Encouraging the Submission of Information by Reducing Confirming Costs

Abstract

When a landslide occurs, the person who discovers it will likely report the disaster; however, a person who receives this report will likely need someone on site to check, since the reporter may have misread the information. This allows third parties to make use of the confirmed information. Facilitating such mechanisms for reporting, confirming, and utilizing disaster information is considered to be necessary for sharing details about one. In this paper, we proposed and analyzed an agent-based model that incorporates disaster behavior into the model of Toriumi et al. The reporting of a disaster refers to submitting articles, the confirmation of the information by another person refers to commenting on the articles, and utilizing the information refers to comments responding to the aforementioned comment using the framework of meta-reward games, based on the prisoner’s dilemma game. We then analyze the costs and rewards to encourage cooperation in several social networks. It is found that reducing the cost of commenting (conforming) encourages the submission of information. The properties of the results do not depend on network structure, which is novel and unexpected, and it is expected that the properties of real social networks will be predictable.

1. Introduction

A rumor is defined as a specific proposition for a belief that is passed along from person to person, usually by word of mouth, without secure standards of evidence being present [1]. Rumors often spread during disasters such as the Great Kanto Earthquake, 1923 [2], the eruption of Izu Oshima Island, 1986 [2], and the Great East Japan Earthquake, 2011 [2,3,4], influencing people’s behavior and administrative decisions. Sekiya [2] defines rumors as being temporary, able to spread over a wide area of society, and having a negative social impact. A rumor [2] at the time of a disaster can be divided into four types: prediction before a disaster, return after the disaster, posterior prediction after the disaster, and damage after the disaster. In this paper, we will specifically deal with damage after the disaster.

When a landslide occurs after heavy rain, the person who discovers it will likely report the disaster; however, the person who receives this report will likely send someone on site to check since the reporter may have misread the information. This allows third parties to make use of the confirmed information. Facilitating these mechanisms for reporting, confirming or verifying, and utilizing disaster information is considered to be necessary for sharing details about one. In this paper, we focus on the encouragement of the submission or verification of information using the framework of meta-reward games [5].

The remainder of the paper is organized as follows: In Section 2, we refer to related research on information during disasters. Next, in Section 3, we introduce the framework of the meta-reward game. Then, Section 4 describes simulation settings. Section 5 shows the simulation results, and we discuss the results in Section 6. Finally, we conclude and discuss possible future work in Section 7.

2. Related Works

In ambiguous situations, such as crisis situations, people try to put together a meaningful interpretation of the situation by pooling together their knowledge [6]. With the development of information societies and network technology, information on the Internet is relied upon [7]. As a result, the Internet and social media have become widespread real-time communication methods [8]; however, it is said that the spread of tweets differs from the spread of news [9]. Moreover, corrective behavior on social media is characterized as certified by credible sources [10]. It is also said that people are more likely to share false information because it is more fantastical than true information [11].

Social media has the potential to assist the emergency management domain [12]. Hughes et al. [13] report perspectives about the challenges contributing to emergency management due to social media from the viewpoints of practice and research. For practitioners, there are difficulties in verifying social media data, liability risks, information overload, and a lack of resources with which to manage social media communications and data. The use of performance measures, standards, best practices, digital volunteers, training, and exercises is suggested. They study public activity and demonstrate how social media has changed how ordinary citizens think about how they will respond to emergencies. They describe papers that discuss future research into monitoring and extracting information from social media. Wardle et al. [14] provide a framework for policymakers, legislators, researchers, technologists, and practitioners working on challenges related to information disorder.

In emergencies, timely and accurate information is critical [15]. There is the matter of how to evaluate information, i.e., whether it is right or wrong. In safety- and time-critical situations, people need help reviewing content from multiple sources. The matters of information helpfulness and credibility are considered important by everyday analysts because of bounded rationality [16]. Everyday analysts are required to verify information from sources that are numerous and uncertain. Everyday analysts are citizens who have a discerning eye and accurate localized information. They check information elsewhere with regard to situations they are currently experiencing. The achievement of trust is the goal for them, without additional support to further verify information.

