An evolutionary mechanism of social preference for knowledge sharing in crowdsourcing communities

Abstract

Crowdsourcing community, as an important way for enterprises to obtain external public innovative knowledge in the era of the Internet and the rise of users, has a very broad application prospect and research value. However, the influence of social preference is seldom considered in the promotion of knowledge sharing in crowdsourcing communities. Therefore, on the basis of complex network evolutionary game theory and social preference theory, an evolutionary game model of knowledge sharing among crowdsourcing community users based on the characteristics of small world network structure is constructed. Through Matlab programming, the evolution and dynamic equilibrium of knowledge sharing among crowdsourcing community users on this network structure are simulated, and the experimental results without considering social preference and social preference are compared and analysed, and it is found that social preference can significantly promote the evolution of knowledge sharing in crowdsourcing communities. This research expands the research scope of the combination and application of complex network games and other disciplines, enriches the theoretical perspective of knowledge sharing research in crowdsourcing communities, and has a strong guiding significance for promoting knowledge sharing in crowdsourcing communities.

Keywords

Crowdsourcing community knowledge sharing social preference complex network

1. Introduction

Innovation is the first driving force for leading development and the strategic support for building a modern economic system. At present, China’s innovation mainly relies on its own research departments and laboratories to carry out “closed innovation”, which cannot meet the requirements of the “New Normal” of enterprise innovation under the current sharing economy. At the same time, consumers’ demand for products and services is characterised by travel alienation, which forces enterprises to constantly meet consumer demand through innovation. However, due to the limited internal innovation capabilities of enterprises, the crowdsourcing community innovation model that uses knowledge sharing as a bridge has gradually become an important way for enterprises to understand customers, generate creativity, and promote the optimisation of the enterprise innovation ecosystem. Currently, the scale of crowdsourcing community users is constantly expanding, promoting innovation and change in enterprises. However, there are also problems such as low willingness of community users to participate in knowledge sharing, low level of activity, and a lack of valuable knowledge and information. Therefore, crowdsourcing community managers must comprehensively understand the psychological characteristics of community users, grasp the motivations and behavioural patterns of users participating in knowledge sharing, in order to take effective measures to stimulate the enthusiasm of community members and effectively improve the level of knowledge sharing in crowdsourcing communities.

As a new type of open innovation organisation, crowdsourcing communities have broken through the original organisational boundaries of enterprises, and the innovation effects achieved have been confirmed. Therefore, many well-known domestic and foreign enterprises have established their own crowdsourcing communities to solve innovation problems and make up for their own lack of knowledge resources. Moreover, with the rapid development of information technologies such as big data, the Internet of Things, and artificial intelligence, the role and impact of crowdsourcing community knowledge sharing on enterprise innovation are constantly increasing. People’s participation in knowledge sharing activities in crowdsourcing communities often depends on psychological and situational factors. Therefore, conducting relevant research based on the motivation of community members to participate in knowledge sharing has become a hot topic of concern for scholars at home and abroad. Specifically, crowdsourcing community users’ participation in knowledge sharing is not only driven by material interests, but also often exhibits strong social preferences. Their participation in knowledge sharing is more influenced by reciprocal preferences, altruistic preferences, and fairness preferences. Social preference, as a willingness and attitude tendency, often occurs in group cooperation behaviour. Currently, few scholars have explored the impact of social preference on knowledge sharing behaviour in crowdsourcing communities. Therefore, based on the analysis of the network structure characteristics of knowledge sharing among crowdsourcing community users, combined with social preference theory and complex network game theory, this article deeply explores the psychological and behavioural patterns of crowdsourcing community users participating in knowledge sharing, and explores the evolutionary mechanism of community users participating in knowledge sharing. The specific research questions are as follows:

RQ1 How to construct an evolutionary game model for crowdsourcing community user knowledge sharing combining complex network evolutionary game theory and social preference theory?

RQ2 How can game revenue parameters and network structure parameters affect knowledge sharing in crowdsourcing communities?

RQ3 How can social preferences affect knowledge sharing in crowdsourcing communities?

The remainder part of this article is arranged as follows. Section 2 is a review of relevant literature in this area. Section 3 is the construction of an evolutionary game model for knowledge sharing in crowdsourcing communities, while Section 4 is an evolutionary game analysis of knowledge sharing in crowdsourcing communities based on the WS small world network, and the Section 5 is an evolutionary game analysis of knowledge sharing in crowdsourcing communities considering social preferences. Finally, Section 6 summarises the main contributions, research conclusions, and strategies to promote the knowledge contribution of crowdsourcing communities.

2. Literature review

Complex systems in nature, such as the Internet, power networks, and aviation networks, can be described in a variety of networks that are closely related to our lives. Different complex network fields have caused a lot of research upsurge. Nowak and May [1] has carried on the pioneering research to the prisoner’s dilemma game on the grid network dynamic evolution game, which becomes the beginning of evolutionary game research on spatial complex networks. Inspired by this research, scholars began to study the cooperative evolution of different game models on different network structures, particularly Watts and Strogatz introduced the Small World Network Model in 1998, Barabasi and Albert, following the introduction of scale-free network models in 1999, which makes the study of spatial evolution game has become a hot issue.

