scholarly journals The effect of network topology on optimal exploration strategies and the evolution of cooperation in a mobile population

2019 ◽  
Vol 475 (2230) ◽  
pp. 20190399 ◽  
Author(s):  
Igor V. Erovenko ◽  
Johann Bauer ◽  
Mark Broom ◽  
Karan Pattni ◽  
Jan Rychtář
Keyword(s):  
Network Topology ◽  
Complete Graph ◽  
Evolution Of Cooperation ◽  
Underlying Structure ◽  
Star Graph ◽  
Movement Model ◽  
Arbitrary Group ◽  
Public Goods Games ◽  
Current Location ◽  
Mobile Population

We model a mobile population interacting over an underlying spatial structure using a Markov movement model. Interactions take the form of public goods games, and can feature an arbitrary group size. Individuals choose strategically to remain at their current location or to move to a neighbouring location, depending upon their exploration strategy and the current composition of their group. This builds upon previous work where the underlying structure was a complete graph (i.e. there was effectively no structure). Here, we consider alternative network structures and a wider variety of, mainly larger, populations. Previously, we had found when cooperation could evolve, depending upon the values of a range of population parameters. In our current work, we see that the complete graph considered before promotes stability, with populations of cooperators or defectors being relatively hard to replace. By contrast, the star graph promotes instability, and often neither type of population can resist replacement. We discuss potential reasons for this in terms of network topology.

scholarly journals On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

Group preferential selection promotes cooperation in spatial public goods game

2014 ◽  
Vol 25 (11) ◽  
pp. 1450062 ◽  
Author(s):  
Hong-Bin Zhang ◽  
Hong Wang
Keyword(s):  
Public Goods ◽  
Role Model ◽  
Evolution Of Cooperation ◽  
Square Lattice ◽  
Public Goods Game ◽  
Learning Mechanism ◽  
Preferential Selection ◽  
Cooperative Evolution ◽  
Public Goods Games

We study the evolution of cooperation in public goods games on the square lattice, focusing on the co-player learning mechanism based on the preferential selection that are brought about by wealthy information of groups where participants collect and search for potential imitators from those groups. We find that co-player learning mechanism based on the choice of weighted group can lead to the promotion of public cooperation by means of the information of wealthy groups that is obtained by participants, and after that the partial choice of public goods groups is enhanced with the tunable preferential parameter. Our results highlight that the learning interactions is not solely confined to the restricted connection among players, but co-players of wealthy groups have the opportunity to be as a role model in the promotion of cooperative evolution. Moreover, we also find the size of learning affects the choice of distant players, cooperators (defectors) having more paths to exploit the phalanx of opponents to survive when the value of preferential parameter is small. Besides, the extinction thresholds of cooperators and defectors for different values of noise are also investigated.

scholarly journals Conditional strategies and the evolution of cooperation in spatial public goods games

2012 ◽  
Vol 85 (2) ◽  
Author(s):  
Attila Szolnoki ◽  
Matjaž Perc
Keyword(s):  
Public Goods ◽  
Evolution Of Cooperation ◽  
Public Goods Games

Diversity of game strategies promotes the evolution of cooperation in public goods games

2010 ◽  
Vol 90 (6) ◽  
pp. 68005 ◽  
Author(s):  
Chunyan Zhang ◽  
Jianlei Zhang ◽  
Guangming Xie ◽  
Long Wang
Keyword(s):  
Public Goods ◽  
Evolution Of Cooperation ◽  
Public Goods Games

scholarly journals Effects of Relatedness on the Evolution of Cooperation in Nonlinear Public Goods Games

2018 ◽  
Author(s):  
Kira Coder Gylling ◽  
Åke Brännström
Keyword(s):  
Evolutionary Game ◽  
Evolution Of Cooperation ◽  
Evolutionary Diversification ◽  
Public Goods Games ◽  
Interaction Partners ◽  
Different Types ◽  
Comprehensive Picture ◽  
Pure Strategies ◽  
Benefits And Costs ◽  
Made In