Although 67 percent of the world’s population use the Internet [17], the means by which facts are verified is a problem. Miyabe et al. analyzed rumor tweets on Twitter in normal and emergency situations, such as the Great East Japan Earthquake on 11 March 2011 [3]. It has been demonstrated that information was altered less on Twitter than by word of mouth and that rumor tweets tended to spread explosively. People who submit a rumor rarely correct their own submission, and, even if a correction tweet about a rumor is sent out, the rumor tweet is not immediately stopped. In contrast, Takayasu et al. [4] showed that one correction tweet, which originated from a city hall account, on the Great East Japan Earthquake spread wildly. They demonstrated a stochastic agent-based model which was inspired by the contagion model of epidemics, that can reproduce observed rumor dynamics [4].

There are models of information diffusion, such as the Ising model, the Sznajd model, the SIR model, the SICR model, game theory, and social networking service models [7]. Agarwal et al. showed that, by posting verified information on social media, social media users were able to make informed decisions on whether to support or oppose a rumor being circulated by using a game theoretic model [18]. Kubo et al. showed that deception in the confirmation of disaster information is likely to lead to the occurrence of disinformation [19]. They then found that if this deception can be detected and punished, this tends to suppress the occurrence of disinformation by using an evolutionary game [19].

Toriumi et al. [5] dealt with meta-reward games in n-person complete graphs. They confirmed the importance of meta-rewards, showing that if meta-rewards are not introduced, people rarely submit articles when the number of users is not sufficiently high. Then, if the reward for article submission is more than the cost of submitting an article, commenting and comment responding will increase. They used genetic algorisms for deciding the behavior. There, each agent has two parameters: the probability of submitting articles and that of commenting (or responding to comments). Each agent evolves the strategies of the two parameters; that is, each agent learns the probabilities. The method is efficient in long-interacting environments but is difficult for inexperienced first-time participants, such as in a disaster situation. Miura et al. [20] analyzed questioning as well as answering behaviors and extracted four factors: helping motivation, reciprocity motivation, social motivation, and reward motivation. The reward motivation supports the meta-reward games.

Furthermore, Osaka et al. [21] conducted research that considers direct reciprocity. By making it easier for agents to comment on agents that have given them rewards, cooperation is promoted, even without a meta-reward equivalent to a comment being offered in return; however, they showed that free riders emerge and cooperation breaks down.

Hirahara et al. revealed that different network structures make a difference to social media trends [22]. The scale-free model showed that social media can be prevalent even when the reward for commenting are lower than the costs of commenting. It was shown that the network topology characteristics during an emergency situation remained unchanged under normal circumstances [9].

3. Model

3.1. Framework of a Meta-Reward Game

Social media is classified as a public good, a type of good that is consumed equally by everyone in society [23], because the information shared can be accessed and used by anyone [5]. Some mechanisms with which to promote contributions to public goods are proposed by Nowak et al., such as indirect reciprocity; helping those who have helped others was necessary for the evolution of human societies [24]. The more advanced models by Axelrod are normative games and meta-normative games [25]. The normative games [25] attempt to promote cooperation in groups by introducing the behavioral principle of punishing non-cooperators as an extension of the n-person prisoner’s dilemma. Meta-norm games that impose punishments are not conducive to voluntary information provision, evaluation, and utilization. In lieu of meta-norm games, a meta-reward game is modeled in social media [5,22] because it is impossible to punish those who do not post, comment, or respond to comments on social media [5]. The submission of articles is a cooperation action in terms of the prisoner’s dilemma, whereas a defect would be not submitting articles. Commenting on articles is a cooperation action, as well as being framed in terms of the prisoner’s dilemma, whereas a defect would be not commenting on articles. Responding to comments is a cooperation action, as well as being framed in terms of the prisoner’s dilemma, whereas a defect would be not responding to comments.

This paper adopts a meta-reward game that will examine the rewards and costs of voluntarily providing and confirming information during disasters, where people are rewarded by posting, commenting, or responding to comments on social media. Each agent has three binary choices to submit an article, S1: submit or S2: not, V1: comment or V2: not, and W1: respond to a comment or W2: not. In the case of submitting an article, agent Ai pays the cost, F, for submitting and neighbors who connect to agent Ai directly gain a benefit, M, by receiving information from the article. Next, agent Aj, who is a neighbor agent of Ai, decides whether to comment on agent Ai’s article. Finally, agent Ak, who is a neighbor of agent Aj, decides whether to respond to agent Aj’s comment. As shown in Figure 1, the agents Ai, Aj, and Ak should be distinct agents, where agents cannot comment on their own articles and cannot respond to comments on their own comments. In this paper, submitting an article relates to posting information about the damage after a disaster. In deciding their behavior quickly in a disaster situation, each agent chooses the most profitable action at each time step, unlike in [5]. Commenting on the article relates to verifying the information, and responding to comments relates to the response for the verification. Here, no distinction is made between correct and incorrect.