In 1992, Nowak and May first introduced the two-dimensional grid network structure into the Prisoner’s Dilemma Game Model. Along this pioneering research idea, coupled with the development of complex network science, scholars conducted in-depth discussions on evolutionary games on different network topologies, including regular networks. A large number of studies based on the Prisoner’s Dilemma Game Model generally believe that the network space structure is conducive to the emergence of cooperation, but Hauert and Doebeli [2] found that two-dimensional regular networks have a negative impact on the emergence of cooperation in the snowdrift game process. Even so, exploring the cooperative emergence mechanism on the grid network is still the focus of researchers. Szabó et al., [3] found that the Kagome regular lattice network with overlapping triangles is more conducive to promoting the emergence of cooperative behaviours. Based on the evolutionary game research on irregular networks, Abramson and Kuperman [4] first studied the prisoner’s dilemma game on small world networks, and found that the probability of disconnection is closely related to the evolutionary behaviour of the system. The snowdrift game on the small world network has also aroused the interest of scholars. The cooperative emergence behaviour on the small world network is discussed based on the morphing eagle pigeon game of snowdrift game. The research results show that the behaviour of game individuals is closely related to the topology characteristics, the benefit cost ratio, the strategies adopted and the rules of strategy updating. Tomassini et al. [5] discussed the cooperative emergence behaviour on the small world network based on the morphing eagle pigeon game of snowdrift game, the research results show that the behaviour of game individuals is closely related to the topology characteristics, the benefit cost ratio, the strategies adopted and the rules of strategy updating. The degree distribution of many complex networks in the real world is in the form of power law, and the influence of this scale-free network structure on the evolution of cooperative behaviour has aroused scholars’ attention. Santos et al. [6] found that network heterogeneity can promote cooperation in prisoner’s dilemma game, snowdrift game and deer hunting game compared with regular networks.

Different policy evolution rules for evolutionary games on the same network structure are likely to lead to different evolution results of the system. New policy update rules are constantly applied to the cooperative evolution of groups, thus promoting the process of evolutionary game research on complex networks. Nowak and May [1] first used the imitation of optimal rules to conduct a pioneering study of evolutionary games on the spatial network. Because imitation of optimal rules cannot accurately describe people’s irrational decision-making and strategy learning effects, Szabo and Toke [7] proposed Fermi rule, that is, game players update game strategies according to the difference between their neighbour’s earnings. Szabo et al. [3] further studied the influence of individual rationality level parameters in Fermi update rules on cooperative evolution. Szabo et al. [8] proposed the strategy updating rule of replication dynamics and the game players will imitate the game strategy of the better player with a specific probability according to the game income difference. Lieberman [9] proposed policy update rules based on Moran process. Considering the phenomenon of conformity in real life, Szolnokic and Perc [10] proposed policy update rules based on conformity drive.

People’s behaviour decisions are inevitably affected by internal or external factors. Therefore, scholars have conducted research on the influence of specific factors of the real social system on the evolution of group cooperation. Fehr and Simon [11] found that the altruistic punishment of defectors was the key motivation to explain cooperation through an experiment involving 240 students. Traditionally, people believe that punishment can promote public cooperation more than reward, but because the cost of punishment is difficult to be compensated from the increased benefits of cooperation, researchers pay more attention to the impact of reward on cooperation behaviour. Szolnoki and Perc [12] studied the impact of reward mechanism on cooperation evolution in the process of space public goods game. At present, the impact of punishment and reward mechanism on group cooperation behaviour is still a research hotspot. In addition, the impact of more specific mechanisms such as reputation, tolerance and income redistribution on the evolution of group cooperation has attracted the attention of researchers, and has formed a large number of achievements.

Coevolutionary game on complex networks is an important topic in evolutionary game research. In recent years, scholars have carried out a lot of research on cooperative behaviour in common evolutionary game from the aspects of network structure and game individual strategy, game individual attribute and individual strategy. Zimmermann and Eguiluz [13] studied the cooperative evolution of the prisoner’s dilemma game model on dynamic networks, In this study, the game individual adopts the strategy of imitating the best neighbour, and the results show that the ER stochastic network based on the probability of reconnection can show a very high level of cooperation. Santos and Pacheco [14] studied the evolution of group cooperation based on Fermi update rules. Szolnoki et al. [15] studied the effects of individual attributes – age on spatial prisoner’s game dilemma, in which it is found that the heterogeneity of age distribution is very important to explain the difference of cooperator density in spatial grid. Tian [16] guided by the theoretical framework of spatial evolution game research, proposing creditworthiness mechanism, non-uniform contribution mechanism and partner selection mechanism based on individual dynamic attributes, which enriches the cooperative evolution mechanism of spatial reciprocity, it is of great significance to deeply understand the mechanism of cooperative behaviour emergence.

