Bargaining Experiments With Deadlines and Random Delays

OWEN R. PHILLIPS (*) I. INTRODUCTION Many bargaining situations involve deadlines and delays in the transmission of offers. Corporate takeovers, legal settlements, and labor union contracts are examples of bargains that can have random delays in their negotiations, along with deadlines on when an agreement must be reached. Relatively ordinary purchases that have a negotiated price, for example, a residential real estate transaction, can have noticeable delays in the formulation and transmission of proposals with a specified time at which negotiations cease. In virtually every bargaining environment there will be some unknown delay in moving offers and counteroffers back and forth between parties. These bargaining delays are particularly important when there is a deadline. Deadlines are often set by bargaining parties at the point negotiations begin, but sometimes the deadline is externally imposed through decay of the potential gains from agreement. Random delays happen for two reasons. They can occur because it does take time to deliver a proposal. Delays in communication have historically been a major reason for the random arrival of offers. For example, Stephen Ambrose, in his biography of Lewis and Clark, observes that "[A] critical fact in the world of 1801 was that nothing moved faster than the speed of a horse. No human being... no letter, no information, no idea, order, or instruction of any kind moved faster" (1996, 52). A second cause, and in modern times probably a more important cause of delay, is the time it takes to deliberate a decision. This is the time it takes to formulate a promised proposal or react to an offer. Agents, frequently as part of a team, must consider proposals and formulate a counteroffer if necessary. In an organization, a key person from the negotiating team may not be present at the time a proposal is received, or approval may be required by someone outside the team to make a final decision, or perhaps the offer must b e ratified by a body of individuals. Often a complicated agreement requires analysis by a legal staff. The deliberation time may be part of a strategic effort to manipulate outcomes given a deadline. Whatever the reasons, deliberation delays are an important part of the bargaining environment. (1) A theoretical study of how random delays affect bargaining behavior is simplified by making the transmission of proposals a random function of time, which would include possible delays in both delivery and deliberation. Ma and Manove (1993) present a subgame perfect solution for such a game. Our article in one sense is a test to see if agents gravitate toward the subgame perfect solution. We create an experimental bargaining environment that has a random hold-up in the exchange of proposals. This is the first experimental study of which we are aware that investigates the impact of random delays on bargaining behavior. Two agents are given the opportunity to split a dollar amount in a known time interval. If agreement is not reached at the end of this time, subjects receive nothing. Agents make offers and counteroffers by sending messages through a computer network. The set-up is like sending and receiving electronic mail, except as an experimental treatment our network is programmed randomly to delay the messages. At the moment the first offer is entered into the computer, a clock begins ticking toward a deadline. This offer is randomly delayed in its transmission to the receiving agent. In one of our treatments, the clock continues ticking even as this offer arrives to the receiving agent, and he or she decides whether to accept or to make a counteroffer. In a second treatment, the clock is paused to give agents time to think about accepting or countering the proposal. Counteroffers, if made, also are randomly delayed in their transmission. We compare behavior in these designs against a control experiment that does not have the random delay factor, but still keeps a deadline on the period of negotiation. …