Game Equilibrium of False Information Diffusion in Public Crisis on Interpersonal Network
ITM Web of Conferences
Game Equilibrium of False Information Crisis on Interpersonal Network Diffusion in Public
Kai LI 1
Jia-Jia HAO 0
0 School of Economics and management Yanshan University Qinghuangdao , China
1 Foreign Affairs Center of Ministry Industry and Information Technology Beijing , China
The public crisis evolution will make a variety of impact on society, the public and the mass media will also focus on public crisis. In the evolution of public crisis, objective and non-objective information about the crisis will arise. Such harmful but not objective information is “false information”. Various factors working together lead to the false information diffusion in public crisis. We will identify eight factors inducing false information in public crisis, and study the game equilibrium process of false information diffusion in public crisis on interpersonal network, and determine the equilibrium which was looked for. When the public identify that their interests are lower than the equilibrium, the false information is accepted, then false information on this node begins diffusing; When the public identify that their interests are higher than the equilibrium, the false information is identified, then diffusion on this node ends.
With the rapid development of economic, the social and economic environment will become more
complex and difficult to predict. By this time, the probability of public crisis occurring closely
together will be enhanced greatly. When the public crisis happens, people tend to express their views
of the event. But in the process of information diffusion, the content of the information may conflict
with true information due to some artificial and inevitable factors. The false information such as
rumor, gossip, hearsay, which is not in accordance with real information will surely contribute to the
fear and anxiety of the public create more factors that lead to social instability. This is an main source
of secondary damage of public crisis.
So what is the connotation of the “false information” in public crisis? What are the factors that led
to the false information in public crisis? What kind of role did the inducing factors play in the
spreading of false information in public crisis of game equilibrium? The research of these propositions
has great importance in the scientific definition of the false information in public crisis. Meanwhile, to
specify the inducing factors of false information in public crisis and their roles in the spread of game
equilibrium is critical for us to grasp the development direction of the false information in public crisis
and the factors that public care about in the event development .
2 The connotation of the false information in public crisis
The evolution of the public crisis is actually a series of diffusion effects of crisis information. With
the appearing of an huge amounts of information, some discordant voices will arise. It will raise the
possibility of public who lack recognition to echo it. At this time “false information” will appear.
What is “false information”? “False information” is not the information in a real sense, it’s the
information that is “untruthfulness or unrealistic”. False information has some other appellations,
such as dummy message, inferior information, expanding information, the selfish information.
False information in public crisis is the information that looks like the real but actually not. False
information is the information transmitted in the non-public media channels. It is a kind of harmful
information that is not true, not objective, not conductive to social stability and easy to mislead the
In addition to the research on the definition of false information, some scholars have studied the
process of false information diffusion. They suggest that the essence of false information diffusion in
public crisis is a class of complex nonlinear evolution process. Thompson et al. established the
rumor model which is similar to the Daley-Kendall model. Considering the effect of the population’s
diversity in the rumor spreading, they found that people’s activity is the most sensitive parameter that
will influence the spread of rumors. They also found that increasing activity can control the size of the
rumor spreading. Kawachi developed the dynamics model in finite and infinite dimensional with
considering varying accepting degrees of different populations, and then derived the rumor diffusion
threshold. Based on the influence of different contact for eventually diffusion. Seki et al. discussed
the results through mathematical simulation. Huo et al. studied the interactive model between
rumors spreading and the government's emergency utility and drew the phase diagram of the system
through data simulation . On the basis of these, they put forward strategies and policy
recommendations about emergency management. Zhong et al. divided the information into real
information and false information and discussed the process of crisis information diffusion from the
perspective of ecology. They built the model of social crisis information diffusion which is based on
Lotka-Volterra model. Then carried out simulation and empirical analysis for social crisis information
diffusion and found that the diffusion of crisis information is closely related to the diffusion
coefficient and diffusion rate.
Some of the researchers think that crisis information only has two states: Absolute truth and totally
untrue. However, in our real life there is some information which seems real but actually not. There is
also some which seems far from objective truth, but is the real information in fact. The reason of
information become seemingly far from objective truth is that the partial distortion of strictly true
objective information leads to the qualitative change of a small part information. Its essence is real
and less harmful to the society. We define information with characters above as virtual information in
this paper. The information that seems objectively true is false information as a whole with a part of
the true appearance. We defined the information as the false information in this paper. The purpose of
this study is to reveal the game equilibrium of false information diffusion. As long as the information
is related to the public crisis, whether rumors or gossip or rumors are included in this paper.
3 Assumptions of false information Diffusion in public crisis
The process of false information diffusion in public crisis is a process of decision-making in two sides.