Meanwhile, evolutionary game research on complex networks has gradually begun to focus on the preferences of game individuals, and become a hot issue of research. Wu, et al. [17] think that the preference of choosing influential neighbours can improve the level of cooperation in network systems, especially in small world networks. Xie et al . [18] introduced the subjective demand preference of game individuals in behavioural consistency and discussed the role of behavioural consistency demand in promoting group cooperative behaviour on grid network and small world network. In addition, More scholars begin to introduce the theory of finite rationality and social preference into the evolution of individual decision choice and group cooperation. Kulakowski and Gawron [19] found that active altruistic game players can promote cooperative behaviour. Tang [20] establishs reciprocal behaviour preference function under social preference and discusse the influence of reciprocal and altruistic behaviour on cooperative behaviour in detail. Liu [21] constructed a game model of customer fit evolution in different network topologies considering social preferences in the context of mobile Internet, it is found that social preference can promote the evolutionary equilibrium of customer fit in network community.

Crowdsourcing community is a technical platform and social organisation platform for effectively storing and exchanging knowledge and data [22]. Knowledge sharing in crowdsourcing community is an important way for enterprises to understand customers, to generate creativity and to promote enterprise innovation [23], Effective incentive design is crucial to playing the role of crowdsourcing model [24]. The continuous participation of community users is the key factor for the success and sustainable development of crowdsourcing communities [25] Crowdsourcing communities have the structure of small world networks [26] Therefore, it is of great practical significance to combine small world networks with evolutionary game theory to clarify how the network topology of crowdsourcing communities affects the emergence and evolution mechanism of knowledge sharing behaviour. In addition, people’s participation in crowdsourcing community knowledge sharing often depends on psychological and situational factors, and usually shows strong social preferences. Their participation in knowledge sharing is more influenced by reciprocal preferences, altruistic preferences and fair preferences. As a tendency of will and attitude, few scholars explore the influence of social preference on knowledge sharing behaviour of crowdsourcing community. Therefore, the simulation analysis of decision evolution and equilibrium of knowledge sharing participation behaviour of crowdsourcing community users based on social preference is helpful to understand the psychological and behavioural laws of community users participating in knowledge sharing.

In general, the research on evolutionary games on Complex Network has achieved fruitful results after more than 30 years of development, laying a good theoretical foundation and numerous methodological supports for subsequent research. However, due to the increasing complexity of individual attributes in the Internet Age, the individual characteristics of players must be considered. In order to explain the contributions of this paper more clearly, the research methods of this paper are compared with previous literature, as shown in Table 1.

Table 1
A brief summary table contrasting the existing methods

[height=0.5cm,width=5cm]MethodIssue	Issue 1	Issue 2	Issue 3
Method 1: Different game models are used to study the cooperation behaviour between users on Complex network from a single perspective such as network topology, game strategy rules and specific mechanisms	Relatively simple research design	The research method is relatively single and lacks empirical research on the effects of multiple factors	Not considering the social preferences of the gamer
Method 2: Study the combined effects of various factors such as network structure types, game evolution rules, game models, specific mechanisms, and individual attributes of games on group cooperative behaviour	Complex research design	Combining the effects of multiple factors for research	Not considering the social preferences of the gamer
Method 3 (This paper): Studying the influence of multiple factors on group cooperation under the consideration of social preference	More complex research design	Combining the effects of multiple factors for research	Consider the social preferences of game players

3. Construction of evolutionary game model of knowledge sharing in crowdsourcing community

3.1 Construction of WS (Watts and Strogatz) Small World Network Model

To some extent, WS small world networks can describe the characteristics of crowdsourcing community user groups. Construction algorithm as follows: (1) Starting from the ring nearest neighbour coupling network with N nodes, each of these nodes is connected to K/2 adjacent nodes, K is even, $N>>K>>\ln N>>1$ . (2) Reconnect each side of the network randomly qx a random reconnection probability, that is, one end of each side remains the same; the other end is connected to a node randomly selected; there is only one side between any two nodes; and each node can not be connected to itself. Based on this algorithm, each node produces qxNK/2 long-range edges associated with other nodes.

3.2 Evolutionary game model and strategy rules of knowledge sharing in crowdsourcing community

3.2.1 Premise hypothesis

The game individuals of knowledge sharing behaviour are users of crowdsourcing community. There is a continuous interaction and reciprocal relationship between them, continuous knowledge sharing and value creation, and contribute knowledge to the sustainable and healthy development of crowdsourcing community. But crowdsourcing community also has “hitchhiking” users, and therefore it is more suitable to describe it with snowdrift game model. Considering the feasibility of the study, the following hypothesis are made:

(i)
Users involved in knowledge sharing in crowdsourcing communities are limitedly rational. Because of the cognitive finiteness of the game individual in the crowdsourcing community, its knowledge sharing decision-making behaviour cannot be completely rational and hence finite rationality is the basis for the establishment and analysis of the evolutionary game model of knowledge sharing in the crowdsourcing community. This hypothesis is consistent with the social preference theory.
(ii)
There are two kinds of game strategies for knowledge sharing of users in crowdsourcing community, knowledge sharing and knowledge not shared. Knowledge sharing behaviour in crowdsourcing community includes participating in knowledge sharing and commenting on knowledge sharing by others, excluding simple browsing behaviour.
(iii)
The total revenues and the total cost of knowledge sharing can be measured.
(iv)
The evolutionary game of knowledge sharing of crowdsourcing community users can be carried out many times and game users constantly adjust their game strategies according to specific game rules until they reach equilibrium state.

