When we repeat these kind of experiments we start to create mathematical models of patterns of behavior. Mathematical models are very important in game theory and in video game design. We use them to create complex social and combat mechanics and AI interactions. We use them to create strategy scenarios in Real-Time Strategy games. And we use them to balance PvP strategy games of all sorts.
It really is a math equation with a human component. Mathematics is core to almost all game design as it relates to game theory. For the purposes of this course it is not necessary to display and explain all of the different ways to model game theory scenarios. It is, after all, not a math course. Rather we will seek to understand the overall concepts and allow those who want to, to further explore the detailed math models. What we will focus on is the concepts of strategy in game theory and how it relates to game design.
The Science of Strategy
Can people’s thought processes and actions be reduced to a set of probability numbers like crafting the wing of an airplane? Do people function like foreseeable algorithms to the point of accurate predictability? In this case, we can only focus on two people where the “winner” only gains what the “loser” loses. It does not consider a host of other possible variations in human behavior, complexity, experience, or motivation. The truth is most things are much more complex than the Prisoner’s Dilemma. What game theory really does is look at how people choose solution strategies that have defined value over other solutions.
The Nash Equilibrium
In 1994, mathematician John Nash, who was the subject of the movie, A Beautiful Mind, won a Nobel Prize for his work on economics using game theory. Nash developed solution concepts as formal rules of how strategies will be adopted by people in states of competition. Specifically, the Nash Equilibrium states that each player is assumed to understand the optimal strategies of all other players, and that no one will gain by one competitor changing only their strategy. In other words, if all players have adopted a strategy that is the best strategy in relation to others strategies, we have an equilibrium. Like the perfectly balanced game paper, rock, scissors – each strategy dominates another one and is countered by another as well. In a video game, this means a balance of strategies among all players, which is essential for good game design.