Bargaining problems formalize situations where agents can enter a mutually beneficial arrangement—that is, one that will make each party better off than they would be otherwise—and must decide how to divide their joint payoff.

Nash bargaining problem

A two-person bargaining problem consists of the following data:

A feasibility set $F \subseteq R^{2}$ , a closed, often convex set where elements are agreements;

A disagreement point $d = (d_{1}, d_{2}) \in F$ , where $d_{1}, d_{2}$ are the payoffs guaranteed to player 1 and player 2, respectively, if they cannot come to a mutual agreement.

A solution to the bargaining problem is an agreement $ϕ \in F$ . The problem is said to be nontrivial if agreements in $F$ are better for both parties than the disagreement point $d$ .

The Nash bargaining solution is the division of payoffs that maximizes the product of each player’s utility gains (relative to the status quo or disagreement utilities). The Nash bargaining solution predicts that when the players receive identical payoffs and value their payoffs the same, then resources will be divided equally; however, a player with low status quo utilities is said to have weak bargaining power and predicted to obtain less from a successful bargain.

References

Cite key	One-line takeaway
@2023levineResource, “Resource-rational contractualism”	Uses the simple, tractable case of bargaining problems to motivate (resource-)rational analyses of more complex social decision-making problems.

BONNIE'S NOTES

Table of Contents

Bargaining problems

References

Further reading

Graph View

Backlinks