Game Theory – A Brief Introduction
A game is typically a structured form of outdoor play, often undertaken for fun or entertainment, and occasionally utilised as an educational tool as well. Games are very different from work, which normally are performed for pay, and from fine art, which are often more of an expression of personal or aesthetic impressions. In contrast, games are typically interactive, requiring the use of both eyes and mind in order to “win” the game. Most of us are familiar with video games, the ubiquitous joysticks and pointers that control the action of a computer-generated game but what many of us don’t realise is that games can also be played using a hands-on approach, using the motions of the body. Video games often incorporate elements of strategy into their design, requiring players to think carefully and creatively to emerge victorious.
Games can be divided into two main categories – pure strategy, where there is no direct interaction between the player and the computer-generated world, and pure simulation, where the player is directly involved in the simulation of the game’s environment. Pure strategy games are usually very competitive, with a focus being placed on mastering and applying a series of strategies to succeed. Simulation games, meanwhile, require players to think logically about how to best proceed, often employing abstract thinking techniques such as deduction, probability, etc. The key difference lies in the fact that the simulation requires the player to exert some skill on the overall outcome, while strategy requires no such effort.
Simulations and pure strategy games share certain common features, but in their most abstract form, they differ fundamentally in their fundamental structures. Pure strategy games are based on a set of game-theoretical principles, of which equilibrium is one of the most important. This means that in a game of strategy, all players will pursue a course of action that will minimize the likelihood of the other players getting ahead and taking control of the scenario.
This in turn implies that there are certain variables that can affect this equilibrium and that these variables are known as Prisoners of War (POW). An example of a POW is called the Prisoners’ Dilemma. In a POW game, all players face the dilemma of whether or not to cooperate and share the rewards with all other players who choose to defect. However, unlike the classic prisoner game, in a POW game each player acts alone and is rewarded only if he or she cooperates with all the others. Thus, even if every player chooses to defect, there will still be a smaller group of players who will share in the rewards.
The Prisoners’ Dilemma in this case is a very simple situation, but it is still a classic game theory. In a different style of game theory, we have what is known as the dictator game. In a dictator game, the players are given three cards and told that they are to form a “coalition” and share out the rewards between all of them. Once the coalitions are formed, each player will know not only what cards are up for grabs, but how much each player is willing to share out the rewards.
In this way, there is a subtle balance required. Different players need to feel confident about themselves in order to form coalitions and reap the rewards. A good leader must strike the right balance between order and chaos. To do so, a leader must calculate the strength of his or her position, the strength of his or her subordinates and the weakness of each player. Once this has been determined, then the leader can decide on the best strategy. Of course, this also entails a good deal of strategic thinking on the part of the leaders.