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.

Item Type: | MPRA Paper |
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Original Title: | Analysis of dynamic symmetric three-players zero-sum game with a leader and two followers without differentiability of payoff functions |

Language: | English |

Keywords: | symmetric zero-sum game, Stackelberg equilibrium, leader, follower |

Subjects: | C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games |

Item ID: | 91919 |

Depositing User: | Yasuhito Tanaka |

Date Deposited: | 12 Feb 2019 11:48 |

Last Modified: | 30 Sep 2019 13:06 |

References: | Korzhyk, D., Yin, Z., Kiekintveld, C., Conitzer, V. and Tambe, M. (2014), ``Stackelberg vs. Nash in security games: An extended investigation of interchangeability, equivalence, and uniqueness,'' Journal of Artificial Intelligence Research, 41, pp. 297-327. Matsumura, T., N. Matsushima and S. Cato (2013) ``Competitiveness and R\&D competition revisited,'' Economic Modelling, 31, pp. 541-547. Ponssard, J. P. and Zamir, S. (1973), ``Zero-sum sequential games with incomplete information,'' International Journal of Game Theory, 2, pp. 99-107. Satoh, A. and Y. Tanaka (2014a) ``Relative profit maximization and equivalence of Cournot and Bertrand equilibria in asymmetric duopoly,'' Economics Bulletin, 34, pp. 819-827, 2014. Satoh, A. and Y. Tanaka (2014b), ``Relative profit maximization in asymmetric oligopoly,'' Economics Bulletin, 34, pp. 1653-1664. Tanaka, Y. (2014), ``Relative profit maximization and irrelevance of leadership in Stackelberg model,'' Keio Economic Studies, 50, pp. 69-75. Tanaka, Y. (2018), ``Stackelberg type dynamic symmetric three-players zero-sum game with a leader and two followers,'' mimeo. Vega-Redondo, F. (1997) ``The evolution of Walrasian behavior,'', Econometrica, 65, pp. 375-384. Yin, Z., Korzhyk, D., Kiekintveld, C., Conitzer, V. and Tambe, M. (2010), ``Stackelberg vs. Nash in security games: Interchangeability, equivalence, and uniqueness,'', Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems, pp. 1139-1146, International Foundation for Autonomous Agents and Multiagent Systems. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/91919 |