Sequential bargaining

Sequential bargaining (also known as alternate-moves bargaining, alternating-offers protocol, etc.) is a structured form of bargaining between two participants, in which the participants take turns in making offers. Initially, person #1 has the right to make an offer to person #2. If person #2 accepts the offer, then an agreement is reached and the process ends. If person #2 rejects the offer, then the participants switch turns, and now it is the turn of person #2 to make an offer (which is often called a counter-offer). The people keep switching turns until either an agreement is reached, or the process ends with a disagreement due to a certain end condition. Several end conditions are common, for example: * There is a pre-specified limit on the number of turns; after that many turns, the process ends. * There is a pre-specified limit on the negotiation time; when time runs out, the process ends. * The number of possible offers is finite, and the protocol rules disallow to offer the same agreement twice. Hence, if the number of possible offers is finite, at some point all them are exhausted, and the negotiation ends without an agreement. Several settings of sequential bargaining have been studied. * Dividing the Dollar: two people should decide how to split a given amount of money between them. If they do not reach an agreement, they get nothing.…

Sequential bargaining (also known as alternate-moves bargaining, alternating-offers protocol, etc.) is a structured form of bargaining between two participants, in which the participants take turns in making offers. Initially, person #1 has the right to make an offer to person #2. If person #2 accepts the offer, then an agreement is reached and the process ends. If person #2 rejects the offer, then the participants switch turns, and now it is the turn of person #2 to make an offer (which is often called a counter-offer). The people keep switching turns until either an agreement is reached, or the process ends with a disagreement due to a certain end condition. Several end conditions are common, for example: There is a pre-specified limit on the number of turns; after that many turns, the process ends. There is a pre-specified limit on the negotiation time; when time runs out, the process ends. The number of possible offers is finite, and the protocol rules disallow to offer the same agreement twice. Hence, if the number of possible offers is finite, at some point all them are exhausted, and the negotiation ends without an agreement. Several settings of sequential bargaining have been studied. Dividing the Dollar: two people should decide how to split a given amount of money between them. If they do not reach an agreement, they get nothing. This setting can represent a buyer and a seller bargaining on the price of an item, where the valuations of both players are known. In this case, the amount of money is the difference between the buyer's value and the seller's value. Buyer and Seller: a buyer and the seller bargain over the price of an item, and their valuations of the item are not known. A general outcome set: there is an arbitrary finite set of possible outcomes, each of which yields a different payment to each of the two players. This setting can represent, for example, two parties who have to choose an agreed arbitrator from a given set of candidates. Nejat Anbarci studied a setting with a finite number of outcomes, where each of the two agents may have a different preference order over the outcomes. The protocol rules disallow repeating the same offer twice. In any such game, there is a unique SPE. It is always Pareto optimal; it is always one of the two Pareto-optimal options of which rankings by the players are the closest. 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. For example, if the rankings are a>b>c>d and c>b>a>d, then the unique SPE is b (with k=2). If the rankings are a>b>c>d and d>c>b>a, then the SPE is either b or c (with k=3). In a later study, Anbarci studies several schemes for two agents who have to select an arbitrator from a given set of candidates: In the Alternating Strike scheme, each agent in turn crosses off one candidate; the last remaining candidate is chosen. The scheme is not invariant to "bad" alternatives. In contrast, the Voting by Alternating Offers and Vetoes scheme is invariant to bad alternatives. 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. Erlich, Hazon and Kraus study the Alternating Offers protocol in several informational settings: With complete information (each agent knows the other agents' full ranking), there are strategies that specify a subgame-perfect equilibrium for the agents, and can be computed in linear time. They implement a known bargaining rule. With partial information (only one agent knows the other's ranking) and no information (one agent knows the other's ranking), there are other solution concepts that are distribution-free.

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