3.2.2 The knowledge sharing game model of crowdsourcing community based on snowdrift game

When users in the crowdsourcing community share knowledge, the user strategy set includes knowledge sharing strategy C and knowledge not shared strategy D. If they are willing to share knowledge together, they need to pay a common knowledge sharing cost c and can obtain their own knowledge sharing revenue b. $b>c>0$ represents the situation of the revenue of both users when they adopt the knowledge sharing strategy is $b-c/2$ . If both users adopt the knowledge not shared strategy, The benefits of both are 0. If one party chooses not to share knowledge and the other party chooses to share knowledge, both parties will benefit. Therefore, the game model has two Nash equilibria, namely, strategy combination (knowledge sharing, knowledge sharing) and (knowledge not shared, knowledge not shared). Taking into account the uncertainty of the selection of the game opponents’ strategies and the convenience of the game evolution calculation on the complex network, we introduce the return parameter $r=c/(2b-c)$ when both parties cooperate, and obtain the equivalent simplified model of the snowdrift game return matrix, as shown in Table 2.

Table 2
Simplified revenue matrix of knowledge sharing based on snowdrift game

[height=0.5cm,width=1.7cm]ij	C	D
C	1, 1	$1-r$ , $1+r$
D	$1+r$ , $1-r$	0, 0

3.2.3 Benefit function of knowledge sharing game for crowdsourcing community users

According to simplified revenue matrix of knowledge sharing based on snowdrift game in Table 1, Ui stands for user revenue function:

$\displaystyle U_{i}=S_{i}\left({{\begin{array}[]{cc}1&{1-r}\\ {1+r}&0\\ \end{array}}}\right)S_{j}^{T}$ (1)

where $S_{i}$ denotes the game strategy vector of user $I$ ; $S_{j}^{T}$ denotes the transposition of the game strategy vector j by the adjacent user $j$ ; the knowledge sharing strategy $C$ takes [1, 0]; and the knowledge not shared strategy takes [0, 1], $\left({{\begin{array}[]{*{20}c}1&{1-r}\\ {1+r}&0\\ \end{array}}}\right)$ denotes the revenue matrix of knowledge sharing game, in which $0\leqslant r\leqslant 1$ .

Substitute the game revenue function into the evolutionary game based on the network structure of crowdsourcing community, we can get the total game revenue function $U_{i}(t)$ of the users $i$ involved in knowledge sharing in crowdsourcing community in the $t$ round:

$\displaystyle U_{i}\left(t\right)=\mathop{\sum}\limits_{j\in w_{i}}S_{i}\left(% t\right)?\left({{\begin{array}[]{*{20}c}1\hfill&{1-r}\hfill\\ {1+r}\hfill&0\hfill\\ \end{array}}}\right)S_{j}^{T}$ (2)

where $W_{i}$ denotes the set of game neighbour $j$ connected by users $i$ of crowdsourcing community, $S_{i}(t)$ the strategy vector of user $i$ in the $t$ round, and $S_{j}(t)$ the transpose of the game strategy vector of all users $j$ connected by the user $i$ in the $t$ round.

3.2.4 Adjustment rules of knowledge sharing evolutionary strategy

Considering the actual situation of crowdsourcing community users and the basic assumptions of evolutionary game theory, individuals often show limited rationality in making knowledge sharing decisions. It means that game individuals need to learn continuously in the game process to find better strategies, that is, evolutionary game equilibrium is the result of multiple strategy adjustments. Therefore, crowdsourcing community users based on finite rationality usually adopt specific game strategy rules in the process of knowledge sharing game, but because game strategy has strong robustness to external interference, even if the game opponent strategy changes. Finally, the strategy equilibrium can be achieved.

According to the psychological characteristics of knowledge sharing participation behaviour of crowdsourcing community users, considering the uncertainty of optimisation, imitation and decision-making behaviour in the process of knowledge sharing of community users, the replication dynamics rules based on imitating winners are used as game strategy adjustment rules for knowledge sharing participation behaviour of crowdsourcing community users. The replication dynamics rule based on the imitation winner is based on the size of the connectivity of the game neighbours in the network as the basis for the selection of imitation objects. Firstly, determine the degree ( $K_{j}$ ) all game neighbours of user $i$ , and then calculate the proportion of each game neighbour degree to the sum of all game neighbours connectivity, taking this proportion as the probability of imitating object selection. Finally, base probability $P_{i}$ ( $S_{i}\leftarrow S_{j}$ ) on the difference between user $i$ and user $j$ total revenue of $t$ round game mimics the winning game neighbour strategy as the user i strategy of the $t+1$ round game.

