Sirlin’s World of Warcraft Teaches the Wrong Things as part of a conversation with a friend and I got to pondering his concept of yomi. I’ve previously mentioned it as having an influence on my game designs, so I’ll just quote his short definition:
Street Fighter taught me about yomi: knowing the mind of the opponent. You can’t just play the odds and do the textbook-correct responses, you have to adapt and anticipate your opponent’s moves. The game is merely a medium through which you play against the other player.
Games vary in how much they require skill at yomi, and it occurred to me that a game including yomi skill precludes a game having a Nash equilibrium.
a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his or her own strategy unilaterally. If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium.
Stated simply, Amy and Bill are in Nash equilibrium if Amy is making the best decision she can, taking into account Bill’s decision, and Bill is making the best decision he can, taking into account Amy’s decision. Likewise, a group of players is in Nash equilibrium if each one is making the best decision that he or she can, taking into account the decisions of the others.
Games like Street Fighter, Kongai, poker, chess, are interesting because they don’t have evolutionarily stable strategies, every player is obliged to change their strategy in response to another player’s change. If a game (or one decision in a game) has a Nash equilibrium, there is no value to yomi, the player doesn’t need to know what the other player plans.