Bargaining theory
Bargaining is an ubiquitous human activity that involves negotiation between parties to reach a mutually agreeable outcome. It is a process in which parties try to maximize their own benefit while compromising enough to avoid a deadlock.
Rubinstein’s bargaining model is a game-theoretic framework that analyzes this negotiation process. Developed by Ariel Rubinstein in his world-famous 1982 Econometrica paper, it involves two players who alternate offers over how to divide some resource. The model assumes:
- Alternating offers: players take turns making offers to each other.
- Time preference: players have a preference for reaching an agreement sooner rather than later, often modeled through a discount factor that devalues future payoffs.
- Rationality: players are rational and aim to maximize their own utility.
Rubinstein discovered the unique subgame perfect equilibrium (SPE) outcome of this natural game. He showed that it is efficient and depends on the players’ discount factors. The outcome demonstrates how patience (as reflected by the discount factor) can influence the division of resources, with more patient players securing better deals. As both parties become completely patient, the unique SPE of this game converges to the well-known Nash bargaining solution. While Rubinstein’s original proof is quite complex, simple proofs of his result were later obtained. His model was also extended to multiple-player environments, most notably by Sergiu Hart & Andreu MasColell in a 1996 Econometrica paper.
In this workshop,
- Students will play Rubinstein’s bargaining model on a computer,
- I will formally define the game,
- I will derive the unique SPE of the game,
- I will discuss commonly observed deviations from the unique SPE,
- I will introduce some extensions of Rubinstein’s model to the multiplayer case.
Participants should bring a device that allows them to access the internet, read instructions, and select actions. Participants should have some knowledge on the basic Game Theory tools