What is the Theory of Games?

What exactly does the Theory of Games deal with?

The Theory of Games (ToG) studies strategic interactions: situations in which separate decision makers (individuals, organisations, robots, animals etc.) interact in a context in which the decisions they are called on to make have an effect on the result of the interaction, a result that is in everybody’s interest. A similar situation can be made into a game in which the decision makers are the players. Typically, but not exclusively, the ToG studies games in which individuals consciously act in a strategic way: they are aware that their actions and those of the other players have effects on the result.

Having clarified the object of ToG, let us take a brief look at the method. Firstly it should be said that, in a similar way to other theories of observable phenomena, ToG has the dual goal of organising our knowledge regarding certain types of circumstances (namely their typification) and increasing our understanding of these phenomena in order to better explain and predict them. For this purpose ToG uses the method of abstraction in a powerful and systematic way, always trying to ignore the details of phenomena in order to focus on the essential elements that characterise a certain strategic interaction, possibly relating it to a type of phenomena that shares the same essential features with it.

 

How can a game be represented?

Let us briefly introduce the elements making up a game. First of all, it is important to identify the participants, called players, who are the individuals called on to make decisions within the game. For instance, in chess there are 2 players, in poker there are from 3 to 6 players, whereas in so-called massively multiplayer online games the number of players can arrive at several thousand.

Once the players have been identified, the next step is to define which of the possible choices is available for each player. In a representation of the game called extended form, a detailed description including all the possible moves is provided. Each player can be asked to make decisions several times and in different situations. Furthermore, when the time comes to make a decision, the player may or may not know the previous moves of the other players. Games in which moves are always observable by all the players are called games of perfect information. For instance, chess is a game of perfect information, whereas battleships is a game of imperfect information. The imperfection of information is represented graphically with a dotted line which connects knots – in other words the previous stories in the game – among which the player is uncertain, as he has not observed some of the moves already made.

 

It is possible to predict the final outcome of a game?

The goal of ToG is to predict players’ behaviour in the game being analysed. To do so, it is necessary to go ahead with the definition of the solution to a game. There is no univocal concept in terms of the solution, but without doubt the Nash equilibrium represents the most famous and widely used.

A strategy outline, one for each player, is called a Nash equilibrium when nobody can obtain a better result by changing strategy, given the strategies adopted by the others. In other words, a Nash equilibrium is an effective outline of strategies as compared to individual deviations.

In extended games of perfect information, a widely used solution idea is backward induction. The solution for backward induction can be found starting from final decisions, those that provide for a direct choice between final results. These decisions are simple: the choice will be guided by the convenience for the player called on to make it, who will choose the best result for himself. After having fixed the final choices, let us go on to consider those immediately preceding them: the players called on to make such decisions, will make the best choice for themselves, knowing how the other players will behave. After having also identified these choices in this way, the preceding choices need to be considered and so on, until the roots of the tree are reached, in this way determining balanced behaviour. It can be noticed that backward induction solution represents a Nash equilibrium of the game, whereas it cannot be said that all Nash equilibriums of games are backward induction solutions.

We would like to hint at a last solution concept connected to forward induction. This model of thinking presumes that the previous moves have been made rationally, and on this basis it is attempted to arrive at the implications on how the future game will develop. So a certain choice may contain a message that the opponent will have to take into account.

 

What does the Strategic Quotient have to do with it?

The Strategic Quotient (SQ) is intended to be a measurement that uses the same method of calculation as the IQ, but that differs in terms of the essence of what it is to be measured.

The SQ has been designed as a standard measurement of the strategic skills of individuals, namely a concise quantification of the individual’s ability to obtain the best result possible in a strategic situation.

So, the SQ can be distinguished from the IQ because it is not meant to measure cognitive skills in general, but is intended to measure the particular abilities which are most relevant to the problem of taking the best decision in a strategic situation, namely in a situation in which the result of one’s own decisions depends critically not only on one’s own choices but also on the choices of others. In a strategic situation it is essential to have the ability to predict others’ decisions, to correctly evaluate the relevant role and to estimate the usefulness of the information that one has and that is possessed by others.

 

To learn more about

Game Theory Society
Psychometrics Society
Stanford Encyclopedia of Philosophy – Game Theory
Wiki – Game Theory
Wiki – Psychometrics
Didactic Web-Based Experiments in GAME THEORY