Bargaining is a very important concept in economics, most notably in game theoretical frameworks. A common problem which one comes across is how to split the pie between two players.  The question is as follows:

There are two players; A, and B. They are given by a pie which they must split between themselves. In Period 1, Player A proposes a division, and Player B accepts or rejects this division. If Player B accepts the division proposed by Player A, then the game ends at that time itself and both players walk away with their share of the pie. If Player B rejects, then Player B proposes the division in Period 2. Now Player A has the option of accepting or rejecting the division. Again the same conditions apply, and the game can continue or end in Period 2. However, for each Period the game goes on for, the size of the pie keeps diminishing by a certain amount. There are a certain number of periods the game can go on for, before the value of the pie becomes zero. 

So how should the pie be divided?

This problem is important, both as an introduction to bargaining games, as well as a introduction to thinking about ‘dynamic’ issues in economics — where agents think across time periods (as opposed to static frameworks where agents are only thinking about the current period of time).

 

I have made a small presentation about this problem and how to resolve it. To check it out, click here!