**Playing for Real: A Text on Game Theory**, by Ken Binmore.

In a text on game design you’ll often find a short advisory note somewhere in the introduction that distinguishes game *design* from game *theory*. Game theory has nothing to do with the entertainment industry and is best summarised as the mathematical foundation of economics. It attempts to provide a model of rational decision making in which players strive find strategies to optimise their payoffs. The ‘games’ analysed are usually very simple bargaining problems and are not exactly what we’d consider “fun”. Why then would I be recommending a game theory text on a blog about game design?

There are several reasons. The most obvious is that a lot of multiplayer *are* bargaining problems. An understanding of at least the basics of economic behaviour is important if you are going to create any kind of trading game. It is very easy to unbalance a virtual economy if you don’t know what you’re doing and a broken economy is rarely fun.

Furthermore, game theory teaches us something about the general problem of strategic decision making involving many players. It introduces us to useful concepts such as zero-sum games, mixed strategies, cooperative games, and utility theory. Even when players don’t follow the ‘rational’ strategies game theory dictates, we can still recognise it as the goal to which they are striving.

In fact, the more counter-intuitive results of game theory form some of the most interesting games to play, because the best strategies are subtle and controversial. Every game designer should be aware of games such as the Prisoner’s Dilemma and Chicken. These simple combinations of reward mechanics can create complex player interactions, which we can incorporate into our games. Alternatively, such dynamics may be unexpected and unwanted. Understanding their origins gives us the ability to control them.

There are many books on game theory addressed at a variety of different audiences, depending on their level of mathematical sophistication. I recommend this one as a comfortable middle ground. The ideas are reasonably accessable to a non-mathematician but there is also enough mathematical rigour to satisfy the theorists. Later chapters do get rather math-heavy, but there it still benefit to be gained by skimming the proofs and just reading the descriptions.

While game theory may seem dry and academic, it provides valuable insights into strategic behaviour, which is at the heart of many of our games. It is therefore a valuable tool in the game designers toolkit, one I definitely recommend you acquire.

Mixed strategies are key to understanding players’ interaction with the game and each other. A player will tend to optimize how they play, and will settle into a (Nash) equilibrium. If that equilibrium allows “interesting choices” it will be a good game with balance and playability. Many (most?) games are too complex to fully analyze in this way, but even a basic understanding of the principle can be helpful.