The cost can be presented in two ways: Rubinstein and Wolinsky[2] studied a market in which there are many players, partitioned into two types (e.g. "buyers" and "sellers").
Pairs of players of different types are brought together randomly, and initiate a sequential-bargaining process over the division of a surplus (as in the Divide the Dollar game).
Fudenberg and Tirole[3] study sequential bargaining between a buyer and a seller who have incomplete information, i.e., they do not know the valuation of their partner.
They show that, under some weak assumptions, there exists a unique perfect sequential equilibrium, in which: Nejat Anbarci[5] studied a setting with a finite number of outcomes, where each of the two agents may have a different preference order over the outcomes.
It can be found by finding the smallest integer k for which the sets of k best options of the two players have a non-empty intersection.
In a later study, Anbarci[6] studies several schemes for two agents who have to select an arbitrator from a given set of candidates: In all schemes, if the options are uniformly distributed over the bargaining set and their number approaches infinity, then the unique SPE outcome converges to the Equal-Area solution of the cooperative bargaining problem.
Subjects' behavior depends on the number of turns, their experience with the game, and their beliefs about fairness.
[9] They studied back-and-forth sequential bargaining in over 25 million listings from the Best Offer platform of eBay.