Informational uniqueness of closed-loop Nash equilibria for a class of nonstandard dynamic games

Market processes can be analyzed by means of dynamic games. In a number of dynamic games multiple Nash equilibria appear. These equilibria often involve no credible threats the implementation of which is not in the interests of the players making them. The concept of sub game perfect equilibrium rules out these situations by stating that a reasonable solution to a game cannot involve players believing and acting upon noncredible threats or promises. A simple way of finding the sub game perfect Nash equilibrium of a dynamic game is by using the principle of backward induction. To explain how this equilibrium concept is applied, we analyze the dynamic entry games.

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Closed-loop stackelberg solution and threats in dynamic games

Optimization Techniques - Lecture Notes in Control and Information Sciences ◽

10.1007/bfb0036401 ◽

2006 ◽

pp. 261-269 ◽

Cited By ~ 1

Author(s):

B. Tołwiński

Keyword(s):

Dynamic Games ◽

Closed Loop ◽

Stackelberg Solution

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Open-loop and feedback Nash equilibria in constrained linear–quadratic dynamic games played over event trees

Automatica ◽

10.1016/j.automatica.2019.05.042 ◽

2019 ◽

Vol 107 ◽

pp. 162-174

Author(s):

Puduru Viswanadha Reddy ◽

Georges Zaccour

Keyword(s):

Dynamic Games ◽

Nash Equilibria ◽

Open Loop ◽

Linear Quadratic ◽

Feedback Nash Equilibria ◽

Event Trees

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Two-Player Location Game in a Closed-Loop Market with Quantity Competition

Complexity ◽

10.1155/2020/4325454 ◽

2020 ◽

Vol 2020 ◽

pp. 1-12

Author(s):

Xiaofeng Chen ◽

Qiankun Song ◽

Zhenjiang Zhao

Keyword(s):

Minimum Distance ◽

Nash Equilibria ◽

Closed Loop ◽

Transportation Cost ◽

Competitive Dynamics ◽

Backward Induction ◽

Local Market ◽

Induction Method ◽

Quantity Competition ◽

Circle Model

This paper considers the two-player location game in a closed-loop market with quantity competition. Based on the Cournot and Hotelling models, a circle model is established for a closed-loop market in which two players (firms) play a location game under quantity competition. Using a two-stage (location-then-quantity) pattern and backward induction method, the existence of subgame-perfect Nash equilibria is proved for the location game in the circle model with a minimum distance transportation cost function. In addition, sales strategies are proposed for the two players for every local market on the circle when the players are in the equilibrium positions. Finally, an algorithm for simulating the competitive dynamics of the closed-loop market is designed, and two numerical simulations are provided to substantiate the effectiveness of the obtained results.

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