<p>I am just wondering whether the following question has already been answered in game theory: Fix an arbitrary (say, finite) two-player strategic form game. Under what condition, does one player (say, Player 1) want to be the first-mover than the second mover?</p>

<p>For example, we know that moving first is better in Cournot competition and moving second is better in Rock-paper-scissors. Is there a general condition on the payoffs of two-player games under which we can tell whether Player 1 should go first or second, if he could choose?</p>

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2018-08-19T21:20:59.783Z
It may seem a little circular, but in an [impartial](https://en.wikipedia.org/wiki/Impartial_game) [combinatorial game](https://en.wikipedia.org/wiki/Combinatorial_game_theory), the game is a second player win when its [nimber](https://en.wikipedia.org/wiki/Nimber) is 0 and a first player win otherwise.  More generally, including non-impartial games, those games with a value of 0 are second player wins while those which are [fuzzy with 0](https://en.wikipedia.org/wiki/Fuzzy_game) are first player wins
Henry
<game-theory>
General Results on First or Second Mover Advantage?
tom
# General Results on First or Second Mover Advantage?

(Asked by: username_0 on 2018-08-19)

I am just wondering whether the following question has already been answered in game theory: Fix an arbitrary (say, finite) two-player strategic form game. Under what condition, does one player (say, Player 1) want to be the first-mover than the second mover?

For example, we know that moving first is better in Cournot competition and moving second is better in Rock-paper-scissors. Is there a general condition on the payoffs of two-player games under which we can tell whether Player 1 should go first or second, if he could choose?

**Tags:** game-theory

> **Comments:**
> **username_1**: It may seem a little circular, but in an [impartial](https://en.wikipedia.org/wiki/Impartial_game) [combinatorial game](https://en.wikipedia.org/wiki/Combinatorial_game_theory), the game is a second player win when its [nimber](https://en.wikipedia.org/wiki/Nimber) is 0 and a first player win otherwise.  More generally, including non-impartial games, those games with a value of 0 are second player wins while those which are [fuzzy with 0](https://en.wikipedia.org/wiki/Fuzzy_game) are first player wins  

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