The Theory of Bargaining
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 (1982) 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 non-cooperative 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,
- I will formally define the game and its assumptions,
- I will state and 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,
- I will discuss some interesting applications of Rubinstein’s model
Participants are expected to have some game theory knowledge, especially subgame perfect equilibrium.
Which transversal skills will the session develop?
- critical thinking
- problem solving
- decision making
Keywords:
- bargaining
- theory
- microeconomics
- game theory