Bargaining 101 (#12): Rubinstein Bargaining

Game Theory 101: Bargaining: https://www.amazon.com/Game-Theory-10...

This lecture looks at infinite horizon bargaining, named after economist Ariel Rubinstein. Player 1 begins by proposing a division of the surplus to player 2. If player 2 accepts, the surplus is successfully divided, and the game ends. If not, after a bit of delay, player 2 makes a proposal to player 1. If player 1 accepts, the surplus is successfully divided, and the game ends. If not, after a bit of delay, player 1 makes another proposal. This process continues until a proposal is accepted.

After a bit of work, we will discover that this game has a unique subgame perfect equilibrium. In it, player 2 immediately accepts player 1's proposal. The delay creates inefficiencies, and so player 1 is incentivized to offer just enough to entice player 2 to accept. In the process, player 1 gets to keep a larger share of the surplus, with the exact amount depending on how impatient the players are.