The selection probability of the imitation object

$\displaystyle P_{ij}=\frac{K_{j}}{\mathop{\sum}\nolimits_{j\in w_{i}}K_{j}}$ (3)

where $W_{i}$ denotes a collection of all neighbours in the crowdsourcing community that are directly connected to the user $i$ , $\sum_{j\in w_{i}}K_{j}$ denotes the sum of the degree of all neighbours directly connected to the user $i$ .

The probability of knowledge sharing game strategy imitation

$\displaystyle P_{i}\left({S_{i}\leftarrow S_{j}}\right)=\frac{U_{j}-U_{i}}{D% \cdot\max\left({K_{i},K_{j}}\right)}$ (4)

where $U_{i}$ and $U_{j}$ denote the game revenue of users $i$ and $j$ ; $D$ denotes the difference between the maximum and minimum revenue parameters in the revenue matrix; and $\max\left({K_{i},K_{j}}\right)$ denotes the larger degree of user $i$ and user $j$ . The meaning expressed by this formula is that when the user $i$ adjusts the game strategy of knowledge sharing, if the game revenue $U_{j}$ of the randomly selected connected user $j$ is greater than the game revenue $U_{i}$ of the user $i$ , the user $i$ replicates the probability value of the game strategy of the user $j$ during the next round of game. The profit parameter of knowledge sharing game is substituted into Eq. (4). Since the maximum parameter of the game profit matrix is $1+r$ and the minimum parameter is 0, the following equation is obtained:

$\displaystyle P_{i}\left({S_{i}\leftarrow S_{j}}\right)=\frac{U_{j}-U_{i}}{% \left({1+r}\right)\cdot\max\left({K_{i},K_{j}}\right)}$ (5)

The replication dynamics rules based on imitating the winners truly describe the game evolution process and adjustment learning status of users participating in knowledge sharing in the crowdsourcing community, and also reflect that users in the crowdsourcing community will be affected by users with high connectivity in the network when they choose the game strategy of knowledge sharing, which is in line with the psychological characteristics that the network public is more vulnerable to the influence of authoritative figures or opinion leaders At the same time, it also fully shows that there is a strong uncertainty in the process of knowledge sharing game strategy selection of crowdsourcing community users.

4. Evolutionary game of knowledge sharing in crowdsourcing community on ws small world network

4.1 Simulation setups

On the basis of WS small-world network structure model and knowledge sharing game model and its revenue function, the evolutionary game model of crowdsourcing community knowledge sharing WS small-world network structure is constructed based on imitating the rules of replication dynamics of winners and simulating the evolution process of crowdsourcing community knowledge sharing with simulation in Matlab, so that we can discuss the influence of the number of iterations of game evolution, the revenue parameters of game and the network structure parameters on the game equilibrium of knowledge sharing evolution of crowdsourcing community users without considering social preference.

(i)
All community users choose knowledge sharing strategy C with probability P as their own initial game strategy in the first round, so the initial density of knowledge sharing strategy C crowdsourcing community users is P0 equal to the P.
(ii)
After each round of knowledge sharing game, all users in the crowdsourcing community will determine the next round of game strategy according to the rules of imitating the winner’s copy dynamics strategy adjustment based on the revenue of this round of game.
(iii)
The evolution mechanism of user knowledge sharing in crowdsourcing community is explained by analysing the evolution of knowledge sharer density P and knowledge sharer equilibrium density Pc of users in crowdsourcing community, where P is the proportion of users who choose the knowledge sharing strategy after each round of game, and its curve will change with the change of time series; Pc denotes the equilibrium density of knowledge sharers when the game is dynamic and stable. This study refers to the viewpoint of Xie et al. [27] and takes the average value of 20 consecutive rounds of equal knowledge sharing strategist density p or the last 30 rounds of knowledge sharing strategist density P in the simulation test as the value of Pc.

4.2 Building evolutionary game model of knowledge sharing on WS small world network

(i)
The crowdsourcing community with the characteristics of WS small world network structure is generated. Considering the convenience and feasibility of simulation experiments, the number of users N set to 500.
(ii)
Each user in the crowdsourcing community and the adjacent users in the generated WS small world network carry out 100 rounds of repeated games according to the knowledge sharing game model and the revenue matrix (Table 1) according to the knowledge sharing game model. The initial density of knowledge-sharing strategies for crowdsourcing community users WS small-world networks is about equal to P0, and all community users use the initial density P0 as the initial game strategy.
(iii)
Each user evolves the game strategy based on the replication dynamics adjustment rule based on imitation winning (Eq. (5)), that is, selects a neighbour from the neighbour set according to the influence. Then the game strategy of the next round is formed by the probability selection based on the total income difference.