The utilities, U_i, U_j, and U_k, of agents Ai, Aj, and Ak, respectively, are given as follows for each interaction with a neighbor. We carried this out because we could not find the formula in [5].

Ui (S1) = M − F,
Ui (S2) = M,
if Aj comments,	Uj (V1) = −C, Ui (S1) = Ui (S1) + R,
if Aj does not comment,	Uj (V2) = 0,
if Aj does not comment and Ak responds to a comment,	Uk (W1) = −C″, Uj (V1)= Uj (V1) + R″,
if Aj does not comment and Ak does not respond to a comment,	Uk (W2) = 0

Then, the utilities, U_i, of agent Ai are given as follows, where N_is, N_iv, and N_iw are the numbers of submitting, commenting, and responding to comments agents within the neighbors of agent Ai, where l refers to an integer. In this study, we set the behavior of the agent as three steps, S1 or S2, V1 or V2, and W1 or W2. A sample of behavior is shown in Figure 2.

U_i (4l, S1) = M N_is − F + R N_iv,
U_i (4l, S2) = M N_is

(1)

U_i (4l, V1) = −C N_is + R″ N_iw,
U_i (4l, V2) = 0

(2)

U_i (4l, W1) = −C″ N_iv,
U_i (4l, W2) = 0

(3)

Here, each agent decides their behavior every four steps. Depending on the behavior for steps 1, 2, and 3, each agent decides their behavior at 5, 6, and 7, as shown in

Table 1. Behavior of agents and the decision at time t. * refers to decision. Each agent decides per four time steps.

T	1	2	3	4	5	6	7	8
Action	S1/S2	V1/V2	W1/W2	*	S1/S2	V1/V2	W1/W2	*

.

3.2. Best Response Rule

Based on the best response rule, if U_i (4l, S1) is more than U_i (4l, S2), agent Ai chooses S1; otherwise, agent Ai chooses S2. If U_i (4l, V1) is more than U_i (4l, V2), agent Ai chooses V1; otherwise, agent Ai chooses V2. Then, if U_i (4l, W1) is more than U_i (4l, W2), agent Ai chooses W1; otherwise, agent Ai chooses W2. If the utilities are the same, it is set that agent Ai chooses the previous choice.

3.2.1. When Costs F, C, and C″ Are Positive

According to (3), agent Ai does not comment respond if cost C″ is positive. Then, no agents respond to comments; that is, the total number of responding to comments agents, N_iw, comes to 0. According to (2), agent Ai does not comment if all N_iw values are 0 and cost C is positive. Then, no agents comment; that is, the total number of commenting agents, N_iv, comes to 0. According to (1), agent Ai does not submit if all N_iv values are 0 and cost F is positive. Then, no agents submit; that is, the total number of submitting agents, N_is, comes to 0. Therefore, no agents submit, comment, and respond to comments; that is, all behavior is defective in terms of the prisoner’s dilemma when all costs are positive.

3.2.2. When Cost F, C, and C″ Are Zero and Reward M, R, and R″ Are Positive

According to Equation (3), it is possible that agent Ai responds to comments if cost C″ is zero. Then, some agents comment respond. According to (2), agent Ai comments if cost C is zero and reward R″ is positive. According to (1), agent Ai submits if cost F is zero and reward R is positive. Therefore, agents can submit, comment, and respond to comments when all costs are zero and all rewards are positive. That is, behavior depends on the costs and rewards.

4. Simulation Settings

In the simulation, the settings are as follows: In the population, there are 100 agents in the ring-structure social network. Cost C″ and reward R″ of responding to comments are the same as those of commenting. In a single simulation, 100 time steps are executed and the simulations involve 100 trials per each initial value. The initial values are the proportion of submitting agents, p(0), those of commenting agents, q(0), and those of responding to comments, r(0). Here, the three initial values are the same for simplification. The parameters are displayed in

Table 2. Parameters in the cases. F refers to the cost of submitting an article and M refers to the benefit of receiving an article. C refers to the cost of commenting on an article and R refers to the reward of receiving a comment. The definition of Type is given in Section 6.

