scholarly journals The Evolution of Price Competition Game on Complex Networks

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Feng Jie Xie ◽  
Jing Shi
Keyword(s):  
Complex Networks ◽  
Real World ◽  
Price Competition ◽  
Small World ◽  
Square Lattice ◽  
Small World Network ◽  
Scale Free Network ◽  
The Real ◽  
Scale Free ◽  
Free Network

The well-known “Bertrand paradox” describes a price competition game in which two competing firms reach an outcome where both charge a price equal to the marginal cost. The fact that the Bertrand paradox often goes against empirical evidences has intrigued many researchers. In this work, we study the game from a new theoretical perspective—an evolutionary game on complex networks. Three classic network models, square lattice, WS small-world network, and BA scale-free network, are used to describe the competitive relations among the firms which are bounded rational. The analysis result shows that full price keeping is one of the evolutionary equilibriums in a well-mixed interaction situation. Detailed experiment results indicate that the price-keeping phenomenon emerges in a square lattice, small-world network and scale-free network much more frequently than in a complete network which represents the well-mixed interaction situation. While the square lattice has little advantage in achieving full price keeping, the small-world network and the scale-free network exhibit a stronger capability in full price keeping than the complete network. This means that a complex competitive relation is a crucial factor for maintaining the price in the real world. Moreover, competition scale, original price, degree of cutting price, and demand sensitivity to price show a significant influence on price evolution on a complex network. The payoff scheme, which describes how each firm’s payoff is calculated in each round game, only influences the price evolution on the scale-free network. These results provide new and important insights for understanding price competition in the real world.

scholarly journals Eigenvalue-based entropy in directed complex networks

PLoS ONE ◽  
2021 ◽  
Vol 16 (6) ◽  
pp. e0251993
Author(s):  
Yan Sun ◽  
Haixing Zhao ◽  
Jing Liang ◽  
Xiujuan Ma
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Network Models ◽  
Small World ◽  
Laplacian Matrix ◽  
Directed Network ◽  
Small World Network ◽  
Scale Free Network ◽  
Scale Free ◽  
Free Network

Entropy is an important index for describing the structure, function, and evolution of network. The existing research on entropy is primarily applied to undirected networks. Compared with an undirected network, a directed network involves a special asymmetric transfer. The research on the entropy of directed networks is very significant to effectively quantify the structural information of the whole network. Typical complex network models include nearest-neighbour coupling network, small-world network, scale-free network, and random network. These network models are abstracted as undirected graphs without considering the direction of node connection. For complex networks, modeling through the direction of network nodes is extremely challenging. In this paper, based on these typical models of complex network, a directed network model considering node connection in-direction is proposed, and the eigenvalue entropies of three matrices in the directed network is defined and studied, where the three matrices are adjacency matrix, in-degree Laplacian matrix and in-degree signless Laplacian matrix. The eigenvalue-based entropies of three matrices are calculated in directed nearest-neighbor coupling, directed small world, directed scale-free and directed random networks. Through the simulation experiment on the real directed network, the result shows that the eigenvalue entropy of the real directed network is between the eigenvalue entropy of directed scale-free network and directed small-world network.

TIME-DELAY ROBUSTNESS OF CONSENSUS PROBLEMS IN REGULAR AND COMPLEX NETWORKS

2007 ◽  
Vol 18 (08) ◽  
pp. 1339-1350 ◽  
Author(s):  
ZHENGPING WU ◽  
ZHI-HONG GUAN
Keyword(s):  
Time Delay ◽  
Complex Networks ◽  
Nearest Neighbor ◽  
Small World ◽  
Node Degree ◽  
Small World Network ◽  
Scale Free Network ◽  
Star Network ◽  
Scale Free ◽  
Free Network

Recent advances in complex network research have stimulated increasing interests in understanding the relationship between the topology and dynamics of complex networks. Based on the theory of complex networks and computer simulation, we analyze the robustness to time-delay in linear consensus problem with different network topologies, such as global coupled network, star network, nearest-neighbor coupled network, small-world network, and scale-free network. It is found that global coupled network, star network, and scale-free network are vulnerable to time-delay, while nearest-neighbor coupled network and small-world network are robust to time-delay. And it is found that the maximum node degree of the network is a good predictor for time-delay robustness. And it is found that the robustness to time-delay can be improved significantly by a decoupling process to a small part of edges in scale-free network.

RISK ASSESSMENT OF ATTACK-INDUCED CASCADE IN COMPLEX NETWORKS

2011 ◽  
Vol 22 (08) ◽  
pp. 765-773
Author(s):  
ZHE-JING BAO ◽  
WEN-JUN YAN ◽  
CHUANG-XIN GUO
Keyword(s):  
Risk Assessment ◽  
Complex Networks ◽  
Quantitative Evaluation ◽  
Small World ◽  
Random Networks ◽  
Small World Network ◽  
Scale Free Network ◽  
Scale Free ◽  
Probability Of Occurrence ◽  
Free Network

For the complex networks, including scale-free, small-world, local-world and random networks, the global quantitative evaluation of attack-induced cascade is investigated in this paper by introducing the risk assessment, which integrates the probability of occurrence with the damage size of attacks on nodes. It is discovered by simulations, among the several kinds of networks, that the small-world network has the largest risk assessment of attack-induced cascade; the risk assessment of three other networks are all very low and the most protection against attack should be given to the small-world network accordingly. Furthermore, the percentage of the most fragile nodes in the scale-free network is very low, compared with that in the small-world network.

