Stackelberg equilibrium of dynamic symmetric multi-players zero-sum game with a leader and followers without differentiability of payoff functions

This paper studies a Stackelberg type symmetric dynamic $n$-players zero-sum game. There is one leader and $n-1$ followers. Players have the symmetric payoff functions. 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 followers determine the values of their strategic variables given the value of the leader's strategic variable. In the static game, on the other hand, all players simultaneously determine the values of their strategic variable. We do not assume differentiability of payoff functions. This paper shows that the sub-game perfect equilibrium of the Stackelberg type symmetric dynamic zero-sum game is equivalent to the equilibrium of the static game if and only if the game is fully symmetric