behavior strategy

Definition

A behavior strategy of a game in an extensive form game is a function mapping each of his information sets to a probability distributions over the set of possible actions at that information set.

• $\mathcal{U}_i$ collection of information sets of player $i$
• $A(U_i)$ set of possible actions at $U_i$
• $b_i : \mathcal{U}_i \to \cup_{U_i \in \mathcal{U}_i} \Delta(A(U_i))$, behavior strategy of player $i$, where $b_i(U_i) \in \Delta(A(U_i))$

Strategy vector

see mixed/behavior strategy vector

Also see equivalent mixed and behavior strategies

See also

• admissible Nash equilibrium strategy pair
• better pair of strategies
• mixed strategy
• pure strategy
• strategy

References

1. https://en.wikipedia.org/wiki/Strategy_(game_theory)
2. T. Başar and G.J. Olsder, Dynamic Noncooperative Game Theory, 2nd edition, Classics in Applied Mathematics, SIAM, Philadelphia, 1999, pp. 5, 18, 79.
3. M. Maschler, E. Solan, and Shmuel Zamir, Game Theory, Cambridge University Press, 2013, p. 221.
4. https://math.stackexchange.com/questions/1345773/what-is-the-difference-between-mixed-strategy-and-behavioral-strategy-games