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Game Theory in Video Games: How You’re in a Prisoner’s Dilemma

In the last decade, online gaming, especially massively multi-player online gaming, has become a topic of discussion amongst game theorists. However one soon notices that each resource or article about the topic seems to come from one of two types of sources. One source of discussion is academics with strong understanding of game theory and mastery of the nuanced field. This leads to a discussion which is in-depth but impenetrable and nearly unreadable (to the layman).  This also is rarely specific to a type of game and gives no help to a player. The other source is experienced players of online games who have detected patterns from their play and then realized the game theory implications of it. These articles are equally unreadable by those who don’t know the specifics of the game being discussed. I wanted to join the fields by starting serious game theory discussion from the perspective of experienced game enthusiasts.

In team-based games there is obviously an incentive to work as a team and support those around you for a common goal. In all the games I’ll be discussing that is the case. But there is another factor which affects the way we decide to play the game. This is a more hidden feature of online gaming that I’ll call the “fun factor”. It is hard to describe but common to many games. It is the inherent value we gain from playing the most fun role in a game even if it isn’t the most helpful to the team. Examples range from the vague, such as being damage dealer in a multi-player online battle arena game, or the specific, such as playing the Sniper class in Team Fortress 2.  From the competition of the two factors comes a strange payoff matrix (pictured and discussed below). In one regard you want to play a supportive character and help your team so you can win, in the other regard you want to play a fun character, even if it means losing. You are also on a team of people who are making this decision.

To aid the discussion I have made a payoff matrix using the following assumptions. Firstly it is more fun to play without the team in mind, that is, you receive 1 point for playing a supportive role and you receive 2 points for playing a fun role. Also we’ll assume you receive 2 point for winning and no points for losing. You can only win if both you and all your teammates decide to support each other.

Player

(Teammates, Player)

Support Team

Play for Fun

Teammates

Support Team

(3,3)

(1,2)

Play for Fun

(2,1)

(2,2)

Here you can see where the game theory is important to the discussion. Clearly the best option for everybody is the Support their team and work together for a win. You get to have some fun playing and also get to win the game. That position is Nash equilibrium.  But in the real world you can see that if you are fearful that somebody will choose to break free from this Nash equilibrium, you are better off hedging your bets and assuring that you receive at least 2 points but playing for fun. That is why you will often see experienced players forming perfect team compositions and gladly taking a supportive role. But newer players, who lack to experience, will play for fun and cause the players around them to play for fun as well.

Players can use this knowledge to decide how they want to play but designers of games can use this information as well. Game companies are concerned with the maximum payout for their players, the “social welfare” of the matrix. To accomplish this there is usually a ranking system which groups high “skill” players (players who win games by working together). This system also drives together players who lose often, likely do to their choice to play for fun and not to win. That way the game company can move people away from the situations which involve a social welfare of 3 and towards the situations which have welfare payouts of 4 and 6, thereby making everybody enjoy their game more.

Examples of source type 1 (experience game theorists):
http://www.digra.org/dl/db/06278.10422.pdf
http://www.santafe.edu/media/workingpapers/09-11-042.pdf

Examples of source type 2 (experience gamers):

http://na.leagueoflegends.com/board/showthread.php?t=2498690

http://na.leagueoflegends.com/board/showthread.php?t=2572218

-TheRealHumanzeell

Comments

One Response to “ Game Theory in Video Games: How You’re in a Prisoner’s Dilemma ”

  • Mark Wright

    I think a great example of this is the Capture the Flag mode in Black Ops 2:

    “Capture the Flag (shortened to CTF) is a mode that pits two teams of six players each, with the objective to grab the other team’s flag and return it to your base. Note that if the enemy team has your flag, it must be returned to your base before you can capture their flag.

    Each match is divided into two rounds of 5 minutes each, with each flag returned to your base rewarding your team with one point. Three points are needed to win a round, or the team with the most points in the round will win in the case of a tie. In the case of a tie score (of rounds), then the match will go into overtime, where the time limit is shortened and the score limit is reduced to one.”

    http://gamewise.co/games/45771/Call-of-Duty-Black-Ops-II/Multiplayer/Modes/Capture-the-Flag

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