Stackelberg type dynamic zero-sum game with leader and follower

Tanaka, Yasuhito (2018): Stackelberg type dynamic zero-sum game with leader and follower.

Abstract

We consider a Stackelberg type dynamic two-players zero-sum game. One of two players is the leader and the other player is the follower. The game is a two-stages game. In the first stage the leader determines the value of its strategic variable. In the second stage the follower determines the value of its strategic variable given the value of the leader's strategic variable. On the other hand, in the static game two players simultaneously determine the values of their strategic variable. We will show that Sion's minimax theorem (Sion(1958)) implies that at the sub-game perfect equilibrium of the Stackelberg type dynamic zero-sum game with a leader and a follower the roles of leader and follower are irrelevant to the payoffs of players, and that the Stackelberg equilbria of the dynamic game are equivalent to the equilibrium of the static game.

• Item Type: MPRA Paper
• Language: English
• Keywords: zero-sum game, Stackelberg, dynamic zero-sum game
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

References

Kindler, J. (2005), ``A simple proof of Sion's minimax theorem,'' American Mathematical Monthly, 112, pp. 356-358.

Komiya, H. (1988), ``Elementary proof for Sion's minimax theorem,'' Kodai Mathematical Journal, 11, pp. 5-7.

Sion, M. (1958), ``On general minimax theorems,'' Pacific Journal of Mathematics, 8, pp. 171-176.

Tanaka, Y. (2014), ``Relative profit maximization and irrelevance of leadership in Stackelberg model,'' Keio Economic Studies, 50, pp. 69-75.