=Paper=
{{Paper
|id=Vol-3304/paper17
|storemode=property
|title=Benefits Analysis of Chinese Cities on Urban Networks Based on Evolutionary Games
|pdfUrl=https://ceur-ws.org/Vol-3304/paper17.pdf
|volume=Vol-3304
|authors=Xiaoyang Wang,Lilan Tu,Yichao Wang
}}
==Benefits Analysis of Chinese Cities on Urban Networks Based on Evolutionary Games==
https://ceur-ws.org/Vol-3304/paper17.pdf
Benefits Analysis of Chinese Cities on Urban Networks
Based on Evolutionary Games
Xiaoyang Wang1,2, Lilan Tu1,2, Yichao Wang1,2
1
Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and
Technology, Wuhan 430065, China
2
College of Science, Wuhan University of Science and Technology, Wuhan 430065, China
Abstract
This paper investigates inter-city cooperation and city benefits based on complex network
theory and evolutionary game theory. The games are played on urban networks. First of all, a
game payoff matrix with penalty is constructed. Then, according to complex networks theory,
using the first, second and third tier cities in China, we construct a BA scale-free network as
the initial network. At the end of a round of the games, each city disconnects from
uncooperative cities, then randomly selects neighbors of uncooperative cities to connect. And
each city chooses a neighbor's strategy as the strategy in the next round with a certain
probability. Repeating the game for 20 rounds, we come to the following conclusions. (1) The
higher the ranking of cities, the greater the payoffs. The increase of game rounds increases the
benefits of second-tier and third-tier cities;(2) After 20 rounds of games, the benefits, strategies
and urban networks tend to be stable. The benefits are closely related to the urban networks,
but not to the stability strategies of the cities.
Keywords 1
Evolutionary game, urban networks, the frequency of cooperation, benefits, average degree
1. Introduction
Since 1970s, due to the adjustment of economic structure and the world competition, the competition
of cities for limited growth and financial potential has become increasingly fierce. Traditional
mandatory coordination imposed by the state and coordination through market exchange are no longer
effective ways to solve these problems [1]. Inter-city cooperation is a new policy choice to overcome
the negative impact of urban competition [2]. With the deepening of globalization, marketization and
decentralization, Chinese cities have also experienced structural adjustment. In recent years, the
Chinese government has attached great importance to urban cooperation and regional cooperation, such
as the Beijing-Tianjin-Hebei City-region, the Yangtze river delta region and the Guangdong-Hong
Kong-Macau Greater Bay Area. Scholars used different regions to study the cooperation between cities
[3-5]. Most references study the cooperation in some specific regions, but there are few studies on the
cooperation between cities across regions or between all cities in China.
With the rise of research on complex networks, some scholars have analyzed the real world by
establishing urban networks [6-9]. Urban networks are the application of network theory to answer
theoretical and empirical questions arising from urban research [10]. Camagni [11] and Capello [12]
extended the concept of "network externality " [11] originally put forward in economics to "urban
network externality". Network externality refers to the fact that cities can increase marginal benefits in
complementary relationships and gain additional benefits from cooperation in urban networks [13].
Therefore, the use of city networks allows for a better analysis of the benefits between cities.
ICBASE2022@3rd International Conference on Big Data & Artificial Intelligence & Software Engineering, October 21-
23, 2022, Guangzhou, China
EMAIL: wxy3014@wust.edu.cn (Xiaoyang Wang); tulilan@wust.edu.cn (Lilan Tu); wangyc@wust.edu.cn (Yichao Wang)
ORCID: 0000-0003-4341-2518 (Xiaoyang Wang); 0000-0001-5768-7104 (Lilan Tu); 0000-0003-2247-0516 (Yichao Wang)
© 2022 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
139
Based on the above analysis, a game model with penalty will be proposed in this paper. Then, a BA
scale-free urban network will be constructed. The games will be played on the urban networks. After a
round of game, the strategies of each city and urban networks will be updated. The benefits and
cooperation behavior of cities and the evolution law of urban networks will be discussed.
