Determinacy of Two-Player Games with Perfect Information

Pranshu Gaba
Friday, 25 Mar 2022, 16:15 to 17:15
A game with *perfect information* is a game in which no information is hidden from the players. All players know the rules and the state of the game at all times. Some examples of games with perfect information are Chess, Checkers, Go, and Nim.
In two-player zero-sum games, a player has a *winning strategy* if they can always win no matter how the other player plays. A game is
*determined* if one of the players has a winning strategy. Given a two-player game with perfect information, we would like to find out if it is determined.
In today's talk, we discuss some results on two-player games with perfect information:
- We show that all finite games are determined.
- We construct an example of an infinite game that is not determined.
- We define a topology on infinite games. We use this to show the determinacy of some special classes of infinite games.
All results are from:
[1] "Theory of Games and Economic Behavior" by von Neumann and Morgenstern, 1947.
[2] "Infinite Games with Perfect Information" by Gale and Stewart, 1953.

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