4.3 Analysis on the evolution of knowledge sharing in WS small world network

Based on the evolution game model of crowdsourcing community users’ knowledge sharing on the WS small world network structure, the simulation experiment is conducted to analyse the impact of the WS small world network structure on the evolution trend of crowdsourcing community users’ knowledge sharing, and specifically analyse the evolution trend and equilibrium state of the crowdsourcing community users’ knowledge sharing game under the joint action of the game revenue parameter r and the “broken edge random reconnection” probability qx under a certain initial density.

(i)
Evolution of the density P of knowledge-sharers

The Matlab is used to program and analyse the variation trend and evolution law of different random reconnection probability qx with iteration times when the initial density is 0.3 and the game income parameter is 0.7. Figure 1 shows a simulation result of knowledge sharing evolution of crowdsourcing community users based on WS small world network. The results show that the density of knowledge-sharers on WS small world network P fluctuate to a certain extent with the increase of iteration times, and the probability of random reconnection of broken edges qx. This important small world network structure parameter promotes the density of knowledge-sharers. The larger the probability of random reconnection, the higher the overall level of density P knowledge-sharers.

Figure 1.
Evolution of density of knowledge sharing on small world network.

(ii)
Analysis of the evolution results of the equilibrium density pc of knowledge sharing

Figure 2.
Evolution of equilibrium density of knowledge sharing on small world network.

Based on the analysis of the evolution results of the density P of knowledge-sharers, analysis of the evolutionary equilibrium of knowledge sharing among crowdsourcing community users in WS small world network shows, when the initial density P0 equal to 0.3, the distribution of equilibrium density Pc of knowledge sharing will be under the action r different random reconnection probability qx and game income parameters. Figure 2 is a simulation experiment WS the evolution of knowledge sharing among crowdsourcing community users on small world networks. This result is intended to describe the initial density of 0.3. of the relationship between the random reconnection probability and the game income parameter and the equilibrium density Pc of knowledge-sharers when the step size is 0.14286, where the broken line diagram based on the equilibrium density of knowledge-sharers under different game income parameters Pc the change of random reconnection probability qx broken edge, and the broken line diagram based on the relationship between game parameters r and the equilibrium density of knowledge-sharers under different initial densities. From the results, the initial density and random reconnection probability have no significant impact on the game evolution of knowledge sharing. Rather it is that the higher the game income parameter, the lower the equilibrium density of knowledge sharing.

5. Evolutionary game of knowledge sharing in crowdsourcing communities considering social preferences

5.1 Revenue function of knowledge sharing in crowdsourcing communities considering social preferences

The existence and intensity of social preferences play an important role in the continuous knowledge sharing behaviour of users in the crowdsourcing community, as well as the quantity and quality of knowledge sharing. Crowdsourcing community users’ knowledge sharing behaviour can not only affect their own profits, but also affect other community users connected with them, thus forming certain social profits. Therefore, it is assumed that the revenues of users in the crowdsourcing community are jointly affected by the benefits of themselves and users in other communities, and the continuous interaction and knowledge sharing between users promote the evolution of the knowledge sharing game in the crowdsourcing community. According to this assumption, the revenue function $U_{i}$ of the crowdsourcing community users in a single round of knowledge sharing under social preference is

$\displaystyle U_{i}=\mathop{\sum}\limits_{j\in W_{i}}U_{i}^{s}\left({S_{i},S_{% j}}\right)+\lambda\mathop{\sum}\limits_{j\in W_{i}}U_{j}^{i}\left({S_{i}}\right)$ (6)

where $W_{i}$ denotes the set of all neighbours connected to user $i$ in the crowdsourcing community network, $U_{i}$ denotes the revenue of user $i$ , and $U_{j}^{i}$ denotes the revenue of the neighbour $j$ connected to the user $i$ related to its game strategy, $U_{i}^{s}\left({S_{j},S_{i}}\right)$ denotes the revenue generated by the game strategy of user $i$ in the crowdsourcing community, which is jointly determined by the behaviour decisions of itself and the connected user $j$ , $\lambda$ indicates the social preference coefficient of user $i$ , where 0 $\leqslant\lambda\leqslant$ 1, the larger the value of $\lambda$ , the higher the degree of social preference, $\lambda U_{j}^{i}$ denotes the social benefits of user $i$ , which depends on the revenues of the connected user $j$ related to his game strategy and the degree of one’s own social preferences.

According to the total revenue function $U_{i}(t)$ of the user $i$ of the crowdsourcing community participating in the knowledge sharing game in the $t$ round and the revenue function $U_{i}$ of the crowdsourcing community user in the single round of knowledge sharing game based on social preference, the revenue function $U_{i}^{p}\left(t\right)$ of the crowdsourcing community user in the knowledge sharing evolution considering social preference is constructed,as shown in Eq. (7).

