### Game Theory in Video Games

As we have seen, game theory wasn’t conceived for the purpose of making video games, but the concepts are a perfect match. From the simplest form of zero-sum games we can take and expand game theory to match the design strategies for most video games. Variety in games stems from how these concepts are presented, altered, or combined. We should be noticing a lot of crossover in these game theory concepts at this point. Now we will look at some specific game theory concepts and see how they are applied to some popular video game genres.

**Symmetric / Asymmetric**

When we talk about symmetric vs asymmetric game design we are talking about different methods of achieving balance in game play. A symmetric design gives all players the exact same skills and resources. There is zero difference in the actions one player can take over another. Games in the Halo series fit a mostly symmetric design: each player moves at the same speed; each player can take exactly the same amount of damage; and each player has the same access to the same set of skills, weapons and game options. In doing this, the designers have created perfect balance among players; at least in the sense of potential player vs player scenarios. Only skill at manipulating the controller separates one player’s advantage at the game from another. Sports games are another good example of symmetric designs because each team or player should be almost evenly matched in terms of skill levels their choices for actions in-game.

Asymmetric games also seek to ultimately balance player vs player but still offer some variety in playable characters. For most games like this, the skills and abilities of player characters are a series of benefits and tradeoffs. Let’s look at Team Fortress 2 as an example of an asymmetric game design. In Team Fortress 2 each character class is slightly different. Some are faster with the tradeoff of having fewer hit points. Some have more powerful weapons with a tradeoff of being bigger targets. There are many combinations of benefits and penalties, but ultimately there is still balance. In essence, each benefit has a certain value that is countered by an equal penalty. This allows for many methods to victory while maintaining a fair and balanced experience.

**Cooperative / Competitive**

With the rise of the Internet came MMO gaming and new ways to create games that are both cooperative and competitive on a grand scale. In general, cooperative games are games where people work together to find solutions to victory and competitive games are games where they work against each other to win.

In cooperative games, it is possible for all players to lose the game or for all players to win the game. While not a dedicated cooperative game, World of Warcraft has many cooperative elements. The best example is in the game’s boss raids where perhaps dozens of players will gather with one goal in mind: defeat the boss or die trying. In this scenario, all the players must coordinate their attack together for an all or nothing fight to the finish. If the boss is defeated, everyone shares in the victory. If the boss is not defeated, everyone shares in the loss.

Most games, however, are designed to be competitive. Someone (or many players) will win and the rest will lose. There are countless examples of this premise such as any sports game or any game with player vs player elements. It is in these types of games game theory becomes so relevant and important in terms of creating strategies in a game that are balanced and yet are not exercises in pointlessness.

**Zero-sum / Non Zero-sum**

Zero-sum games are ones in which one player’s gains are directly related to another player’s loss. Some zero-sum games provide what is called perfect information; that is, all players know all of the actions of the other players. While not strictly a video game, chess is a perfect example of a zero-sum game, where players have perfect knowledge of the other player’s actions. Zero-sum games without perfect knowledge could include many Real-Time Strategy (RTS) games where one player’s knowledge of the other player’s actions may be limited by certain factors such as fog of war or lack of directly witnessing all of their actions. Extremely simple games such as Rock, Paper, Scissors are good examples of zero-sum games without perfect knowledge because the actions of all players are simultaneous and no one can accurately predict what an opponent will do. In addition, victory conditions are clear to all players with a single universal solution to achieving the goal of winning.

On the opposite side is Non Zero-sum games. In these games, there is no universal obviously accepted solution or destruction of resources. In many ways, non zero-sum game theory operates more like real life scenarios, so it makes sense that games that utilize non zero-sum game theory are mostly real-life simulation games like SimCity. Resource management does not necessarily permanently deplete resources and the games are generally non-competitive. Still, even simulation games do not completely stray from zero-sum concepts. Zoo Tycoon, for example has a money system that can eventually end the game because the player goes broke.

Pen and paper role playing games are the best examples of non zero-sum game theory. Players cooperate, they are not limited by a given set of solutions and the imaginary resources they can draw upon to solve problems are effectively, unlimited.

**Simultaneous / Turn-based**

There are huge differences in game play when players take turns than when everyone takes simultaneous actions. In a game theory view, it is a difference of information available. In simultaneous play, information is constant, but a player must manage their own ability to take actions with their ability to track the actions of an opponent. In a turn-based game, players can stop and examine game information at a more relaxed pace.

Many RTS games use a turn-based system. Each player gets a turn to examine the known information in the game; army placements, available resources, etc. and then gets to react to these elements with little or no time constraints. Once the player takes all the actions they can or want, it is the next player’s turn to do the same. Heroes of Might and Magic games are excellent examples of this.

Fighting games are good examples of simultaneous game theory in action. Each player chooses an attack or defensive move without any knowledge of what the opponent will do and all decisions are made at the same time. It is sort of like playing rock, paper, scissors, but with many more possible combinations. Knowledge of what the other play has done becomes irrelevant to what they will do next, and there is no way of knowing what they will do next. These are games of action and reaction with no time to ponder prior knowledge.

**Perfect Information / Imperfect Information**

What a player knows is an important aspect of any video game structure. Having access to certain knowledge changes gameplay as that knowledge is added to or reduced. In game theory, this is divided into perfect knowledge and imperfect knowledge.

Games with perfect knowledge mean that all the players not only know the game structure and rules, they also have complete information on all events in the game that have previously occurred. For instance, in a game of chess, each player is witness to every move their opponent makes is a perfect knowledge game. Imagine a game where there are 16 vs 16 player matches. There is very littler chance that any one player could have perfect knowledge of all things that have occurred in that kind of a match. In a large match like this players operate under imperfect knowledge, which is the sum of what they have seen and experienced plus the information that they receive from the Heads Up Display. Keep in mind what information your player will have available when designing.

From here we start to mix and match the above concepts, iterate on what works and what doesn’t and soon come to some core strategies that have balance, purpose, and are fun to play.