Decentralized Decision Making in the Game of Tic-tac-toe

Abstract

Traditionally, the game of Tic-tac-toe is a pencil and paper game played by two people who take turn to place their pieces on a 3times3 grid with the objective of being the first player to fill a horizontal, vertical, or diagonal row with their pieces. What if instead of having one person playing against another, one person plays against a team of nine players, each of whom is responsible for one cell in the 3times3 grid? In this new way of playing the game, the team has to coordinate its players, who are acting independently based on their limited information. In this paper, we present a solution that can be extended to the case where two such teams play against each other, and also to other board games. Essentially, the solution uses a decentralized decision making, which at first seems to complicate the solution. However, surprisingly, we show that in this mode, an equivalent level of decision making ability comes from simple components that reduce system complexity.

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