2. Model
In the evolutionary game model, the players are the governments of first, second and third tier cities.
In this paper, we assume that the players are all finite rational. The games are played on the networks,
in which the nodes represent the cities, and the edges represent the game relationship between the cities.
If there is a edge between two cities, the two cities play the game once and calculate the benefit P
according to the payoff matrix in Table 1.
Table 1
The payoff matrix
City 2
cooperation uncooperation
cooperation R + 0.5R′ − C ( d ) R − C (d ) + N −V
City 1
uncooperation R − N +V R
In Table 1, R is the payoff from the games played by city 1 and city 2, and R′ is all the excess
benefit from the cooperation between the two cities. This benefit is equally distributed to both cities.
C is the cost of cooperation generated by the cooperation. The cost of cooperation C is related to the
distance d between the two cities. The greater the distance, the higher the cooperation cost C . V is the
opportunity payoff obtained for the uncooperative city. And N is the default penalty for the
uncooperative city. The penalty is directly compensated to the cooperative city.
If there are connected edges between city i and other ni cities, then city i plays ni games
ni
simultaneously. Sum the payoffs from ni games to get the total benefit Pi = pk for city i in that
k =1
round. By analogy, the total benefit of each city in each round of the game can be obtained. At the end
of a round, the city i disconnects from the uncooperative cities and randomly chooses one of the
betrayer's neighbors to connect to. In the next round of the game, city i picks its neighbor j 's strategy
with probability wi ← j = 1 / 1 + exp ( Pi − Pj ) as its own strategy. The city i chooses a neighbor of the
same tier as its own with probability 0.8 as its imitation neighbors, or a neighbor of a different tier than
its own with probability 0.2.
Figure 1: Initial urban network
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3. simulation
3.1. Construction of initial urban network
Suppose the urban networks are scale-free networks. In scale-free networks, a few nodes have a
large number of connections, while most nodes have few connections. This is in line with the real
situation of urban commercial distribution in China. According to the "2022 City Business
Attractiveness Ranking List", we classifies first-tier cities and new first-tier cities into first-tier cities,
and uses second-tier cities and third-tier cities as the nodes of the urban networks. And we takes the
latitude and longitude of cities as coordinates to generate a scale-free network (see Figure 1) as the
initial urban network. In Figure 1, the orange, green and blue dots (nodes) represent that the city is the
first, second and third tier cities, respectively. The higher the tier of the city, the more connected edges
and the larger the dots. It can be seen from Figure 1 that the locations of the first-tier cities and the third-
tier cities are relatively uniform, and most of the second- tier cities are located on the edge of China.
3.2. Evolutionary game experiments
Since the cost of cooperation is related to the distance between cities, the distance between cities is
calculated based on the latitude and longitude of each city. And it is divided into three categories,
d ≤ 500 , 500 < d ≤ 1000 and d ≥ 1000 , corresponding to the costs C1 , C 2 and C3 in that order. Let
R=2 , R ′=1 , C1 = 0 , C 2 = 0.5 , C 3 = 1 , V = 1 and N =0.5 . Assume that each city chooses to cooperate
with a probability of 0.5 in the first round of the game and plays 20 rounds of the game. The evolutionary
game is repeated four times in this paper to prevent accidental results. In this section, red, blue, green
and purple are used to represent the four evolutionary games in turn.
The benefits for the 119 cities obtained from the four experiments are depicted in Figure 2. The
horizontal coordinates are the 119 cities, and the vertical coordinates from top to bottom shows the 1st
to 20th rounds of games. The number on the horizontal coordinates is the tiers corresponding to the 119
cities. The darker the color, the greater the benefit of the city. By observing Figure 2, it can be found
that the higher the rank of the city, the greater the benefit. In the previous rounds of the game, the first-
tier cities have darker colors and larger benefit, while almost all of the second-tier and third-tier cities
have lighter colors and smaller gains. With the increase of game rounds, the color of some second-tier
and third-tier cities is obviously deepened, and their benefits are obviously increased. This indicates
that the evolutionary game set in this paper can increase the gain of secondary and tertiary cities. And
Figure 2 shows that the color of the four experiments gradually lightens, indicating that the cities
benefits of these four experiments are smaller.
