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Article Excerpt
1. Introduction: The Role of Communication in Coalition Bargaining
Coalition bargaining sets in motion a host of phenomena, including mergers, joint business ventures, industrial cartels, trade unions, and consumers' cooperatives. (1) Coalition bargaining is by nature multilateral, and so bargainers need concern themselves not only with what to communicate, but with whom to communicate; the pattern of communication matters in a way that is not relevant when the negotiation involves just two parties.
The pattern of communication is influenced, sometimes strongly, by the institutional nature of the negotiation. Multilateral trade treaty negotiations typically link bargainers in ways that allow all private and public discussion (e.g., Sebenius 1984). Real estate buyers and sellers, on the other hand, contract to communicate with each other exclusively through a realtor. The United States and China communicated in the early 1970s through Pakistan, which appeared to parlay its role to its own advantage. (2)
Sometimes, bargainers voluntarily restrict communication. In 1999, the copper industry was significantly altered when Phelps Dodge Corporation managed a hostile takeover of fellow copper producers, Asarco Incorporated and Cyprus-Amax Minerals, Inc. Cyprus and Asarco had earlier announced their own friendly two-way merger plan, without having responded to Phelps Dodge's inquiries into a three-way merger (Mining Magazine 1999). In contrast, British Aerospace negotiated the sale of its subsidiary, Rover, to BMW, while carrying on separate and simultaneous conversations with Rover's strategic alliance partner, Honda (Pilkington 1996).
While it seems intuitively clear that the communication pattern has a critical influence on coalition outcomes, there has been little work to document the nature of that influence. An experiment by Murnighan and Roth (1977) compared private and public communication to public, and found an effect for privacy. An independent study by Rapoport and Kahan (1976), however, found no effect. (3) More recently, Valley et al. (1992) studied a buyer-seller transaction in which all communication is passed through a middleman, and found that the type of information available to the middleman influences the settlement. (4)
To investigate the effect of the communication pattern, we conducted an experiment that systematically manipulates the institutional constraints on communication in a three-person coalition bargaining game (as we will see, voluntary constraint also plays a role in what we observe). We compare five communication configurations: one which permits all public and private messages, one in which all messages are necessarily public, and three configurations in which a single bargainer controls the flow of messages. This broad manipulation of the communication structure potentially exposes regularities that might not be apparent in the more narrowly-based manipulations of earlier work.
We benchmark the experiment against one of the few coalition bargaining models that explicitly deals with communication: Myerson's (1977) cooperative game model. (5) A key innovation of Myerson's (1977) approach is the modification of the coalition characteristic function to take account of the communication configuration. Within this framework, we consider two solution concepts: (1) the Shapley value, the solution concept Myerson (1977) considered, and (2) the core. These are cooperative game models, and so we allow relatively free-form bargaining. Other than a time deadline and the restrictions imposed by the communication configuration, our bargainers are free to send messages pretty much as they please.
We find that varying the communication links causes sharp shifts in both the coalitions that form and the profits earned by individual bargainers. Some findings are surprising. For example, while the two "weak" bargainers benefit from controlling the flow of messages, the "strong" bargainer does not. Weak bargainer control yields the highest frequency of grand coalitions, counter to the conventional intuition that unconstrained communication is most conducive to grand coalitions. We also find, for each configuration save all public, a pattern of equal payoffs across certain types of coalitions and (very) unequal payoff allocation across other types. Neither the Myerson (1977) value nor the modified core fits the data particularly well, although, importantly, the data affirms Myerson's method of handling coalitions lacking a connected communication path.
It turns out, somewhat paradoxically, that once we understand which coalitions equally split the payoff, most of the other regularities follow rather naturally from a trace of the competitive pressures in the environment. The coalitions that tend to settle on an equal split are those with the highest per capita value. The unequal splits then tend to look like immediate competitive responses to the equal split proposals. There is a strong tendency to extend two-person coalition proposals in private, and this appears to act as a strategic friction, inhibiting competitive bidding to a certain extent. Private offers are not possible in the public treatment, and here the coalition allocations have a more uniformly competitive look.
2. The Experiment: A Game, Communication Configurations, and Two Benchmark Models
There are three bargainers: S, C, and T. The characteristic function is defined by
v(SCT) = 100, v(SC) = 90, v(ST) = 70,
v(CT) = 40, v(S) = v(C) = v(T) = 0.
This function implies a unique core outcome (this changes when we add communication considerations), the grand coalition with payoffs (S, C, T) = (60,30, 10). The Shapley value is (S, C, T) (46.67, 31.67, 21.66). By these measures, the S bargainer is in the strongest strategic position and T is in the weakest. As we will see, this unequal distribution of strategic strength is a desirable feature given the benchmark models involved.
In our experiments, bargainers conducted negotiations by electronic mail. The five experimental treatments are distinguished by the communication configuration.
(1) Unconstrained. A bargainer can send a message or proposal to one or both of the other bargainers.
(2) Public. Messages and proposals from one bargainer must go to both of the other bargainers.
(3) S-controls. All messages and proposals must originate or pass through S. C and T may send communication to S, but not directly to one another. S is under no obligation to pass a message from one bargainer on to another.
(4) C-controls. All communication must pass through C.
(5) T-controls. All communication must pass through T.
We discuss the models in the context of the game used for the experiment. The Myerson value (Myerson 1977) is the Shapley value for the characteristic function game in which the value of a coalition is set to zero if the set of direct communication links between members fails to form a connected path. Consider, for example, the S-controls treatment: CT can form only if S agrees to act as a go-between, a service that S has a disincentive to perform. Therefore, we modify the characteristic function v by setting the value of coalition CT to zero. We then take the Shapley value of the modified characteristic function: (S, C, T) = (60, 25, 15).
Table 1 lists the Myerson value allocations for the treatments of the experiment. The prediction for the unconstrained treatment is simply the Shapley value. When moving from the unconstrained to the public configuration, the set of connected communication paths is unaffected, so no change is predicted. Giving a single bargainer control of communication leaves the two noncontrolling bargainers without a connected communication path, eliminating the coalition of noncontrolling bargainers from consideration. This raises the average marginal contribution to the grand coalition of the controlling bargainer, which raises his predicted payoff.
It is difficult to challenge the reasoning behind disregarding coalitions without connected communication paths. We retain this feature, and construct an alternative model by substituting the core in place of the Shapley value. We refer to the resulting model as the modified core. The predictions are displayed in Table 2. As with the Myerson (1977) value, the grand coalition is the only coalition predicted, and there is no difference in prediction between unconstrained and public. As with the Myerson (1977) value, giving a single bargainer control of communication effectively eliminates a competitive option of the noncontrolling bargainers. The core predictions are not, however, precise; we can only say that the bargainer who controls communication should receive at least as much as he would in unconstrained.
The Myerson (1977) value and the modified core lead us to expect payoff allocations that are different in many respects. There are also some qualitative similarities. Both concepts exclusively predict grand coalitions, independent of communication configuration. Both imply that removing the ability to privately communicate (as with public) makes no difference. The Myerson (1977) value predicts that gaining control of communication increases the controlling bargainer payoff relative to unconstrained. The modified core implies a somewhat...
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