There are utility values for people to evaluate what decisions should be made, which means the value
of maximum satisfaction. So the diffusion of false information in public crisis is a process of game
equilibrium. But in real life, the public are restrained by attention, emotion, ability and personal
psychological, so the decisions they made are limited. The decision-making process is not complete
and accurate under the interference of each external environment, which means that it is an incomplete
and imperfect decision-making process.
When the false information in public crisis generated, individuals try to express their views from
the aspects of the false information inducing factors in public crisis and to persuade other individuals
to judge the fairness and security of the environment from these perspectives as well. Therefore, the
process of false information diffusion in public crisis is the result from interactions of the eight factors
which are mentioned above. Next, we will study the game equilibrium of false information diffusion
in public crisis from the eight aspects.
Assumption1: Information of different aspects which the recipients try to express is independent,
which means that the eight factors: culture, personal life needs, interpersonal relationship, group
attitude, profit distribution, the sanity of legal system, the government credibility and development
coordination are not related to each other. One of the intentions that contained in the comments is
represented by i , the total information of type i is represented by I i = xi + εi . Where I i represent the
amounts of i , εi is the amount of uncertainty of the intention. εi is one of the normal distribution
random variables. Then, we have E(εi ) = 0, var(εi ) = δi2 . The total intention of a particular aspect that
individuals express is: I = xi + εi .
Hypothesis2: The individuals who haven’t accept the false information in public crisis will
identify the information of their surrounding environment in all aspects which are independent. It
means that they can judge fairness and security from the eight factors of culture, personal life needs,
interpersonal relationship, group attitude, profit distribution, the sanity of legal system, the
government credibility, and development coordination are not related to each other. The intention of a
particular aspect distinguished in the comments of the individual who accepted false information can
be represented by i in public crisis. The total information of type i is represented by
Di = xi + εdi . Di represent the amounts of i . εdi is a normal distribution random variable which
represents the amount of uncertainty intention. We can derive the formula: E(εdi ) = 0, var(εdi ) = δd2i .
The relevance between εi and εdi is ρi . spreaders’ intention from eight aspects are represented by i .
The total intention of a particular aspect that individuals express is D = xi + εdi .
Hypothesis3: When the false information recipient express their intentions, the more information
they express the more satisfied they are. In this article, we assume that this kind of satisfaction is π . It
is proportional to the total amount of information they express. When the individuals who haven’t
accept false information distinguish the information, the more information they identify, the more
satisfied they are. In this article, we assume that this kind of satisfaction is P , which is proportional to
the total information that they identify. For the sake of simplicity, we assume:
πi = I =
Pi = D =
I i =
In the formula (
).(2), i represents the eight kinds of intention contained in the false information
in public crisis.
Hypothesis4: The utility of individual who haven’t accepted the false information is the sense of
achievement after judging the fairness of their surroundings and security. We set it as
u(w, xi ) = e r(w (xi )) . When the recipient expresses false information, the utility of is the satisfaction
after resonate with other individuals. We set it as: u(ti , fi , si ) = E(π w) . Where (xi ) =
the emotional cost that the individuals who haven’t accepted the false information spend on
distinguishing the environment. w = wi represents the satisfaction that the individuals who won’t
ci xi2 is
accept the false information have after identifying the false information(It also can be called the
emotional cost that false information recipients paid ). It is the linear combination of i ,
wi = ti + f i πi + si pi . ti represents the identity amount of the existing fixed environmental fairness
and security. fi represents the rate of being persuaded, si represents the rate of
selfWhere, w0 represents the satisfaction before they identify the false information.
The process of false information diffusion in public crisis is a incomplete process. Which has a
variety of combinations. To solve the balance of many combinations is very complicated and
unnecessary. While the complete false information diffusion model in public crisis are comprehensive
and representative, we solve the equilibrium in the process of the complete diffusion in this paper.
A complete diffusion process of the model for certainty equivalent equation is following:
The equilibrium of formula (4) is following:
persuasion. π w represents the false information recipients’ sense of accomplishment after they
persuaded others. i represents the eight aspects of the intention that the individuals want to express.
Hypothesis5: The model of false information diffusion in public crisis assume that the recipients of
false information in public crisis want to achieve their own maximization of satisfaction by spreading
false information. Meanwhile the individual who does not accept false information in public crisis will
not spread the false information in public crisis and make themselves the most satisfaction in
participation utility condition.
4 The equilibrium of the model
The decision model that the recipients in public crisis spread false information and individuals
who haven’t accepted false information in public crisis identify the information is following:
In the formula of (5).(6).(7).(8).(9), Ωi =
δi2 + δd2i 2ρi δi δdi
that contained in false information in public crisis.
