Munich Personal RePEc Archive

Analysis of dynamic symmetric three-players zero-sum game with a leader and two followers without differentiability of payoff functions

Tanaka, Yasuhito (2019): Analysis of dynamic symmetric three-players zero-sum game with a leader and two followers without differentiability of payoff functions.

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Abstract

We consider a Stackelberg type symmetric dynamic three-players zero-sum game. One player is the leader and two players are followers. All 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. On the other hand, in the static game all players simultaneously determine the values of their strategic variable. We do not assume differentiability of players' payoff functions. We show that the sub-game perfect equilibrium of the Stackelberg type symmetric dynamic zero-sum game with a leader and two followers is equivalent to the equilibrium of the static game if and only if the game is fully symmetric.

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