Search of Nash Equilibrium in Quadratic n-person Game

2016 ◽  
pp. 509-521
Author(s):  
Ilya Minarchenko
Keyword(s):  
Nash Equilibrium ◽  
Person Game

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 Nash versus coarse correlation

2020 ◽  
Vol 23 (4) ◽  
pp. 1178-1204 ◽  
Author(s):  
Konstantinos Georgalos ◽  
Indrajit Ray ◽  
Sonali SenGupta
Keyword(s):  
Nash Equilibrium ◽  
Correlated Equilibrium ◽  
Individual Choice ◽  
Pure Nash Equilibrium ◽  
Expected Payoff ◽  
Equilibrium Payoff ◽  
Payoff Dominance ◽  
Dominated Strategies ◽  
Person Game ◽  
Nash Point

Abstract We run a laboratory experiment to test the concept of coarse correlated equilibrium (Moulin and Vial in Int J Game Theory 7:201–221, 1978), with a two-person game with unique pure Nash equilibrium which is also the solution of iterative elimination of strictly dominated strategies. The subjects are asked to commit to a device that randomly picks one of three symmetric outcomes (including the Nash point) with higher ex-ante expected payoff than the Nash equilibrium payoff. We find that the subjects do not accept this lottery (which is a coarse correlated equilibrium); instead, they choose to play the game and coordinate on the Nash equilibrium. However, given an individual choice between a lottery with equal probabilities of the same outcomes and the sure payoff as in the Nash point, the lottery is chosen by the subjects. This result is robust against a few variations. We explain our result as selecting risk-dominance over payoff dominance in equilibrium.

scholarly journals Strategic equilibrium versus global optimum for a pair of competing servers

2006 ◽  
Vol 43 (04) ◽  
pp. 1165-1172
Author(s):  
Benjamin Avi-Itzhak ◽  
Boaz Golany ◽  
Uriel G. Rothblum
Keyword(s):  
Nash Equilibrium ◽  
Queueing System ◽  
Optimal Solution ◽  
Global Optimum ◽  
Optimal Solutions ◽  
Service Rates ◽  
Unique Nash Equilibrium ◽  
Person Game ◽  
The Given ◽  
Linear Penalties

Christ and Avi-Itzhak (2002) analyzed a queueing system with two competing servers who determine their service rates so as to optimize their individual utilities. The system is formulated as a two-person game; Christ and Avi-Itzhak proved the existence of a unique Nash equilibrium which is symmetric. In this paper, we explore globally optimal solutions. We prove that the unique Nash equilibrium is generally strictly inferior to a globally optimal solution and that optimal solutions are symmetric and require the servers to adopt service rates that are smaller than those occurring in equilibrium. Furthermore, given a symmetric globally optimal solution, we show how to impose linear penalties on the service rates so that the given optimal solution becomes a unique Nash equilibrium. When service rates are not observable, we show how the same effect is achieved by imposing linear penalties on a corresponding signal.

Finding the Pure-Strategy Nash Equilibrium Using a Fixed-Point Algorithm

2013 ◽  
Vol 427-429 ◽  
pp. 1803-1806 ◽  
Author(s):  
Zheng Tian Wu ◽  
Chuang Yin Dang ◽  
Chang An Zhu
Keyword(s):  
Fixed Point ◽  
Nash Equilibrium ◽  
Normal Form ◽  
Pure Strategy ◽  
Payoff Function ◽  
Fixed Point Algorithm ◽  
Linear Programming Formulation ◽  
Active Research ◽  
Person Game ◽  
Strategy Nash Equilibrium

It is well known that determining whether a finite game has a pure-strategy Nash equilibrium is an NP-hard problem and it is an active research topic to find a Nash equilibrium recently. In this paper, an implementation of Dang's Fixed-Point iterative method is introduced to find a pure-strategy Nash equilibrium of a finite n-person game in normal form. There are two steps to find one pure-strategy Nash equilibrium in this paper. The first step is converting the problem to a mixed 0-1 linear programming formulation based on the properties of pure strategy and multilinear terms in the payoff function. In the next step, the Dangs method is used to solve the formulation generated in the former step. Numerical results show that this method is effective to find a pure-strategy Nash equilibrium of a finite n-person game in normal form.

scholarly journals Strategic equilibrium versus global optimum for a pair of competing servers

2006 ◽  
Vol 43 (4) ◽  
pp. 1165-1172 ◽  
Author(s):  
Benjamin Avi-Itzhak ◽  
Boaz Golany ◽  
Uriel G. Rothblum
Keyword(s):  
Nash Equilibrium ◽  
Queueing System ◽  
Optimal Solution ◽  
Global Optimum ◽  
Optimal Solutions ◽  
Service Rates ◽  
Unique Nash Equilibrium ◽  
Person Game ◽  
The Given ◽  
Linear Penalties

Christ and Avi-Itzhak (2002) analyzed a queueing system with two competing servers who determine their service rates so as to optimize their individual utilities. The system is formulated as a two-person game; Christ and Avi-Itzhak proved the existence of a unique Nash equilibrium which is symmetric. In this paper, we explore globally optimal solutions. We prove that the unique Nash equilibrium is generally strictly inferior to a globally optimal solution and that optimal solutions are symmetric and require the servers to adopt service rates that are smaller than those occurring in equilibrium. Furthermore, given a symmetric globally optimal solution, we show how to impose linear penalties on the service rates so that the given optimal solution becomes a unique Nash equilibrium. When service rates are not observable, we show how the same effect is achieved by imposing linear penalties on a corresponding signal.

