Pure-Strategy ε-Nash Equilibrium inn-Person Nonzero-Sum Discontinuous Games

1997 ◽  
Vol 20 (2) ◽  
pp. 238-249 ◽  
Author(s):  
Abderrahmane Ziad
Keyword(s):  
Nash Equilibrium ◽  
Pure Strategy ◽  
Discontinuous Games

Quasi-Transfer Continuity and Nash Equilibrium

2019 ◽  
Vol 21 (04) ◽  
pp. 1950004
Author(s):  
Rabia Nessah ◽  
Tarik Tazdait
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Existence Result ◽  
Mixed Strategy ◽  
Existence Theorems ◽  
Pure Strategy ◽  
Econ Theory ◽  
Discontinuous Games ◽  
Normal Form Games ◽  
Existence Of Equilibria

We introduce a new notion of continuity, called quasi-transfer continuity, and show that it is enough to guarantee the existence of Nash equilibria in compact, quasiconcave normal form games. This holds true in a large class of discontinuous games. We show that our result strictly generalizes the pure strategy existence theorem of Carmona [Carmona, G. [2009] An existence result for discontinuous games, J. Econ. Theory 144, 1333–1340]. We also show that our result is neither implied by nor does it imply the existence theorems of Reny [Reny, J. P. [1999] On the existence of pure and mixed strategy Nash equilibria in discontinuous games, Econometrica 67, 1029–1056] and Baye et al. [Baye, M. R., Tian, G. and Zhou, J. [1993] Characterizations of the existence of equilibria in games with discontinuous and nonquasiconcave payoffs, Rev. Econ. Studies 60, 935–948].

ON COURNOT COMPETITION UNDER RANDOM YIELD

2013 ◽  
Vol 30 (04) ◽  
pp. 1350007 ◽  
Author(s):  
XIAOMING YAN ◽  
YONG WANG
Keyword(s):  
Nash Equilibrium ◽  
Production Cost ◽  
Pure Strategy ◽  
Cournot Competition ◽  
Random Yield ◽  
Cournot Model ◽  
Random Capacity ◽  
Strategy Nash Equilibrium

We look at a Cournot model in which each firm may be unreliable with random capacity, so the total quantity brought into market is uncertain. The Cournot model has a unique pure strategy Nash equilibrium (NE), in which the number of active firms is determined by each firm's production cost and reliability. Our results indicate the following effects of unreliability: the number of active firms in the NE is more than that each firm is completely reliable and the expected total quantity brought into market is less than that each firm is completely reliable. Whether a given firm joins in the game is independent of its reliability, but any given firm always hopes that the less-expensive firms' capacities are random and stochastically smaller.

EQUILIBRIUM BALKING STRATEGIES IN THE REPAIRABLE M/M/1 G-RETRIAL QUEUE WITH COMPLETE REMOVALS

2019 ◽  
pp. 1-20
Author(s):  
Shan Gao ◽  
Deran Zhang ◽  
Hua Dong ◽  
Xianchao Wang
Keyword(s):  
Nash Equilibrium ◽  
Queueing Theory ◽  
Fundamental Problem ◽  
Pure Strategy ◽  
Retrial Queue ◽  
Noncooperative Game ◽  
Net Benefit ◽  
Negative Customers ◽  
Stable Strategy ◽  
Best Response

We consider an M/M/1 retrial queue subject to negative customers (called as G-retrial queue). The arrival of a negative customer forces all positive customers to leave the system and causes the server to fail. At a failure instant, the server is sent to be repaired immediately. Based on a natural reward-cost structure, all arriving positive customers decide whether to join the orbit or balk when they find the server is busy. All positive customers are selfish and want to maximize their own net benefit. Therefore, this system can be modeled as a symmetric noncooperative game among positive customers and the fundamental problem is to identify the Nash equilibrium balking strategy, which is a stable strategy in the sense that if all positive customers agree to follow it no one can benefit by deviating from it, that is, it is a strategy that is the best response against itself. In this paper, by using queueing theory and game theory, the Nash equilibrium mixed strategy in unobservable case and the Nash equilibrium pure strategy in observable case are considered. We also present some numerical examples to demonstrate the effect of the information together with some parameters on the equilibrium behaviors.

Nash equilibrium in discontinuous games

2015 ◽  
Vol 61 (3) ◽  
pp. 553-569 ◽  
Author(s):  
Philip J. Reny
Keyword(s):  
Nash Equilibrium ◽  
Discontinuous Games
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