Basic Game Theory and Design

Basic Game Theory and Design

Davide Bisso

Game Design BS (Full Sail)

Game Theory: payoff Matrix (Normal Form Game)

Seeing as I’m studying to become a Game Designer, choosing the Game Theory: Payoff Matrix seemed most logical. The reason for my decision is partly due, because of how much Game Theory influences a Game Designer. This could range from tweaking stats, adding new features and implementing gameplay. This barely scratches the surfaces for what Game Theory does to Game Design, but I'll leave that for another post. The main thing to take away from this is; as a Game Designer, your overall goal is to give the player an enjoyable and satisfying experience. With the help of Game Theory we can make strategic decisions in order to achieve that goal.

Now you may be thinking, what is the Payoff matrix and how can it benefit us? To answer this question we need to understand, (1) what a game is and (2) how strategy applies to that game.  To put it simply, a game is a framework involving two or more players, where each player's success is determined not only by his/her own strategy, but by the strategies of all the other players in the game (multiplayer game). This leads us into defining strategy. A strategy is a complete plan of action for a player that explains how he/she will behave. Now that we understand these principles we can go back to our main question: “What is the Payoff Matrix and how can it benefit us?”

This question can be answered in many different forms, but I feel the best way to truly understand the overall concept is to illustrate an example. So, lets say we’re playing a typical *RTS game where you’re given just enough resources to either make one Orc or one Elf. Pretty standard. Now, lets assume that Elves always beat the orcs (their agility/dexterity is too much for the brutish orcs). Lets also say that, when an elf fights another elf it’s an even battle. Each player will be awarded half a point. Lastly, lets assume winning the game earns the player one point. With these ingredients we can make a pretty basic illustration, which will look something like this:

Player 1 / Player 2

                                  Player 2 chooses orcs   | Player 2 chooses elves

Player 1 chooses orcs |        (1/2,1/2)            |           (0,1)

Player 1 chooses elves|           (1,0)                |       (1/2,1/2)

From looking at this Payoff Matrix, we can conclude that building an elf is the strictly dominant strategy. If my opponent builds an orc and I counter with an elf, I get 1 point whereas countering with an orc gives me an expected value of 1/2. Same goes for my opponent. If he/she builds an elf and I counter with an orc I am guaranteed to lose and get 0 points whereas countering with an elf, I can expect 1/2. With this notion, it’s clear building elves makes for a better scenario.

Now, if I were to actually create this game, some form of balance would have to be implemented. Experienced players would come to understand that elves win the game every time and that orcs are a pointless race (sorry to all the orc fans out there). From a designer’s perspective, I can say this game has the potential to be fun, but it needs some work. By tweaking stats, creating a new race, or reducing the resources on the orcs by half are some of my quick solutions. 

Thank you for your time and patience. Any feedback would be appreciated.