Complex networks

2018 ◽  
Author(s):  
Graziano Vernizzi ◽  
Henri Orland
Keyword(s):  
Complex Networks ◽  
Small World ◽  
Laplacian Matrix ◽  
Square Lattice ◽  
Small World Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
Free Network ◽  
Scale Free Graphs ◽  
Regular Networks

This article deals with complex networks, and in particular small world and scale free networks. Various networks exhibit the small world phenomenon, including social networks and gene expression networks. The local ordering property of small world networks is typically associated with regular networks such as a 2D square lattice. The small world phenomenon can be observed in most scale free networks, but few small world networks are scale free. The article first provides a brief background on small world networks and two models of scale free graphs before describing the replica method and how it can be applied to calculate the spectral densities of the adjacency matrix and Laplacian matrix of a scale free network. It then shows how the effective medium approximation can be used to treat networks with finite mean degree and concludes with a discussion of the local properties of random matrices associated with complex networks.

The epidemic network construction and immunization based on node strength

2018 ◽  
Vol 32 (26) ◽  
pp. 1850319 ◽  
Author(s):  
Fuzhong Nian ◽  
Longjing Wang ◽  
Zhongkai Dang
Keyword(s):  
Social Networks ◽  
Real World ◽  
Scale Free Network ◽  
Network Construction ◽  
The Real ◽  
Scale Free ◽  
Social Ability ◽  
The Social ◽  
Free Network

In this paper, a new spreading network was constructed and the corresponding immunizations were proposed. The social ability of individuals in the real human social networks was reflected by the node strength. The negativity and positivity degrees were also introduced. And the edge weights were calculated by the negativity and positivity degrees, respectively. Based on these concepts, a new asymmetric edge weights scale-free network which was more close to the real world was established. The comparing experiments indicate that the proposed immunization is priority to the acquaintance immunization, and close to the target immunization.

scholarly journals Evolution of Scale-Free Wireless Sensor Networks with Feature of Small-World Networks

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Ying Duan ◽  
Xiuwen Fu ◽  
Wenfeng Li ◽  
Yu Zhang ◽  
Giancarlo Fortino
Keyword(s):  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Small World ◽  
Wireless Sensor ◽  
Small World Network ◽  
Scale Free Network ◽  
Theoretical Derivation ◽  
Scale Free ◽  
Cluster Heads ◽  
Free Network

Scale-free network and small-world network are the most impacting discoveries in the complex networks theories and have already been successfully proved to be highly effective in improving topology structures of wireless sensor networks. However, currently both theories are not jointly applied to have further improvements in the generation of WSN topologies. Therefore, this paper proposes a cluster-structured evolution model of WSNs considering the characteristics of both networks. With introduction of energy sensitivity and maximum limitation of degrees that a cluster head could have, the performance of our model can be ensured. In order to give an overall assessment of lifting effects of shortcuts, four placement schemes of shortcuts are analyzed. The characteristics of small-world network and scale-free network of our model are proved via theoretical derivation and simulations. Besides, we find that, by introducing shortcuts into scale-free wireless sensor network, the performance of the network can be improved concerning energy-saving and invulnerability, and we discover that the schemes constructing shortcuts between cluster heads and the sink node have better promoted effects than the scheme building shortcuts between pairs of cluster heads, and the schemes based on the preferential principle are superior to the schemes based on the random principle.

scholarly journals SZNAJD MODEL WITH SYNCHRONOUS UPDATING ON COMPLEX NETWORKS

2005 ◽  
Vol 16 (07) ◽  
pp. 1149-1161 ◽  
Author(s):  
YU-SONG TU ◽  
A. O. SOUSA ◽  
LING-JIANG KONG ◽  
MU-REN LIU
Keyword(s):  
Complex Networks ◽  
Small World ◽  
System Size ◽  
The State ◽  
Clustering Coefficient ◽  
Square Lattice ◽  
Node Degree ◽  
Scale Free ◽  
Free Network ◽  
Formation Step

We analyze the evolution of Sznajd Model with synchronous updating in several complex networks. Similar to the model on square lattice, we have found a transition between the state with nonconsensus and the state with complete consensus in several complex networks. Furthermore, by adjusting the network parameters, we find that a large clustering coefficient does not favor development of a consensus. In particular, in the limit of large system size with the initial concentration p =0.5 of opinion +1, a consensus seems to be never reached for the Watts–Strogatz small-world network, when we fix the connectivity k and the rewiring probability ps; nor for the scale-free network, when we fix the minimum node degree m and the triad formation step probability pt.

scholarly journals The evolving concept of air pollution: a small‐world network or scale‐free network?

2016 ◽  
Vol 17 (5) ◽  
pp. 308-314 ◽  
Author(s):  
Linan Sun ◽  
Zuhan Liu ◽  
Jiayao Wang ◽  
Lili Wang ◽  
Xuecai Bao ◽  
...  
Keyword(s):  
Air Pollution ◽  
Small World ◽  
Small World Network ◽  
Scale Free Network ◽  
Scale Free ◽  
Free Network
Sign in / Sign up

Export Citation Format

Share Document