Figure 2: Benefits of 119 cities in 4 experiments
The strategies of the 119 cities in the 4 experiments are depicted in Figure 3. Red, blue, green and
purple represent that the strategies of the cities in the 4 experiments are cooperation, and black
represents the strategies are uncooperation, respectively. The numbers in the horizontal coordinates are
the corresponding tiers of the 119 cities. Figure 3 shows that there are some cities whose strategies are
always cooperation or uncooperation in the four experiments. After 20 rounds of the games, the
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strategies of 119 cities did not change and reached a stable state. In this case, there are 9, 11, 5, and 10
cities’ strategies is uncooperation.
Table 2 lists the number of first-, second- and third-tier cities with uncooperative stability strategy
in the four experiments. The results in Figure 2 show that the city benefits of the four experiments are
becoming smaller. But Table 2 illustrates that the number of cities with uncooperative stability strategy
has not remarkablely increased or decreased. This indicates that the correlation between city benefits
and the number and tier of cities with uncooperative stabilization strategies is not significant.
Figure 3: Strategies of 119 cities in 4 experiments
Table 2
The number of cities with uncooperative stability strategy
The number of The number of The number of
Experiments
first-tier cities second-tier cities third-tier cities
1 0 2 7
2 0 0 5
3 0 0 11
4 1 1 8
Figure 4: Degree of Urban Network in 4 Experiments
As in Figure 2, Figure 4 depicts the degree of the urban networks in 4 experiments. The darker color
indicates the greater degree of that node (city) in that game round, that is, the more cities play with this
city. In the previous rounds of games, the color of the first-tier city is darker, while almost all the second-
tier and third-tier cities are lighter. As the number of game rounds increased, the colors of some second-
tier and third-tier cities has obviously deepened. The evolution results show that the increase of the
number of game rounds can make some second-tier and third-tier cities play with many cities in one
game round, thus increasing the benefits of second-tier and third-tier cities. It also shows that the colors
of the four experiments gradually become lighter, which indicates that the degree of the urban networks
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is gradually becoming smaller in these four experiments. This is the same as the results shown in Figure
2. It indicates that there is a correlation between the city benefit and the degree of the urban network.
4. Conclusion
Since the 1970s, inter-city cooperation has emerged as a policy to overcome the negative effects of
urban competition. In this paper, inter-city cooperation and benefits are studied based on complex
network theory and evolutionary game theory. First, this paper constructs a payoff matrix with penalty.
Second, a BA scale-free network is built using first-, second-, and third-tier cities in China. The games
are played on the networks, where the nodes represent cities and the connected edges represent the
game relationships between cities. At the end of a game round, each city disconnects from the betrayer
and randomly chooses a neighbor of the betrayer to connect. And the city chooses one of its neighbors'
strategy with certain probability as its own strategy in the next game round. Repeating this for 20 rounds,
we find that (1) the higher the rank of the city, the greater the benefits. The increase in the number of
game rounds increases the benefits of secondary and tertiary cities; (2) some cities' strategies are always
cooperation and some cities' strategies are always uncooperation. (3) As the number of rounds of the
game increases, the number of cities playing with secondary and tertiary cities also increases; (4) After
20 rounds of the game, the benefits, strategies, and urban networks of cities stabilize. The benefits of
cities is strongly related to the urban network, and not much related to the stable strategy of cities.
5. Acknowledgements
The authors acknowledge the interesting comments of anonymous referees. This work is supported
by the National Natural Science Foundation of China under Grant 72031009, 61473338, and Hubei
Province Key Laboratory of Systems Science in Metallurgical Process (Wuhan University of Science
and Technology under Grant Z201902)
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