Exploring the Game Theory Behind Among Us
Among Us is a mobile/PC game that is currently gaining a lot of popularity and recognition among users between aged 13 to 20. According to the article, the game involves 10 players, and they are divided into two groups: 1-3 “imposters” and the rest are “crewmate”. The setting of this game is on a spaceship. The role of Crewmates involved completing several tasks, avoiding being killed by the imposters, and investigating to vote off the players that they think are imposters. The imposters need to find opportunities to kill the crewmates, meanwhile sabotage the spaceship to create distractions.
Having played Among Us several times by myself, I really agree with how the article describes this game as a social game like “Monopoly”. On one side, the game allows people to better know each other especially when they are discussing who should be voted out. On the other hand, this video game is successful because it does not only require good gaming skills, but also requires strategic thinking in order for crewmates to logic the imposters and for imposters to successfully disguise. Given this social quality of Among Us, I wondered if we could apply what we have learned in game theory, so that we can model the team decision making and predict if there is a best outcome.
As shown in the matrix below, there are two teams in a game as described above: crewmates (group on the left) and imposters (group at the top). For crewmates, the strategies they can choose are either completing the tasks (T) or trying to identify the imposters (I). For imposters, the two choices they have are to sabotage kill crewmates (K) or to sabotage (S). Now we can try to figure out the payoffs for each strategy:
For the crewmates, when imposters are trying to kill, the payoff for them to find the imposter is 2, and when the imposters are trying to sabotage, the payoff for them to find the imposter is 1, because it is relatively easier to identify an imposter when they just killed someone, and crewmates spot them being very close to the victim. It is very easy for imposters to argue that they were doing tasks when crewmates spot them sabotaging. Additionally, when crewmate choose to complete a task, the payoff will be 1 when the imposters are trying to kill, and 2 if the imposters are sabotaging. This is because when completing tasks, crewmates are less aware of the environment around, and are thus much more likely to get killed. Meanwhile, the lives of crewmates are not at stake when imposters are sabotaging.
Similarly, the reasonings above allow us to estimate the payoffs for imposters. When trying to kill, the payoffs if the crewmates are completing tasks are 2 and 1 if the crewmates are looking for the murderers. When trying to sabotage, the payoffs if the crewmates are looking for imposters is 2 and 1 when the crewmates are completing tasks.
With the reasonings above, we can come up with a matrix:
| Imposters | |||
| K | S | ||
| Crewmates | I | 2,1 | 1,2 |
| T | 1,2 | 2,1 | |
As seen on the matrix, there is no pure strategy Nash equilibrium present because there is no mutual best response for crewmates and imposters. For example, crewmates are willing to investigate when imposters are killing (i.e. being close to a victim), yet imposters will choose to sabotage if they see crewmates not doing tasks and walking around to investigate.
As a result, we can conclude that there is no optimal solution that allows both sides to win. The action of one group is largely dependent on the action of the other group. This finding is interesting because it helped me to understand why the game is appealing to many people: there is an unpredictability in which strategy to choose, and players have to be very observant of others’ actions throughout the game to make the best decision.
Source:
Picture source: Among us on steam. Among Us on Steam. (n.d.). Retrieved September 19, 2021, from https://store.steampowered.com/app/945360/among_us/.
Article source: Lorenz, Taylor. “Among Us: You’re the Impostor.” The New York Times, New York Times, 8 Jan. 2021, www.nytimes.com/2020/10/14/style/among-us.html?auth=login-google1tap&login=google1tap.