Introducing Game Theory: A Graphic Guide (Graphic Guides)

by Ivan Pastine

Human behaviour is probably better approximated by bounded rationality. That is, human rationality is limited by the tractability of the decision problem (how easy it is to manage), the cognitive limitations of our minds, the time available in which to make the decision, and how important the decision is to us.

The idea of Nash equilibrium is both simple and powerful: in equilibrium each rational player chooses his or her best response to the choice of the other player. That is, he or she chooses the best action given what the other player is doing.

One interesting question to ask is whether the Nash equilibrium is Pareto efficient in the Prisoners’ Dilemma Game. An outcome is Pareto efficient if there is no other potential outcome where somebody is better off and nobody is worse off. This notion of distributional efficiency is named after the Italian economist Vilfredo Pareto (1848–1923).

In the Prisoners’ Dilemma, although there is benefit to cooperative behaviour, individual incentives encourage conflict. In the network engineering example, it is possible to overcome this problem if one person controls both routers. But in human interaction achieving cooperation can be more difficult.

For the investor, it is best to be unpredictable about when to engage in a speculative attack. If the central bank could predict the attack, the bank would pre-emptively devalue its currency the day before the attack to avoid losses. The speculators would then be too late to take advantage of the devaluation.

Situations often arise in which people are not sure about what kind of person they are dealing with. These are games of incomplete information, where players are uncertain about the characteristics of the other player and so are uncertain about the payoffs from the possible outcomes of the game. Often this is represented by thinking of the other player as having a type. Each type is associated with different payoffs from the possible outcomes of the game. A player typically knows his or her own type, but it is unknown to the other player. Hence there is asymmetric information.