Evolution of cooperation has traditionally been studied by assuming that individuals adopt either of two pure strategies, to cooperate or defect. Recent work have considered continuous cooperative investments, turning full cooperation and full defection into two opposing ends of a spectrum and sometimes allowing for the emergence of the traditionally-studied pure strategies through evolutionary diversification. These studies have typically assumed a well-mixed population in which individuals are encountered with equal probability, Here, we allow for the possibility of assortative interactions by assuming that, with specified probabilities, an individual interacts with one or more other individuals of the same strategy. A closely related assumption has previously been made in evolutionary game theory and has been interpreted in terms of relatedness. We systematically study the effect of relatedness and find, among other conclusions, that the scope for evolutionary branching is reduced by either higher average degree of, or higher uncertainty in, relatedness with interaction partners. We also determine how different types of non-linear dependencies of benefits and costs constrain the types of evolutionary outcomes that can occur. While our results overall corroborate the conclusions of earlier studies, that higher relatedness promotes the evolution of cooperation, our investigation gives a comprehensive picture of how relatedness affects the evolution of cooperation with continuous investments.

THE PERMUTATIONAL GRAPH: A NEW NETWORK TOPOLOGY

1998 ◽  
Vol 09 (01) ◽  
pp. 3-11
Author(s):  
SATOSHI OKAWA
Keyword(s):  
Network Topology ◽  
Equivalence Classes ◽  
Star Graph ◽  
Complete Graphs ◽  
Graph Topology ◽  
Star Graphs ◽  
Network Topologies ◽  
Graph Families ◽  
The Relationship ◽  
Better Than

This paper introduces the penmutational graph, a new network topology, which preserves the same desirable properties as those of a star graph topology. A permutational graph can be decomposed into subgraphs induced by node sets defined by equivalence classes. Using this decomposition, its structual properties as well as the relationship among graph families, permutational graphs, star graphs, and complete graphs are studied. Moreover, the diameters of permutational graphs are investigated and good estimates are obtained which are better than those of some network topologies of similar orders.

b-Chromatic sum of a graph

2015 ◽  
Vol 07 (04) ◽  
pp. 1550040 ◽  
Author(s):  
P. C. Lisna ◽  
M. S. Sunitha
Keyword(s):  
Bipartite Graph ◽  
Chromatic Number ◽  
Complete Graph ◽  
Complete Bipartite Graph ◽  
Double Star ◽  
Star Graph ◽  
Proper Coloring ◽  
Color Class ◽  
Wheel Graph ◽  
Chromatic Sum

A b-coloring of a graph G is a proper coloring of the vertices of G such that there exists a vertex in each color class joined to at least one vertex in each other color classes. The b-chromatic number of a graph G, denoted by [Formula: see text], is the maximum integer [Formula: see text] such that G admits a b-coloring with [Formula: see text] colors. In this paper we introduce a new concept, the b-chromatic sum of a graph [Formula: see text], denoted by [Formula: see text] and is defined as the minimum of sum of colors [Formula: see text] of [Formula: see text] for all [Formula: see text] in a b-coloring of [Formula: see text] using [Formula: see text] colors. Also obtained the b-chromatic sum of paths, cycles, wheel graph, complete graph, star graph, double star graph, complete bipartite graph, corona of paths and corona of cycles.

scholarly journals Un método algoritmo para el cálculo del número baricéntrico de Ramsey para el grafo estrella

2018 ◽  
Vol 36 (2) ◽  
pp. 169-183
Author(s):  
Felicia Villarroel ◽  
J. Figueroa ◽  
H. Márquez ◽  
A. Anselmi
Keyword(s):  
Finite Group ◽  
Positive Integer ◽  
Complete Graph ◽  
Ramsey Number ◽  
Combinatorial Theory ◽  
Star Graph ◽  
Definition Of

Let G be an abelian finite group and H be a graph. A sequence in G, with length al least two, is barycentric if it contains an ”average” element of its terms. Within the context of these sequences, one defines the barycentric Ramsey number, denoted by BR(H, G), as the smallest positive integer t such that any coloration of the edges of the complete graph Kt with elements of G produces a barycentric copy of the graph H. In this work we present a method based on the combinatorial theory and on the definition of barycentric Ramsey for calculating exact values of the above metioned constant, for some small graphs where the order is less than or equal to 8. We will exemplify the case where H is the star graph K1,k, and where G is the cyclical group Zn, with 3 ≤ n ≤ 11 and 3 ≤ k ≤ n.

scholarly journals Benefits of asynchronous exclusion for the evolution of cooperation in stochastic evolutionary optional public goods games

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Ji Quan ◽  
Junjun Zheng ◽  
Xianjia Wang ◽  
Xiukang Yang
Keyword(s):  
Public Goods ◽  
Evolution Of Cooperation ◽  
Public Goods Games
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