δi2δd2i (1 ρi )
, i represents eight kinds of intention
ci (1 + +rciΩi )
I * = D* = xi* =
ci (1 + +rciΩi )
w* = wi* = [ti + ci (1 + +rciΩi )2 ]
5 The game equilibrium rule of false information diffusion in public
crisis on interpersonal network
) The equilibrium of false information diffusion in public crisis is determined by the following
When the recipients of false information in public crisis spread information, the attitude stability
is δi2 . The certainty of individuals who haven’t accepted false information for fairness and security of
the environment they lived is δd2i ;
The fairness and safety factor that the individuals who haven’t accepted false information in public
crisis avoid the misjudgment for environment is r ;
The emotional cost that individuals who haven’t accepted false information in public crisis will
pay to identify the environmental fairness and security is ci ;
The relevance between recipients spreading information and individuals who haven’t accepted the
false information identifying it is represented by ρi .
Through the analysis above ,we can know that the process of false information diffusion in public
crisis is the communication between the spreader and the which is a result of interaction between
subjective and objective factors.
The objective factors refer to the fairness and security of realistic environment. The subjective
factors refer to the tendency that both of them express and identify information, psychological
reactions and avoiding miscalculation. These factors will affect the transmission and the recognition
of information, and make fluctuations in information diffusion process, which form the main reason
for information difficult to control.
(2) The diffusion process of false information in public crisis is the process that the public judge
the nature of the environment from multiple aspects and make a decision. The public is emotional
complex, so the decision-making process is also the outcome of various complicated factors
interaction. According to the analysis on the result of game equilibrium, the game equilibrium of false
information diffusion process in public crisis is that intentions, the rate of being persuaded, the rate of
self-persuasion change according to deciding factors’ changes. The differences of marginal changes
are shown in Table 1.
rci N ∂Ωi
rci N ∂Ωi
rci N ∂Ωi
∂N 1 rci N ∂Ωi
G = 1+ +rci Ωi ,
ρi δi δdi
2ρi δi δdi + δdi 2
The higher δi2 (the attitude stability of false information recipient in public crisis when express
information) is, the higher the rate of self-persuasion is. At the same time, the possibility of the
individuals who haven’t accepted the false information in public crisis being persuaded is higher; The
higher δd2i (the certainty the individuals have in environment fairness and security)is, the lower the
rate of being persuaded and the rate of self-persuasion are.
The higher r (The factors that the individual who haven’t accepted false information in public crisis)
avoid the misjudgment for the environmental fairness and safety is, the lower the possibility of being
persuaded and self-persuasion are. The more clearly that public can understand the environment
around, the less willingly they want to waste time and effort to identify environmental justice and
security. The result is that the probability to accept false information in public crisis is low.
When ρ = 0, the behavior of the individuals who spread the false information in public crisis is not
related to the intention of the individuals who haven’t accepted the false information in public crisis.
When the false information recipients in public crisis express the false information, the uncertainty of
expression will decline the probability of being persuaded. Meanwhile the ability of them to identify
false information in public crisis will decrease and the satisfaction after identification will also fall. At
this time, this information will only be accepted by a few people. The reason for this phenomenon is
that the information is strictly false information and has small correlations with other individuals. It
shows that the false information that can be diffused is a kind of information which is related to
people’s satisfaction in many aspects, which means the false information in public crisis that can be
diffused is the information that is related to people's vital interests and life desires. This is in
accordance with the definition in this paper.
When ci (the emotional cost that individual who haven’t accepted false information in public crisis
will pay to identify the environmental fairness and security.)increases, the rate of being persuaded and
the rate of self-persuasion will fall.
(3) When the spreaders spread false information or the individuals who haven’t accepted the
information recognize it, the most fundamental motivating factors are different. It means that the
reasons that different individuals accept or refuse false information are different. It's not single factor,
but the interaction of various objective and subjective factors. The false information spreader will
enrich the content of false information according to their own circumstances. At the same time, the
individuals will identify the false information according to the information provided by the spreaders
and their own conditions, which will add to the complexity in game process of spreading and
recognizing false information.
(4) The satisfaction after recognizing false information changes according to the fluctuation of
certainty for each inducing factors in all aspects. It means that the certainty attitude of environmental
fairness and security that the individual who haven’t accepted the false information in public crisis is
associated with the satisfaction after they identify it. The emotion cost that the recipient in public
crisis paid is related to the attitude stability of environmental fairness and security.
δi2 2 ρiδiδdi + δdi2 1 + +rciΩi δi2 2 ρi δ j δdj + δdj 2 1+ +rc j Ω j
persuasion though intention i is higher than the intention j for the individuals who haven’t identified
, the rate of
ρi δ j δdj
the false information in public crisis, si* > s*j . It means that we can identify the false information in
public crisis easier according to the intention of i .
information in public crisis, fi* > f j* . It means that the spreaders and individuals who haven’t
accepted information resonate on the intention i . In this case, the individuals who haven’t accepted
the false information in public crisis will accept false information easily. The individuals who haven’t
accepted the false information in public crisis should distinguish the intention selectively. Sometimes
they cannot obtain the greatest satisfaction even exhausted all intentions. It can also lead to excessive
information identification and increase dissatisfaction.
