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Tl;dr: Players' meta-goals do affect gameplay. And unless all players have the same goals, the entire concept of "best player" isn't well defined, let alone "second best", etc. First a bit of game-theory framework. Let's say each player has a "utility function" which takes as input the game end-state and gives as output how much "utility" they get - an ...


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In a game where there is a scoring function, one can always rank players beyond the winner into 2nd, 3rd, etc. The real question is whether positions beyond first have any value. That question depends on many things, including player psychology, game design, and external incentives. Here are some examples of ways that this varies between games: Example 1:...


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Usually, when chess in analyzed, it's done with the benefits of a decision judged solely on the game state. That is, players are modeled as caring only about winning the game. But of course people are motivated by more than that. Deciding on whether to accept a draw depends on factors external to the actual game. There are many overlapping motivations for ...


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