Case	When Submitting		When Commenting or Responding to Comments		Type
	Cost F	Benefit M	Cost C	Reward R
0	3	1	2	9	X
1	0	1	2	9
2	3	1	2	0	Y
3	3	1	0	0	Z
4	3	1	0	9
5	0	1	0	9

. The parameters in Case 0 are the same parameters as those in [5]. The cost of submitting an article in Case 1 is less than that in Case 0. The commenting reward in Case 2 is less than that in Case 0 and less than that of the commenting cost, which is also dealt with in [5]. In Case 3, the cost of commenting and the rewards are less than those in Case 0. In Cases 4 and 5, the costs are less than those in Cases 0 and 1.

4.1. Social Network

Submitting an article relates to posting information about the damage after a disaster. Commenting on an article relates to verifying the information; responding to comments relates to the comment for the verification. For implication, each agent is assumed to have a neighborhood and interact in a defined location. Therefore, if an agent submits an article about a landslide, a neighbor agent verifies the information, not a distant agent.

Three types of networks are used.

4.2. Complete Graph

The first of these is a complete graph. The degree, k, is set as 99; that is, the network refers to an all-coupled network. Therefore, all cases in Table 2 are dealt with. The network is shown in Figure 3a. This network topology is simple and corresponds to small, closed, or primitive worlds. They may be unrealistic, but we utilize them for later comparisons.

4.3. Local Network

The second is a local network. The social network of agents is represented by a regular network with degree k. Each agent connects to the nearest k agents. The degree, k, is set to 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20 in increments of 2. There, the parameters of all of the cases in Table 2 are dealt with. A sample network of degree, k, 10 is shown in Figure 3b. This network topology is simple and corresponds to a regional social network. In a local network, each agent interacts with its neighborhood.

4.4. Complex Network

The third is a complex network. A social network of agents is represented by a small-world network and a scale-free network using the Kawachi algorithm [26], originally from a regular network of 1000 agents with 10 links. Then, their average degrees are 10. The number of agents, n, is set as 1000 because it is difficult to make a complex network of 100 agents. A node whose number of links is large must be much larger, whereas a node whose number of links is small must be much smaller. With a set probability, α, one link between agents is deleted. Then, if the degree of the agent is greater than the degree of the opponent agent, it is rewired to another agent; otherwise, the opponent agent is rewired to another agent. When all links of each node have been considered once, the procedure is repeated γ times. The probability, α, and times, γ, are shown in

Table 3. Probability, times, clustering coefficient, and characteristic path length.

	Small World	Scale Free
Probability, $\mathsf{\alpha }$	0.01	1.0
Times, $\mathsf{\gamma }$	3	20
Standardized clustering coefficient	0.99	0.11
Standardized characteristic path length	0.21	$\mathrm{\infty }$

.

We also show the social networks in terms of their two parameters, clustering coefficients, and characteristic path lengths [26]. The clustering coefficient is the extent to which the nodes adjacent to any node are linked to each other. The characteristic path length is the median of the means of the shortest path lengths connecting each node to all the others.

The small-world network is shown in Figure 3c, and the scale-free network is shown in Figure 3d. Here, small-world networks employ people who do not live in the same area but are returning home or staying for work, etc. Then, we investigated the role of weak ties in small-world networks compared with regular networks. Scale-free networks introduce few people who have many connections and many people who have fewer connections. Then, we investigated the role of the number of links in scale-free networks compared with regular networks. These complex networks represent real social networks or social media networks.

5. Simulation Results

5.1. Complete Graph

The simulation results in a complete graph are shown in Figure 3. In Figure 3a, the horizontal axis shows the initial value, p(0), which is the proportion of initial submitting agents, and the vertical axis shows the final value, p*, which is the average proportion of final submitting agents. In Cases 0, 1, and 2, the proportion of submitting agents is highest when the initial value is 0.5. In Cases 3, 4, and 5, the proportion of submitting agents increases in proportion to the initial value.

In Figure 4b, the horizontal axis shows the initial value, q(0), which is the proportion of initial commenting agents, and the vertical axis shows the final value, q*, which is the average proportion of final commenting agents. In Cases 0, 1, 3, 4, and 5, the proportion of commenting agents grows in proportion to the initial value. In Case 2, the proportion is always 0.0.