, the rate of being persuaded
6 Diffusion process of false information in public crisis on interpersonal
The thought of liberty and democracy spur people to continually judge the fairness of the
surroundings, especially when public crisis happens. With the increasing frequency of judgment, the
of social development and the imbalance of the profit distribution lead to dissatisfaction with their
surroundings. At this time, people want to express their dissatisfaction by proper channels and they
expect the dissatisfaction can be solved. But some evasive and laissez faire behaviors of some
departments have intensified people's sense of injustice. So people will express their views in the
range of their communication, which can’t show the real facts completely. The information with part
of distortion mingles with the citizen's personal feelings of events and it is biased. But the unfairness
and security of their surrounding environment let them believe that their views of the event are correct.
Thus the false information in public crisis will be inspired. The process is shown in Figure 1.
When false information in public crisis generates, the public will judge the fairness according to
the resources they occupied, the culture they accepted, their personal status, etc. If the public’s
decision results are that the public environment is fair, then the false information in public crisis does
not involve the public interest. The enthusiasms of the public to express false information will
disappear. This is the phenomenon that “we don’t care the thing that has nothing to do with us”. They
just take the event or situation as the topic of communication rather than take it as a way of expressing
The public's awareness of
fairness and security
The pursuit of
interests due to
appealing and fighting to
express personal views in
The occupation of
The balance of
Personal life status
the completeness of laws
social discontent. So the false information in public crisis is identified successfully and will stop
spreading. And when the public’s decision results are that they are not treated fairly or they feel the
environment around them isn’t safe, they want to express their dissatisfaction in some ways. If they
get the deserved interests from normal complaint channels, it will stop spreading. If the complaint
through formal channels is not successful, people will choose to accept false information and diffuse it
in their interpersonal network. The process is shown in Figure 2.
7 The interventions of false information diffusion in public crisis
) When public crisis generates, some objective and subjective factors, which contain the fairness and
safety of the real environment, the tendency of different individual to spread and identify the false
information, psychological reaction, avoiding mistakes, will affect the process of false information
diffusion. They will lead to false information spreading or stopping spreading. At the same time, the
interaction of subjective and objective factors increase supervision difficulties of false information in
public crisis. When we want to intervene the process of false information diffusion in public crisis, we
can begin from two aspects.
From the aspects of the external soft environment, the relevant departments should plan as a whole,
increase the balance of social development, reduce the phenomenon of distribution unequally and
increase public’s satisfaction of their surroundings. Beyond that, the relevant departments should also
increase the degree of supervision and regulation from the environment for living. For example, they
can meet the public’s needs of safe environment from the aspect of environmental enhancement,
improving medical level, improving the quality of education, raising employment rate, etc. They
should complete the corresponding laws and regulations, and specify the responsibility scope of the
relevant departments. When the public interests are violated and complain to the relevant departments,
the departments should resolved it in time. The phenomenon of shirking responsibility and omission
should be put an end in order to increase the public's sense of security.
From the aspects of the public themselves, the stability of attitude, the emotion cost of identifying
false information in public crisis and the part authenticity of the false information’s kernel are the
factors that can affect individuals to accept false information. That is the instability of external
environment can make the public to suspect their safety. The relevant departments should establish
feasible crisis guarantee system and implement it in order to reduce the doubts of the public. They
should do a good job of crisis aftermath, eliminate the motion of unfair and insecurity, enhance the
public’s certainty degree of environmental fairness and safety, which means they should reduce the
cost of identification of the false information and the attitude stability. Thus when public crisis
happens, the public are not willing to and also have no need to spread false information.
(2)When the spreaders spread false information or the individuals who haven’t accepted the
information recognize it, the most fundamental motivating factors are different. It means that the
reasons that different individuals accept or refuse false information are different. The individuals will
distinguish the intention selectively. Sometimes they cannot obtain the greatest satisfaction even
exhausted all intentions. It can also lead to excessive information identification and increase
dissatisfaction. If they resonate on intentions, the individuals will accept the crisis information. So
when the false information generates, the relevant departments should intervene it according to
different principal contradictions in different areas, which requires the apartments to do well in crisis
management and specify the principal contradictions that will dissatisfy the public in different areas.
(3) False information in public crisis is concerned more by the public. If force to stop its spreading,
we will infuriate the spreaders and make matters worse. Indirect measures should be taken in the
relevant departments, rather than deny part of the authenticity .At the same time in the process of
resource allocation, we should insist on human-oriented principle, the principle of high efficiency,
sustainability, fairness principle and reduce the degree of public’s complaint and dissatisfaction about
the social system and decrease the number of inducing factors about false information diffusion in
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