The Aumann Agreement Game Explained
The Aumann Agreement Game is a concept in game theory that refers to the idea of mutual knowledge and common knowledge. It was first introduced by Robert Aumann, an Israeli-American mathematician, in the 1970s as a way to understand how people make decisions in social situations.
In the Aumann Agreement Game, two players are given a number between 0 and 100, which represents the amount of money they will both receive if they agree on the same number. The catch is that they can only communicate by leaving notes with each other, and they do not know what number the other player has chosen.
The game is played in rounds. In each round, each player can either stick with their current number or switch to a new number based on the information they have received from the other player`s note. The game continues until both players agree on the same number.
The Aumann Agreement Game is an example of a game of incomplete information, where players do not have access to all the information needed to make the best decision. In this case, the players do not know what number the other player has chosen, but they can use the information from the notes to make a more informed decision.
The game also demonstrates the concept of common knowledge, which refers to information that is known by all the players in a game. In the Aumann Agreement Game, the notes left by each player become common knowledge once they are read by the other player. This means that both players know that the other player has received the same information.
The Aumann Agreement Game has been used to study how people make decisions in social situations where information is incomplete or uncertain. It has applications in fields such as economics, political science, and psychology.
One example of the game in action is in international negotiations, where countries must come to agreements on issues such as trade and diplomacy. The Aumann Agreement Game can help policymakers understand how to communicate and negotiate effectively in these situations by taking into account the incomplete information and common knowledge involved.
In summary, the Aumann Agreement Game is a valuable tool for understanding decision-making in social situations with incomplete information. It demonstrates the concept of common knowledge and has applications in fields such as economics and political science. As we continue to navigate complex social and economic systems, understanding the principles of the Aumann Agreement Game will continue to be important.