In Figure 4c, the horizontal axis shows the initial value, r(0), which is the proportion of initial responding to comments agents, and the vertical axis shows the final value, r*, which is the average proportion of final responding to comments agents. In Cases 0, 1, and 2, the proportion of responding to comments agents is about 0 for any initial value. In particular, in Case 2, agents cannot choose to respond to comments or not, because there is no agent comment, as shown in Figure 4b. In Cases 3, 4, and 5, the proportion of commenting agents grows in proportion to the initial value.

In Figure 4d, the horizontal axis shows the initial value, q(0), which is the proportion of initial commenting agents, and the vertical axis shows the final value, qq*, which is the average proportion of final not commenting agents. In all cases, the proportion of not commenting agents decreases in proportion to the initial value, except for the initial value of 0. The sum of the proportion of commenting agents q* and that of not commenting agents qq* may not equal 1, especially when p* is zero; that is, no agents do not submit articles.

In Figure 4e, the horizontal axis shows the initial value, r(0), which is the proportion of initial responding to comments agents, and the vertical axis shows the final value, rr*, which is the average proportion of final not responding to comments agents. In Cases 0 and 1, the proportion of not responding to comments agents is about 1.0, except for initial values of 0.0 and 1.0. Those are 0 in Case 2. In Case 2, agents cannot choose to respond to comments or not, because there is no agent comment, as shown in Figure 4b. In Cases 3, 4, and 5, the proportion of not commenting agents decreases in proportion to the initial value, except for the initial value of 0. The sum of the proportion of responding to comments agents, r*, and that of not responding to comments agents, rr*, may not equal 1, especially when q* is zero; that is, no agents do not comment.

5.2. Local Network

The simulation results of Case 0 in a local network are shown in Figure 5. In Figure 5a, the proportion of submitting agents is highest when the initial value is 0.5. Compared with Case 0 in Figure 4a, the results are similar when the degree, k, is large, whereas the result is shifted to the right with respect to the initial value, p(0), when the degree, k, is small. In Figure 5b, the proportion of commenting agents increases in proportion to the initial value. Compared with Case 0 in Figure 4b, the results are similar when the degree, k, is large, whereas the result decreases when the degree, k, is small. In Figure 5c, the proportion of responding to comments agents is about 0 in any initial value. These results are similar to Case 0 in Figure 4c.

In Figure 5d, the proportion of not commenting agents decreases in proportion to the initial value when the initial value is not 0.0. Compared with Case 0 in Figure 4d, the results are similar when the degree, k, is large, whereas the result decreases when the degree, k, is small. In Figure 5e, the proportion of not responding to comments agents is close to 1.0 when the initial value is not 0.0 or 1.0. Compared with Case 0 in Figure 4e, the results are similar when the degree, k, is large.

The simulation results of Case 1 are omitted as the results are similar to those of Case 0.

The simulation results of Case 2 in a local network are shown in Figure 6. In Figure 6a, the proportion of submitting agents is highest when the initial value is 0.5. Compared with Case 2 in Figure 4a, the results are similar when the degree, k, is large, whereas the results are shifted lower when the degree, k, is small. Figure 6b shows the proportion of commenting agents. Similar to Case 2 in Figure 4b, the results are 0 in any degree, k, and any initial value. In Figure 6c, the proportion of responding to comments agents is 0 in any degree, k, and any initial value, which is similar to Case 2 in Figure 4c.

Figure 6d shows the proportion of not commenting agents. The results decrease when the degree, k, is small. Compared with Case 2 in Figure 4d, the results are similar when the degree, k, is large. In Figure 6e, the proportion of not responding to comments agents is 0 in any degree, k, and any initial value. Compared with Case 2 in Figure 4e, the results are similar.

The simulation results of Cases 3, 4, and 5 are similar; therefore, the results of Case 4 are shown in Figure 7. In Figure 7a, the proportion of submitting agents grows in proportion to the initial value, which is similar to Case 4 in Figure 4a. The smaller k is, the more it deviates from the results of Case 4 in Figure 4a. In Figure 7b, the proportion of commenting agents grows in proportion to the initial value, which is similar to Case 4 in Figure 4b. The smaller k is, the more it deviates from the results of Case 4 in Figure 4b. In Figure 7c, the proportion of responding to comments agents grows in proportion to the initial value, which is also similar to Case 4 in Figure 4c.

In Figure 7d, the proportion of not commenting agents decreases in proportion to the initial value. In Figure 7e, the proportion of not responding to comments agents decreases in proportion to the initial value. These results are similar to Case 4 in Figure 4d,e; the smaller k is, the more it deviates from the results of Case 4 in Figure 4d,e.

