Recently, the Werewolf game, one of multiplayer incomplete information games, is recognized as a promising research testbed for articial intelligence. In this work-in-progress paper, in order to obtain useful knowledge on the Werewolf games, log analyses of human players in the Werewolf BBS are conducted. By applying inductive logic programming to the log data of six games in the BBS, we attempt to extract classi cation rules on being attacked, executed and voted, whose bodies compose predicates representing players' past behaviors. In preliminary experiments, classi cation rules capturing characteristic behaviors among multiple agents were successfully obtained.
The Werewolf game is one of conversation-based role-playing party games. The game consists of two teams, werewolf team and villager team. Only werewolves can recognize their teammates, while villagers are given no information to which team each player belongs. Some villagers have a special role and they can obtain additional information by their own ability. Such information heterogeneity is one of main characteristics of the game. In the game, villagers try to nd and execute all werewolves, while werewolves try to deceive and eliminate villagers by attacking them. The Werewolf game has two phases, day and night. These two phases are iterated during the game. Players discuss to nd out werewolves or to deceive villagers in day phase. At the end of day phase, an executed player is decided by majority voting. In night phase, werewolves select a villager and attack him/her. Executed or attacked players get kicked out of the game.
The Werewolf game is recognized as a promising research testbed for arti
cial intelligence. Several research on the game have been reported recently. For
example, a method of game logs analysis based on attunements and rebuttals
is proposed to extract useful knowledge for the strategy construction[
In this work-in-progress paper, in order to obtain useful knowledge for building intelligent software agents for the Werewolf game, log analyses of human players are conducted by using inductive logic programming.
The Werewolf BBS1 is an online community website for the Werewolf game where a text-based chat system is provided for playing the games. The Werewolf BBS is a real time communication system. One day in the Werewolf game corresponds to one day in the real world. Players can communicate each other by text only. No voice and video messages can be exchanged.
All conversations by players are recorded during the game. There are four types of log data in the Werewolf BBS. We focus on the \white logs" which all players can browse as a target of our analysis. 3 3.1
We prepare six standard and average games for the analysis. Three of them are the games werewolf teams won and the rests are the games villager teams won. Fifteen players having enough experience participate in each game. While werewolf teams consist of three werewolves and one lunatic, villagers teams have eleven players including three villagers having special roles. Three games the werewolf team won have eight days to the end. They contain 1234.0 records on average. The rest three games the villager team won have seven days and contain 1166.6 records on average. 3.2
We prepare twelve predicates to represent players' behaviors by considering the
Werewolf protocol[
In addition to the facts, we prepare twelve intensional rules for handling behaviors in previous days as background knowledge in ILP. All rules have the form of
Pred( Game:Day, N, Player, Args ) :prev days( N ), PDay is Day - N,
Pred( Game:PDay, Player, Args ).
and represent that a player Player took an action Pred N days ago from Dayth day in a game Game. The predicate prev days/1 is an auxiliary predicate de ned as prev days(N):- member(N, [0,1, ,X]) where X is a parameter to control the maximum time difference. We set X to 3 in the experiments. The predicate P red is instantiated by twelve predicates for the facts. For example, by using `comingout', we obtain a rule for the past (and current) behavior on comingout as comingout( Game:Day, N, Player, Role) :prev days( N ), PDay is Day - N, comingout( Game:PDay, Player, Role ). where an argument Role shows the role a player Player claims. The rule which captures past behaviors on `line' is shown below.
line( Game:Day, N, Player, A, B ) :prev days( N ), PDay is Day - N, line( Game:PDay, Player, A, B ).
This rule states that a player Player estimated that two players A and B belong to the same team N days ago from Dayth day in a game Game. 3.3
In this work-in-progress paper, three classi cation tasks are treated.
The rst task is to derive classi cation rules which characterize the behaviors of executed players. A predicate executed( Game:Day, Player ) is used for this task, which represents a player Player was executed on the Dayth day in a game Game. From the log data, 39 positive examples and 528 negative ones are extracted.
