extensive form game

Definition (two person zero-sum finite game)

An extensive form of a without chance moves is a finite tree structure with

1. a specific vertex indicating the starting point of the game
2. a payoff function assigning a real number to each terminal vertex of the tree, determining the payoff (or respectively, loss) to P2 (respectively, P1)
3. partition of the nodes of the tree into two player sets, $\overline{N}^1$ and $\overline{N}^2$ for P1 and P2 respectively
4. subpartition of each player set into information sets $\{\eta_j^i\}$, such that the same number of intermediate branches emanates from every node belonging to the same information set, and no node follows another node in the same information set

(convention: P1 minimizer, P2 maximizer)

References

1. T. Başar and G.J. Olsder, Dynamic Noncooperative Game Theory, 2nd edition, Classics in Applied Mathematics, SIAM, Philadelphia, 1999, pp. 36-39.
2. M. Maschler, E. Solan, and Shmuel Zamir, Game Theory, Cambridge University Press, 2013, p. 43.