Constructive design of open-loop Nash equilibrium strategies that admit a feedback synthesis in LQ games

Automatica ◽  
2021 ◽  
Vol 133 ◽  
pp. 109840
Author(s):  
Mario Sassano ◽  
Alessandro Astolfi
Keyword(s):  
Nash Equilibrium ◽  
Open Loop ◽  
Equilibrium Strategies ◽  
Feedback Synthesis ◽  
Nash Equilibrium Strategies

NASH EQUILIBRIUM STRATEGIES REVISITED IN SOFTWARE RELEASE GAMES

2020 ◽  
pp. 1-21
Author(s):  
Yasuhiro Saito ◽  
Tadashi Dohi
Keyword(s):  
Nash Equilibrium ◽  
Optimization Theory ◽  
Applied Probability ◽  
Equilibrium Strategies ◽  
Release Policy ◽  
Software Release ◽  
Nash Equilibrium Strategies ◽  
Person Game

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.

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

2018 ◽  
Vol 20 (01) ◽  
pp. 1750030 ◽  
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.

ADVERTISING DECISIONS IN A VERTICAL DISTRIBUTION CHANNEL

2009 ◽  
Vol 11 (03) ◽  
pp. 273-284 ◽  
Author(s):  
BRUNO VISCOLANI
Keyword(s):  
Nash Equilibrium ◽  
Vertical Distribution ◽  
Distribution Channel ◽  
Joint Effect ◽  
Market Segments ◽  
Equilibrium Strategies ◽  
Optimal Decisions ◽  
Two Agents ◽  
Segmented Market ◽  
Nash Equilibrium Strategies

A manufacturer and a retailer are the members of a simple distribution channel for a particular product in a segmented market. The advertising efforts of the two agents have a joint effect on the goodwill of the different market segments and then on the demand. The channel members aim at maximizing their profits, by choosing suitable advertising media and efforts. We focus mainly on competition between manufacturer and retailer, obtaining Nash equilibrium strategies, in the contexts of linear and concave demand. We consider also the possibility of cooperation, obtaining the coordinated channel optimal decisions.

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