$\displaystyle U_{i}^{p}\left(t\right)=\mathop{\sum}\limits_{j\in W_{i}}S_{i}% \left(t\right)\left({{\begin{array}[]{cc}1&{1-r}\\ {1+r}&0\\ \end{array}}}\right)S_{j}\left(t\right)^{T}+\mathop{\sum}\limits_{j\in W_{i}}S% _{i}\left(t\right)\left({{\begin{array}[]{cc}\lambda&0\\ 0&0\\ \end{array}}}\right)S_{j}\left(t\right)^{T}$ (7)

where $S_{i}\left(t\right)$ denotes the strategy vector of the crowdsourcing community user $i$ in the $t$ round game, the $S_{j}\left(t\right)^{T}$ denotes the transposition of the strategy vectors of the crowdsourcing community user $i$ the connected neighbour user $j$ in the $t$ round game, $\left({{\begin{array}[]{cc}1&{1-r}\\ {1+r}&0\\ \end{array}}}\right)$ denotes the revenue matrix of knowledge sharing game among crowdsourcing community users, the r denotes the game revenue parameter, $\left({{\begin{array}[]{cc}\lambda&0\\ 0&0\\ \end{array}}}\right)$ denotes the social preference matrix, that is, the revenue obtained by the users of crowdsourcing community due to the influence of social preferences in the knowledge sharing game, $\lambda$ denotes the social preference coefficient, when $\lambda$ is 0, the social preference does not exist, and the revenue function is the same as that when the social preference is not considered.

5.2 Evolutionary game of knowledge sharing of crowdsourcing communities in WS small world network considering social preference

The simulation experiment of knowledge sharing evolution of crowdsourcing community users on WS small world network considering social preference is programmed by Matlab algorithms. According to the game model of knowledge sharing and the replication dynamics rule based on imitating the winner, 100 rounds of repeated game are carried out. The initial density P0 0.3 and the game revenue parameter $r$ 0.7.

(i)
Evolution of the density P of knowledge-sharers WS small-world networks

If the social preference coefficient is 0.1 and 0.7, the evolutionary game process of knowledge sharing in crowdsourcing community on WS small world network structure is simulated. When the initial density is 0.3 and the game revenue parameter is 0.7, The variation trend and law of knowledge share density with iteration times under different random reconnection probability. Figure 3 is a simulation result of knowledge sharing evolution when the preference coefficient is 0.1 and 0.7. The experimental results show that the density of knowledge-sharers on WS small world network $P$ fluctuate to a certain extent with the increase of iteration times, but the random reconnection probability qx promote the evolution of knowledge sharing regularly. The higher the density, the greater the social preference coefficient and the stronger the evolution of knowledge sharing.

Figure 3.
Evolution of density with different social preferences on small world network.

(ii)
The evolution of equilibrium density $p_{c}$ of knowledge sharing WS small world networks

The simulation experiment is carried out on WS small world network with initial density of 0.3, game return parameter of 0.7, random reconnection probability of broken edges and social preference. The experimental results are shown in Fig. 4. The experimental results show that the equilibrium density of knowledge sharers increases with the increase of social preference coefficient and the probability of random reconnection of broken edges, while the initial density has no obvious effect on the equilibrium density of knowledge sharers.

Figure 4.
Evolution of equilibrium density with social preferences on small world network.

6. Discussion and conclusions

The study of evolutionary games on complex networks began in 1992 when Nowak and May first introduced the two-dimensional grid network structure into the prisoner’s dilemma game model [1]. After nearly thirty years of research, rich research results have been achieved. Researchers have adopted different game models to study the continuous interaction and cooperative behaviour evolution between users on complex networks from the perspectives of network topology, game strategy rules, and specific mechanisms, laying a solid theoretical foundation and numerous methodological support for the study of evolutionary games on complex networks. For evolutionary games on complex networks, factors such as the type of network structure, game evolution rules, game models, specific mechanisms, and individual attributes of the game are closely related. A specific network structure, coupled with reasonable game evolution rules, can effectively promote the emergence of cooperation. Therefore, the impact of several factors working together on group cooperative behaviour has become a current hot issue. Considering the increasing complexity of individual attributes in the current Internet era, combining individual attributes of games with specific game rules to study the impact of more realistic network structures on cooperative evolution will be an exploration of theoretical and practical significance. Through the review of research literature in the second part, it is found that few scholars currently study knowledge sharing based on the characteristics of network structure, and most of the studies are qualitative research from a static perspective, and few empirical studies are conducted from a dynamic perspective; In terms of research methods, the research design is relatively simple, the research methods are relatively single, and there is a lack of detailed empirical research combining multiple methods to address knowledge sharing issues; from a research perspective, studying knowledge sharing in crowdsourcing communities from the perspective of social preferences is a new exploration. Using complex network theory and evolutionary game theory, an evolutionary game model for crowdsourcing community knowledge sharing considering social preferences and not considering social preferences is constructed from a dynamic perspective. By simulating the decision-making behaviour of users in knowledge sharing on small world network structures, the evolutionary effects of social preferences, network topology structure, and game revenue parameters on knowledge sharing are verified, research has found that social preferences have a regular promoting effect on knowledge sharing in crowdsourcing communities. This evolutionary game model expands the research scope of the combination and application of complex network games with other disciplines, further enriches the theoretical perspective of knowledge sharing research, and helps to grasp the psychological and behavioural patterns of knowledge sharing participation behaviour of crowdsourcing community users, which is also an important contribution of this article.

