# Convert a sequential move game into a simultaneous move game

A statement from Ponssard and Zamir "Zero-sum sequential games with incomplete information" at the bottom of the first page reads

AM's result is for zero-sum two-person games in which the two players move simultaneously. This includes of course games in which the moves are made sequentially: Player I moves first, player II is informed of player I's move and then makes his own move. (Such a game can be looked at as a simultaneous game after redefining the pure strategies of player II.)

I am curious about the last statement in parentheses. How does one "redefine" the strategies of the follower to make the game simultaneous move?

• I think they simply mean that you can rewrite an extensive-form game with a strategy like "first play A then play L if player 2 played X and play R if player 2 played Y" in matrix form and call this strategy ALR. That is, simply redefine the game such that the simultaneous-move action is a simultaneously set contingent plan of actions. Commented Jun 4, 2019 at 16:32

## 1 Answer

This is basically the idea that any extensive form game has a normal form representation.

http://www.sfu.ca/~shihenl/302/Strategies%20Memo.pdf

• Just a general well-meant comment: This community prefers more detailed descriptions of contents behind links that are likely temporary, but I guess it's alright in this case. Commented Jun 4, 2019 at 18:02