PROPORTIONAL THREE-PERSON RED-AND-BLACK GAMES

2008 ◽  
Vol 23 (1) ◽  
pp. 37-50 ◽  
Author(s):  
May-Ru Chen
Keyword(s):  
Nash Equilibrium ◽  
The State ◽  
The Other ◽  
Game Player ◽  
Person Game

Consider a three-person game that occurs in stages. The state of the game is given by the integral amounts of chips that the players have, say x=(x1, x2, x3) with M=x1+x2+x3 fixed. At a stage of the game, player i places ai chips in the pot, an integer between 1 and xi. (Player i is already eliminated from the game if xi=0.) The winner of the pot is then immediately chosen in such a way that player i wins the pot with probability proportional to the index wiai for i with xi>0. The idea is that if player i bets more, then he is more likely to win, but this is modified by weights that parameterize the players’ abilities.Each player is trying to maximize his probability of taking all the chips (i.e., reaching xi=M). In the two-person game, it is known that a Nash equilibrium is for each player to adopt strategy σ of playing timidly (ai=1) or boldly (ai=xi) according to whether the game is in his favor or not (assuming the other also plays σ). In this article, we investigate whether this also is the form of a Nash equilibrium in a three-person game when the weights are of the form (w1, w2, w3)=(w, w, 1−2w) with 0<w<1/2. It turns out that this is true if w<1/3, but not true if w>1/3 and M≥8.

A Necessary and Sufficient Condition for Partial Monotonicity of Noncooperative Games

2020 ◽  
pp. 2050006
Author(s):  
Naoki Matsumoto
Keyword(s):  
Nash Equilibrium ◽  
Pure Strategy ◽  
Noncooperative Games ◽  
Noncooperative Game ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Partial Monotonicity ◽  
Person Game ◽  
Necessary And Sufficient ◽  
Strategy Nash Equilibrium

It is a classical and interesting problem to find a Nash equilibrium of noncooperative games in the strategic form. It is well known that the game always has a mixed-strategy Nash equilibrium, but it does not necessarily have a pure-strategy Nash equilibrium. Takeshita and Kawasaki proved that every noncooperative partially monotone game has a pure-strategy Nash equilibrium, that is, the partial monotonicity is a sufficient condition for a noncooperative game to have a pure-strategy Nash equilibrium. In this paper, we prove the necessary and sufficient condition for a noncooperative [Formula: see text]-person game with [Formula: see text] to be partially monotone. This result is an improvement of Takeshita and Kawasaki’s result.

Smallpox, Risks of Terrorist Attacks, and the Nash Equilibrium: An Introduction to Game Theory and an Examination of the Smallpox Vaccination Program

2009 ◽  
Vol 24 (3) ◽  
pp. 231-238 ◽  
Author(s):  
Richard Hamilton ◽  
Roger McCain
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Emergency Preparedness ◽  
Healthcare Workers ◽  
Terrorist Attack ◽  
Vaccination Program ◽  
Smallpox Vaccination ◽  
Specific Information ◽  
The Status ◽  
Person Game

AbstractIntroduction:The smallpox vaccination emergency preparedness program has been unsuccessful in enrolling sufficient numbers of healthcare workers.Objective:The objective of this study was to use game theory to analyze a pre-event vaccination versus post-event vaccination program using the example of a terrorist considering an attack with smallpox or a hoax.Methods:A three-person game (normal and extensive form), and an in-person game are played for pre-event and post-event vaccinations of healthcare workers facing the possibility of a smallpox attack or hoax.Results:Full pre-event vaccinations of all targeted healthcare workers are not necessary to deter a terrorist attack. In addition, coordinating vaccinations among healthcare workers, individual healthcare worker risk aversion, and the degree to which terrorists make the last move based on specific information on the status of pre-event vaccination all greatly impact strategy selection for both sides. A Nash Equilibrium of pre- and post-event vaccination strategies among a large number of healthcare professionals will tend to eliminate the advantage (of the terrorists) of a smallpox attack over a hoax, but may not eliminate some probability of a smallpox attack.Conclusions:Emergency preparedness would benefit from game theory analysis of the costs and payoffs of specific terrorism/counter-terrorism strategies.

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