Finitely Vs Infinitely Repeated Games
Repeated games may be broadly divided into two classes, depending on whether the horizon is finite or infinite. The results in these two cases are very different. Even finitely repeated games are not necessarily finite horizon, the player may just perceive a probability of another cycle and act accordingly. For example, the fact that everyone has a fixed lifetime doesn't mean that all games should be finite horizon. Also, players might act differently when the horizon is far away as opposed to when it is close by, which can probably be thought of as a time modifier function applied to the payoff. The difference in strategies for finite versus infinite horizon games is a hotly debated topic, and many game theorists have differing views regarding it.
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Famous quotes containing the words infinitely, repeated and/or games:
“What a vast traffic is drove, what a variety of labour is performed in the world to the maintenance of thousands of families that altogether depend on two silly if not odious customs; the taking of snuff and smoking of tobacco; both of which it is certain do infinitely more hurt than good to those that are addicted to them!”
—Bernard Mandeville (1670–1733)
“Manners are the happy way of doing things; each once a stroke of genius or of love—now repeated and hardened into usage. They form at last a rich varnish, with which the routine of life is washed, and its details adorned. If they are superficial, so are the dewdrops which give such depth to the morning meadows.”
—Ralph Waldo Emerson (1803–1882)
“In 1600 the specialization of games and pastimes did not extend beyond infancy; after the age of three or four it decreased and disappeared. From then on the child played the same games as the adult, either with other children or with adults. . . . Conversely, adults used to play games which today only children play.”
—Philippe Ariés (20th century)