5.3. Complex Network

The simulation results of a small-world network and a scale-free network are similar; therefore, the results of the small-world network are shown in Figure 8. In Figure 8a, the properties of the proportion of submitting agents are similar to the results of the complete graph in Figure 4a. The proportion of submitting agents depends on the costs and rewards, as well as the initial value, whereas that of Case 2 deviates slightly from the results of the complete graph. In Figure 8b, the properties of the proportion of commenting agents are similar to the results of the complete graph in Figure 4b. The proportion of commenting agents depends on the costs and rewards, as well as the initial value, whereas that of Cases 0, 1, and 2 deviate slightly from the results of the complete graph. In Figure 8c, the properties of the proportion of responding to comments agents are similar to the results of the complete graph in Figure 4c. The proportion of submitting agents depends on the costs and rewards, as well as the initial value, whereas that of Case 2 deviates slightly from the results of the complete graph. In Figure 8d, the properties of the proportion of not commenting agents are similar to the results of the complete graph in Figure 4d, though some are deviating from the results of the complete graph. The proportion of not commenting agents depends on the costs and rewards, as well as the initial value. In Figure 8e, the proportion of not responding to comments agents is similar to the results of the complete graph in Figure 4e, though some deviate from the results of the complete graph. The proportion of not commenting agents depends on the costs and rewards as well as the initial value.

They are also similar to the results of the local network with degree 10, as shown in Figure 3, Figure 4 and Figure 5.

6. Discussion

6.1. Regarding Social Network

The costs and rewards of commenting and responding to comments are examined through three kinds of networks.

In the complete graph, the results are classified into three types, X, Y, and Z, as shown in Table 2. Type Z corresponds to Cases 3, 4, and 5, where the costs of commenting and responding to comments are zero. In Type Z, the proportion of submitting, commenting, and responding to comments increases in proportion to the initial value, as shown in Figure 4.

In the rest of the cases, the costs of commenting and responding to comments are positive. Cases 0 and 1 are Type X, where the rewards of commenting and responding to comments are positive. In Type X, the proportion of submitting agents is highest when the initial value is 0.5. There are limitations for the proportion of submitting agents, and the proportion of commenting increases in proportion to the initial value, which is similar to Type Z. Moreover, the proportion of responding to comments is always zero.

Case 2 is Type Y, where the rewards of commenting and responding to comments are zero. In Type Y, the proportion of submitting agents is highest when the initial value is 0.5, which is similar to Type X, and the proportion of commenting is always zero. Moreover, the proportion of responding to comments is always zero, which is similar to Type X. By comparing Types X and Y, the same results are shown for the proportion of submitting and responding to comments, but different results are shown for the proportion of commenting; therefore, this difference results from the differences in rewards of commenting and responding to comments.

It has been shown that if the reward for commenting is more than the cost, the proportion of submitting articles, commenting, and responding to comments will increase [5]. Our results support Type Y [5] and show better ways in Type Z.

We found that receiving a reward for commenting on articles and responding to comments affected the proportion of commenting, whereas a cost for commenting on articles and responding to comments did not affect the proportion of submitting and responding to comments. No effect on submitting costs was observed.

Next, let us take a look at local networks. The characteristics are similar to the results in the complete graphs. When the cost of commenting is zero, which is true in Cases 3, 4, and 5, which are Type Z, the proportion of submitting and comment responding tends to increase, as shown in Figure 7. In Cases 0 and 1, which are Type X, the proportion of submitting is not high and the proportion of responding to comments tends to increase, as shown in Figure 5. The proportion of responding to comments is zero in any degree, k, or any initial value. In Case 2, which is Type Y, the proportion of submitting is not high and the proportion of commenting and responding to comments is zero in any degree, k, and any initial value, as shown in Figure 6.

As for the degree of social networks, the smaller the degree, k, the smaller the proportion of agents submitting articles, commenting, and responding to comments. Though the proportion of not commenting and not responding to comments agents is similar to the complete graph, it is also lower than that of the complete graph. Then, the results show that the proportion of not commenting and not responding to comments agents becomes small in a local network.