Based on the complex network evolutionary game theory and social preference theory, an evolutionary game model of crowdsourcing community users’ knowledge sharing based on the characteristics of WS small world network structure is constructed. Through simulation in Matlab, the evolution and dynamic equilibrium of crowdsourcing community users’ knowledge sharing on the network structure are simulated, and the following conclusions are drawn:

(i)

When social preference is not considered, the structural characteristics of WS small world network can promote the evolution of knowledge sharing game to a certain extent. The short average distance and large aggregation regularity of small world networks improve the equilibrium density of knowledge sharers, which is mainly reflected in that the higher the probability of random reconnection of broken edges is, the higher the equilibrium density of knowledge sharers is, but there is some uncertainty In the evolutionary game process of knowledge sharing among crowdsourcing community users on the WS small world network structure, revenue parameters play an important role in the equilibrium density of knowledge sharers. The higher the game revenue parameters are, the lower the equilibrium density of knowledge sharers is; The matching degree between the structure characteristics of WS small world network and the strategy distribution structure of users is the reason for the fluctuation of the equilibrium density of knowledge sharers.

(ii)

When considering social preference, social preference regularly promotes knowledge sharing among crowdsourcing community users on the WS small world network. The larger the value of social preference coefficient, the higher the equilibrium density of knowledge sharers in crowdsourcing community The probability of broken edge random reconnection has a regular impact on the equilibrium density of knowledge sharers in crowdsourcing communities. The greater the probability of broken edge random reconnection, the higher the equilibrium density of knowledge sharers The evolution of knowledge sharing game of crowdsourcing community on WS small world network still shows a certain degree of volatility, but the structural characteristics of small world network slow down the volatility of knowledge sharing evolution, making the change of equilibrium density of knowledge sharers more gentle.

In conclusion, social preference can significantly promote knowledge sharing in crowdsourcing communities. Therefore, crowdsourcing community managers should stimulate community users’ fairness preference, altruism preference and reciprocity preference through various ways, so as to strengthen community users’ knowledge sharing behaviour. For example, community managers should promote knowledge sharing in crowdsourcing communities through fair distribution and reward mechanisms. Through the establishment of the integral system, the construction of the community reward system, the establishment of interest sub communities and other measures, the crowdsourcing community has formed a strong atmosphere of mutual revenue. For the discussion on specific topics, we can invite community members to participate in the invitation system, invite community members who have made greater contributions to serve as moderators of specific sections, stimulate their altruistic motives.

Footnotes

Acknowledgments

This work was partially supported by the Academic Research Projects of Beijing Union University (No. ZK30202106).

Author’s Bios

Jianfeng Meng received his doctoral degree from School of Management, China University of Mining & TechnologyBeijing in the year 2020. He is currently working as an associate professor in the School of Management, Langfang Normal University, China. He has 15 years of teaching experience. His area of interests includes management science, organizational behaviour and human resource management.

Gongpeng Zhang received his doctoral degree from School of Management, China University of Mining & Technology-Beijing in the year 2020. He is currently an associate professor in the Tourism College of Beijing Union University, China And he has 18 years of teaching experience. His research interest covers management science tourist behaviour modeling and simulation E-mail: gongpeng@buu.edu.cn (Corresponding author).

Zihan Li received her doctoral degree from Institute of Agricultural Economics and Development, Chinese Academy of Agricultural Sciences, Beijing, China in the year 2016. Currently she is working as a Lecturer in the School of Management, Langfang Normal University, China. She has 6 years of teaching experience. Her area of interests includes rural development, poverty reduction and rural energy.

Hongji Yang obtained his B.Sc. and M.Phil. in Computer Science in 1982 and 1985 respectively from Jilin University, China, and his PhD in Computer Science in 1994 from Durham University, England. He is currently a Professor at School of Computing and Mathematical Sciences, Leicester University, Leicester, England. His general research interests include Software Engineering and Creative Computing. He served as a Programme Chair at IEEE International Conference on Software Maintenance 1999 (ICSM’99) and the Programme Chair at IEEE Computer Software and Application Conference 2002 (COMPSAC’02). Prof. Yang has been an IEEE Computer Society Golden Core Member since 2010.

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An evolutionary mechanism of social preference for knowledge sharing in crowdsourcing communities

Abstract

Keywords

1. Introduction

2. Literature review

Table 1 A brief summary table contrasting the existing methods

3.1 Construction of WS (Watts and Strogatz) Small World Network Model

3.2 Evolutionary game model and strategy rules of knowledge sharing in crowdsourcing community

3.2.1 Premise hypothesis

Table 2 Simplified revenue matrix of knowledge sharing based on snowdrift game

4.1 Simulation setups

5.1 Revenue function of knowledge sharing in crowdsourcing communities considering social preferences

Footnotes

Acknowledgments

Author’s Bios

References

Table 1
A brief summary table contrasting the existing methods

Table 2
Simplified revenue matrix of knowledge sharing based on snowdrift game