18.16 : Infinitely Repeated Games

An infinitely repeated game is a scenario where players repeatedly engage in the same game without a predetermined end. This concept is crucial in understanding long-term interactions in various fields of the social sciences, including economics and international relations.

Examples:

1. Firms Setting Prices: Companies continuously adjust prices.
2. Trade Negotiations: Countries consistently negotiate trade terms.

Tit-for-Tat Strategy

Cooperative Start: Players begin with a cooperative action, such as setting a high price.

Reciprocity: A player matches the opponent's previous action, maintaining high prices if the opponent does the same.

Retaliation and Forgiveness: If one player lowers the price in one round, the other follows suit in the next round but returns to a high price in the round after the opponent does the same.

Players realize that mutually maintaining high prices (or other such cooperative actions) yields better long-term benefits compared to the short-term gains available from non-cooperative actions.

In the context of infinitely repeated games, players adopt strategies that maximize long-term benefits, recognizing that mutual cooperation is advantageous.

Besides pricing, this strategy is applicable in environmental agreements where countries agree to reduce emissions, maintaining cooperation to avoid long-term detrimental effects.