Game Theory is one mathematical theory that is applied on a multitude of (different) areas, and can be accessed not only via the studies of math, but also from life sciences (like psychology, which encourages students to understand game theory in order to understand some key human behavior patterns). In this short post I will look into the introduction of this theory, in hope to follow up on it in the next post with the actual people involved in research and development of this rich theory.
In game theory, a repeated game (supergame or iterated game) is an extensive form game which consists in some number of repetitions of some base game (called a stage game). The stage game is usually one of the well-studied 2-person games. It captures the idea that a player will have to take into account the impact of his current action on the future actions of other players; this is sometimes called his reputation. The presence of different equilibrium properties is because the threat of retaliation is real, since one will play the game again with the same person. It can be proved that every strategy that has a payoff greater than the minmax payoff can be a Nash Equilibrium, which is very large set of strategies. Single stage game or single shot game are names for non-repeated games.
The most widely studied repeated games are games that are repeated a possibly infinite number of times. On many occasions, it is found that the optimal method of playing a repeated game is not to repeatedly play a Nash strategy of the constituent game (look at the Repeated prisoner’s dilemma example), but to cooperate and play a socially optimum strategy. This can be interpreted as a “social norm” and one essential part of infinitely repeated games is punishing players who deviate from this cooperative strategy. The punishment may be something like playing a strategy which leads to reduced payoff to both players for the rest of the game (called a trigger strategy). There are many results in theorems which deal with how to achieve and maintain a socially optimal equilibrium in repeated games. These results are collectively called “Folk Theorems”. An important feature of a repeated game is the way in which a player’s preferences may be modeled. There are many different ways in which a preference relation may be modeled in an infinitely repeated game, the main ones are :
- Discounting – valuation of the game diminishes with time depending on the discount parameter δ
- Limit of means – can be thought of as an average over T periods as T approaches infinity.
- Overtaking – Sequence
is superior to sequence 
if 