Lightweight Interactions for Reciprocal Cooperation in a Social Network Game

Abstract

The construction of reciprocal relationships requires cooperative interactions during the initial meetings. However, cooperative behavior with strangers is risky because the strangers may be exploiters. In this study, we show that people increase the likelihood of cooperativeness of strangers by using lightweight non-risky interactions in risky situations based on the analysis of a social network game (SNG). They can construct reciprocal relationships in this manner. The interactions involve low-cost signaling because they are not generated at any cost to the senders and recipients. Theoretical studies show that low-cost signals are not guaranteed to be reliable because the low-cost signals from senders can lie at any time. However, people used low-cost signals to construct reciprocal relationships in an SNG, which suggests the existence of mechanisms for generating reliable, low-cost signals in human evolution.

A Appendix

1.1 A.1 Game Information

We analyzed cooperative behavior in the SNG, “Girl Friend BETA.” Table 4 presents the game information. In this SNG, players create individual decks of cards that they collect and then use their decks to perform tasks in the SNG. A powerful deck, constructed from powerful cards, provides an advantage for game play in various situations. The players’ primary motivation in the SNG is to obtain powerful cards. Players can obtain powerful cards as top-ranking rewards (see details later) or by casting lots called “Gacha.”

Players can communicate at any time using three types of simple text messaging. The first type was a message from one player to another (direct messaging). The second type was a message from a player to their group members (group messaging). The third involved posting on the forum for their group (forum posting). These messages had no negative effects on either the senders or receivers, but they also had few or no positive effects². We limited the data to intragroup communication and cooperation.

Table 4. Game information

1.2 A.2 Game Rules

Our analysis target was a raid event (Fig. 2), in which players attack large enemies³ and acquire “event points.” Players competed in the rankings based on their event points, because they received better awards as their rankings increased.

Fig. 2.

Overview of raid event. A player conducts “quests” to find enemies (1). The player begins a battle upon finding an enemy and then attacks the enemy to obtain points (2). Enemies with very high hit points are strong; thus, they can call for help from other group members whom they have helped to win the battle (3). Players who helped had their point gain increased by 1.5 times (4). Players compete in rankings based on their points (5).

Players conduct quests⁴ to find enemies during an event. Players begin battles when they find an enemy and then attack the enemy to obtain points. However, enemies with very high hit points are strong, making it difficult for players to win these battles unaided. Thus, they can call for help from other group members, to win the battle. Players who helped had their point gain increased by 1.5 times. Therefore, players help their fellow group members to acquire more points.

Players’ point gains are proportional to the amount of damage caused during attacks, i.e., more powerful decks earn more event points. A player immediately acquires points upon attacking an enemy, even if the enemy is not defeated. However, a player cannot battle another enemy while already battling another enemy, and that enemies’ hit points increase with each battle; therefore, players must attack enemies repeatedly in the latter half of an event. Thus, a player who finds an enemy or helps a fellow group member must defeat the enemy before taking a next action, or wait until that the enemy leaves⁵.

Players increase the amount of damage caused during their attacks by launching “combo attacks,” alternate attacks by two or more players in which the players need to launch attacks within ten minutes after other players⁶. The longer a chain of combo attacks, the more acquisition points are acquired. Battling enemies together with fellow group members increases the effectiveness of acquisition points.

Players must use a quarter of their attack points to attack; thus, they can attack four times when their point totals are full. There are two methods for replenishing these points: wait for the points to replenish over time or use an item that costs 100 JPY (such items are also sometimes distributed in the game as rewards).

Thus, players must use their resources (items and time) effectively to progress to a higher ranking, e.g., responding to a “help” request from their group members to acquire a point gain increase of 1.5 times, increasing the number of “combo attacks” to increase the amount of damage, and reducing the disable time. We defined payment efficiency as the event points per payment, as in game theory.

1.3 A.3 The Test Scenario

It was impossible to track every cooperative behavior, because players can exhibit various behaviors in the SNG. Hence, we focused on one easily tracked cooperative behavior, and we regarded its frequency as players’ cooperativeness.

We focused on the following scenario based on these rules to define players’ cooperativeness. (a) An enemy is attacked by a player and fellow group members. (b) The enemy’s hit points are very few. In this scenario, players who defeat the enemy will acquire only a few event points, because their attack power is higher than the enemy’s hit points. Thus, their behavior is not efficient for acquiring event points. By contrast, if the players’ attack power is lower than the enemy’s hit points, their behavior is efficient for acquiring event points. Furthermore, they cannot battle another enemy, if battle with one enemy is ongoing, and therefore must wait until they defeat the enemy to exhibit efficient behavior.

Table 5. Payoff matrix for the test scenario consisting of two players and an enemy with very few hit points. The player who attacks the enemy receives S, and the other player receives T. If neither player attacks the enemy, then each receives P. Attack by both players is impossible, because either player can defeat the enemy

In simple terms, consider that two players battled an enemy in this scenario, where their relationship is represented in Table 5. The relationship between the variables is $T> S > P$ in this payoff matrix. Attack is not efficient, when S is less than T. However, if they do not attack the enemy, they waste time by waiting for someone else to attack, i.e., P is lowest. It is not possible to cooperate both players in this scenario, because an attack on the enemy by either player immediately defeats the enemy. The values of this payoff matrix depend on each players situation, e.g., the differences between the two attack powers⁷. In the scenario, both try to avoid the worst situation (i.e., they get P), but they also do not want to pay the cost to avoid the worst situation (i.e., they do not want to get S). This social dilemma is similar to the one in the “Leader game” (Table 1). In that game, Pareto efficiency is achieved when one cooperates, and the other does not. Then, the cooperator receives S, and the noncooperator T. That is, players receive a high payoff by sharing S and T on repeated plays of the game, a process known as ST reciprocity [30]. We recognized this cooperative behavior, which provided the payoff T from one to the other, as a cooperative behavior in this scenario.

Cooperative behavior is an inefficient attack, as shown in Table 5; thus we define $a_{ij}$ as the attack efficiency indicator: $a_{ij} = e_{ij} / M(\varvec{e_{i}})$, where $e_{ij}$ are the event points in player i’s jth attack and $M(\varvec{e_{i}})$ is the median of $\varvec{e_i} = \{e_{i1}, \cdots , e_{iN}\}$ (N is the frequency of player i’s attacks). We considered cooperative behavior to be in the range of $a \le 0.40$. Accordingly, we define $c_i$ as the proportion of cooperative behavior ($a_i \le 0.40$) for player i. We regarded a cooperator as a player where $c \ge 0.10$.