Finally, in complex networks, the results are similar to the results of the complete graph. The proportion of submitting, commenting, and responding to comments agents depends on the costs and rewards, as well as the initial value. Though the proportion of not commenting and not responding to comments agents is similar to the complete graph, it is also lower than that of the complete graph, which is similar to that of a local network. The results show that the proportion of not commenting and not responding to comments agents becomes small in a complex network as well.

6.2. Previous Study

Our previous study showed that collective behavior using a game theoretic model becomes stochastic and is affected by the structure of the social network, the initial collective behavior, and the diversity of the payoff parameter [27]. The stochastic collective behavior comes from the random choice of agents at first. The other study shows that the choices of hub agents, who have so many connections, affect the collective behavior of a scale-free network [28].

A previous study [22] showed that the results in a small-world network were quite similar to those of a complete graph of meta-reward games. Furthermore, it showed quite different results in a scale-free network compared to complete graphs and that scale-free networks make cooperation more prevalent.

From these studies, we expected different properties of results between regular and complex (small-world and scale-free) networks; however, in this study, the results of a scale-free network were similar to those of a small-world network. That is, the proportion of submitting, commenting, and responding to comments agents depends on the costs and rewards, the initial value, and the degree of the network.

It is considered that the difference from the former study [22] originated from the decision behavior, where each agent decides the base posting and comment posting rate via a genetic algorithm. Then, some agents with many links, which are hub agents, play an important role, and the decisions of hub agents may not consider the costs and benefits of other agents who have few links [22].

From the three kinds of networks, the properties of the results do not depend on the network structure, which is a novel and unexpected result. However, thanks to this, the properties in several social networks are expected to be predictable. The proportion of submitting, commenting, and responding to comments agents depends on the costs and rewards, the initial value, and the degree of a network, though the properties can be suppressed by agents with few links. Additionally, few connected links make the proportion of not commenting and not responding to comments agents small; that is, they prevent not commenting and not responding to comments.

6.3. Practical Application

It was found that the costs of commenting, responding to comments, and not submitting articles should be small to encourage submitting, commenting, and responding to comments. Here, the cost of these is considered. In the first phase, the cost of submitting refers to the cost of reporting a disaster. It is considered that the person who discovers it owes it, but the submitting cost does not affect the cooperation. In the third phase, the cost of responding to comments refers to the cost of saying thank you for the verification of a reported disaster. It is considered almost free. In the second phase, the cost of commenting refers to the cost of verifying the cost of a disaster. It is considered that verifying by geographically close populations is reasonable. On the other hand, it is considered that verifying by geographically remote populations is expensive and takes a long time. This shows that certification by distant agents that do not live around the site and connect only via a social network or the Internet is not sustainable.

The results support everyday analysts [15]. Everyday analysts are citizens who have a discerning eye and accurate localized information. In particular, commenting on articles refers to their role. They compare information elsewhere with the situation that they are currently experiencing. The achievement of trust is the goal for them, without additional support to further verify information. The everyday analyst lives around the site and the cost of verifying the information is very low, as well as being necessary to the citizen in practice. Therefore, the simulation results show that everyday analysts are necessary for the persistent confirmation of disasters.

7. Conclusions and Possible Future Work

When a landslide occurs, the person who discovers it will likely report the disaster. However, the person who receives this report will likely send someone on site to check, since the reporter may have misread the information. This allows third parties to make use of the confirmed information. Facilitating such mechanisms for reporting, confirming, and utilizing disaster information is considered to be necessary for sharing the details of one. In this paper, we proposed and analyzed an agent-based model that incorporates disaster behavior into the model of Toriumi et al. The reporting of a disaster refers to submitting articles, confirmation of the information by another person refers to commenting on articles, and utilizing the information refers to responding to the aforementioned comment using the framework of meta-reward games based on the prisoner’s dilemma game. Then, we analyze the relationships between the costs and rewards to encourage cooperation in several social networks.

In the complete graph, the costs of commenting, responding to comments, and not submitting articles should be small to encourage submitting, commenting, and responding to comments. In a complex network, the simulation results are similar to those of a local network in which the proportion of not commenting and not responding to comments is lower than that of the complete graph. There, few connected links prevent not commenting and not responding to comments. The properties of the results do not depend on network structure, which is a novel and unexpected result. It is expected that the properties of real social networks will be predictable.

As for possible future work, for more realistic decisions of people, we will adopt noise. In fact, in this study, all behaved rationally, but there are some people who do not behave rationally. We will then adopt a distinction between correct and incorrect information considering the role of non-rational people during a disaster.