Introducing Game Theory: A Graphic Guide (Graphic Guides)

by Ivan Pastine

whenever how well you do depends on the actions of others as well as your own choices.

While the game between unskilled players tends to have a victor, after a bit of practice you quickly learn to reason via backward induction: you can figure out your opponent’s response to your possible actions and take that into consideration before making your own move.

A classic example is Keynes’ Beauty Contest, in which English economist John Maynard Keynes (1883–1946) likens investment in financial markets to a newspaper competition in which readers have to choose the “prettiest face”; the readers who choose the most frequently chosen face win.

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 Guessing Game and Keynes’ Beauty Contest can explain the interesting fact that in financial markets we observe bubbles – excessively inflated prices – even if all participants are rational. This is because of a lack of common knowledge of rationality.

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.

The game illustrates the difficulty of acting together for common or mutual benefit given that people pursue self-interest.

The network router problem is closely related to the tragedy of the commons, a concept conceived by William Forster Lloyd (1794–1852), much earlier than the conception of the Prisoners’ Dilemma. In an essay about overgrazing of cattle, Lloyd argued that farmers may be acting in self-interest, contrary to the best interest of the whole group, and depleting the feeding potential of the common land.