Some negative properties of nash-equilibrium strategies in stochastic differential games

A software release game was formulated by Zeephongsekul and Chiera [Zeephongsekul, P. & Chiera, C. (1995). Optimal software release policy based on a two-person game of timing. Journal of Applied Probability 32: 470–481] and was reconsidered by Dohi et al. [Dohi, T., Teraoka, Y., & Osaki, S. (2000). Software release games. Journal of Optimization Theory and Applications 105(2): 325–346] in a framework of two-person nonzero-sum games. In this paper, we further point out the faults in the above literature and revisit the Nash equilibrium strategies in the software release games from the viewpoints of both silent and noisy type of games. It is shown that the Nash equilibrium strategies in the silent and noisy of software release games exist under some parametric conditions.

Download Full-text

Nash equilibrium approximation of some class of stochastic differential games: A combined Chebyshev spectral collocation method with policy iteration

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2019.05.014 ◽

2019 ◽

Vol 362 ◽

pp. 41-54 ◽

Cited By ~ 5

Author(s):

Z. Nikooeinejad ◽

M. Heydari

Keyword(s):

Nash Equilibrium ◽

Differential Games ◽

Collocation Method ◽

Stochastic Differential Games ◽

Policy Iteration ◽

Spectral Collocation Method ◽

Spectral Collocation ◽

Chebyshev Spectral Collocation ◽

Chebyshev Spectral Collocation Method

Download Full-text

ε-Nash equilibrium in stochastic differential games with mean-field interaction and controlled jumps

Statistics & Probability Letters ◽

10.1016/j.spl.2019.05.021 ◽

2019 ◽

Vol 154 ◽

pp. 108522

Author(s):

Chiara Benazzoli ◽

Luciano Campi ◽

Luca Di Persio

Keyword(s):

Nash Equilibrium ◽

Differential Games ◽

Mean Field ◽

Stochastic Differential Games ◽

Field Interaction

Download Full-text

A Feedback Nash Equilibrium for Affine-Quadratic Zero-Sum Stochastic Differential Games With Random Coefficients

IEEE Control Systems Letters ◽

10.1109/lcsys.2020.2994642 ◽

2020 ◽

Vol 4 (4) ◽

pp. 868-873

Author(s):

Jun Moon

Keyword(s):

Nash Equilibrium ◽

Differential Games ◽

Stochastic Differential Games ◽

Random Coefficients ◽

Feedback Nash Equilibrium ◽

Zero Sum

Download Full-text

Maximin and Minimax Strategies in Two-Players Game with Two Strategic Variables

International Game Theory Review ◽

10.1142/s021919891750030x ◽

2018 ◽

Vol 20 (01) ◽

pp. 1750030 ◽

Cited By ~ 1

Author(s):

Atsuhiro Satoh ◽

Yasuhito Tanaka

Keyword(s):

Nash Equilibrium ◽

Objective Function ◽

The Other ◽

Minimax Strategy ◽

Equilibrium Strategies ◽

Minimax Strategies ◽

Nash Equilibrium Strategies ◽

Special Case ◽

Maximin Strategy

We examine maximin and minimax strategies for players in a two-players game with two strategic variables, [Formula: see text] and [Formula: see text]. We consider two patterns of game; one is the [Formula: see text]-game in which the strategic variables of players are [Formula: see text]’s, and the other is the [Formula: see text]-game in which the strategic variables of players are [Formula: see text]’s. We call two players Players A and B, and will show that the maximin strategy and the minimax strategy in the [Formula: see text]-game, and the maximin strategy and the minimax strategy in the [Formula: see text]-game are all equivalent for each player. However, the maximin strategy for Player A and that for Player B are not necessarily equivalent, and they are not necessarily equivalent to their Nash equilibrium strategies in the [Formula: see text]-game nor the [Formula: see text]-game. But, in a special case, where the objective function of Player B is the opposite of the objective function of Player A, the maximin strategy for Player A and that for Player B are equivalent, and they constitute the Nash equilibrium both in the [Formula: see text]-game and the [Formula: see text]-game.

Download Full-text