As a second task, we try to obtain classi cation rules for the behaviors of attacked players. We prepare a predicate attacked( Game:Day, Player ) which indicates that the werewolf team succeeded in attacking a player Player on the Dayth day in a game Game. Note that, while executed players are selected from all participants by voting, attacked players must be members of villager team or a lunatic. In addition, hunters sometimes guard the villagers from the attack by werewolves. Thus, positive examples for this task are less than those in the rst task. Only 27 positive examples and 505 negative ones are used.
The third task is to obtain rules on a voting behavior. A predicate voted( Game:Day, Player ) states that a player Player got a vote on the Dayth day in a game Game. In total, the log data contains 89 positive and 478 negative examples, respectively.
An inductive logic programming engine Aleph2 is employed to solve the classication problems shown in the previous section. We used three commands for theory construction (induce/0, induce cover/0 and induce max/0) in order to extract classi cation rules as many as possible. In the following subsections, the results of each classi cation task are described. 4.1
The Aleph system extracts 28 classi cation rules on the execution. An example of derived rule is shown below. The corresponding graphical representations is shown in Fig.1(a). In the gure, each node corresponds to a player. Directed edges represent predicates in the rule body and they show relationships among agents. A number n in the parenthesis means that the corresponding behavior to the edge is observed n days before from when the action in the rule head occurred.
executed( Game:Day, X ) :estimate( Game:Day, 0, Y, X, wolf ), estimate( Game:Day, 1, X, Y, not(wolf) ), agree( Game:Day, 2, X, Z ).
This rule says that: (1)a player Y believes that a player X is a werewolf on the execution day, and (2)the executed player X estimated that a player Y is not a werewolf one day ago, and (3)he/she agreed with a player Z two days ago. We believe that this rule captures an appropriate situation in selecting players to be executed because the executed player X is suspected as a werewolf by other player Y.
This rule can be instantiated by substituting two villagers for X and Z and a lunatic or a werewolf for Y in plural games irrespective of the winning team. In addition, X is never instantiated by a player in the werewolf team. We can infer from the above situation that this rule shows the behavior of a villager targeted by the werewolf team. 4.2
We obtain 23 classi cation rules on \being attacked" by the werewolf team. Within the 23 rules, 15 rules have predicates question, answer, agree or disagree, which show communications with other players. An example of obtained rules, depicted in Fig.1(b), is explained below.
attacked( Game:Day, X ) :estimate( Game:Day, 3, Z, X, not(wolf) ), estimate( Game:Day, 0, Y, X, not(wolf) ), agree( Game:Day, 0, Y, Z ). 2 http://www.cs.ox.ac.uk/activities/machinelearning/Aleph/aleph (a) Execution (b) Attack (c) Vote
This rule shows the following situation : (1)a player Z estimated that an attacked player X is not a werewolf three days before, (2)a player Y also believes that X is not a werewolf and agree with Z on the attacked day. We can easily imagine a basic strategy of the werewolf team from the rule. The team selects a player X to be attacked, who is less likely to be executed by villagers because X is not suspected by other two players Y and Z.
This rule says that : (1)a player Z, who claimed that he/she is a hunter one day ago, asks a player Y some questions, and (2)a player X, who disagreed with the player Y one day ago, got a vote. By applying this rule to the log data, we con rm that this rule ts well into the players getting a few votes. 5
In this work-in-progress paper, by applying inductive logic programming to three classi cation problems, we succeeded in obtaining rules which capture characteristic behaviors among multiple players in the Werewolf BBS.
As one of future works, we plan to incorporate certain predicates representing
each player's view and intention. In the Werewolf game, players having different
roles have different information. For example, wolves can recognize teammates,
but others cannot. Seer players can perceive spurious seers easily because other
player must not be a seer. By utilizing these heterogeneities effectively and by
preparing certain mechanisms to estimate other players intention, we can expect
to develop sophisticated and accurate classi cation rules for each role. For this
purpose, we plan to employ the framework of answer set programming and its
induction algorithm[