Bargaining in the Shadow of the Market

The following sections are included:

• Dedication

• Preface

• Acknowledgments

• Contents

The following sections are included:

• Motivation for Studying this Field

• Models

• Bilateral Bargaining with Complete Information

• Bilateral Bargaining with Incomplete Information

• Search for Outside Options

• Choice of Investment and Outside Options in Bargaining

• Non-Cooperative Coalitional Bargaining

• Conclusion

• References

This paper considers a model of bargaining in which the seller makes offers and the buyer can search (at a cost) for an outside option; the outside option cannot be credibly communicated, and the seller's offer is recallable by the buyer for one period. There are essentially two equilibrium regimes. For sufficiently high search cost, the game ends immediately; otherwise the search occurs in equilibrium. Compared to the case where the buyer can communicate his outside option, the seller is worse off, and the game results in search for a smaller set of values of the search cost, i.e., less equilibrium delay.

This paper analyzes the effect of competition for bargaining partners on the prices that prevail in thin markets. as well as how the matches are simultaneously determined. Three trading processes or bargaining procedures are described. In all the variants that we consider, except for one case of public offers, either there is no pure strategy subgame perfect equilibrium or such equilibria exhibit delay in reaching agreement.

This paper explores the interplay between choice of investment type (specific vs. general), bargaining extensive form and endogenous outside options in the framework of incomplete contracts introduced formally in the work of Grossman, Hart and Moore. We find that the bargaining procedure chosen has significant implications for choice of investment and for the usefulness of the assignment of property rights in enhancing efficiency. Somewhat paradoxically an “auction-like” procedure might need the correct assignment of property rights for a more efficient solution while a sequential offers procedure might do as well as the best assignment of property rights.

We explore a sequential offers model of n-person coalitional bargaining with transferable utility and with time discounting. Our focus is on the efficiency properties of stationary equilibria of strictly superadditive games, when the discount factor δ is sufficiently large; we do, however, consider examples of other games where subgame perfectness alone is employed.

It is shown that delay and the formation of inefficient subcoalitions can occur in equilibrium, the latter for some or all orders of proposer. However, efficient stationary equilibrium payoffs converge to a point in the core, as δ → 1. Strict convexity is a sufficient condition for there to exist an efficient stationary equilibrium payoff vector for sufficiently high δ. This vector converges as δ → 1 to the egalitarian allocation of Dutta and Ray (1989).

Complexity of communication is one of the important factors that distinguishes multilateral negotiation from its bilateral cousin. We investigate how the communication configuration affects a three-person coalition negotiation. Restricting who can communicate with whom strongly influences outcomes, and not always in ways that current theory anticipates. Competitive frictions, including a tendency to communicate offers privately, appear to shape much of what we observe. Our results suggest that parties with weaker alternatives would benefit from a more constrained structure, especially if they can be the conduit of communication, while those endowed with stronger alternatives would do well to work within a more public communication structure that promotes competitive bidding.

We study a game-theoretic model where three political parties (left, median and right) can form coalitions both before and after the election. Before the election, coalitions can commit to a seat-sharing arrangement, but not to a policy platform or a division of rents from office; coalition members are free to break up and join other coalitions after the election. Equilibrium pre-electoral coalitions are not necessarily made up of the most ideologically similar parties, and they form under proportional representation as well as plurality rule. They form not only to avoid splitting the vote, but also because seat-sharing arrangements will influence the post-election bargaining and coalition

This paper has focused on two types of arbitration procedures that are commonly used in the United States, especially in industrial disputes involving public safety personnel who are legally not permitted to strike. The conventional arbitration (CA) procedure gives the arbiter or arbitration panel complete authority to fashion a final award. The final-offer arbitration (FOA) procedure allows the arbiter only to choose one of the two final offers made by the parties. Though some empirical work has appeared comparing the two procedures, the theoretical analysis of the procedures is still incomplete. This paper has concentrated on the effect of uncertainty about the arbiter's preferences on the bargainers, white ignoring other aspects of the comparison such as permitting the arbiter to trade-off among bargaining issues.

The following sections are included:

• A MODEL OF BARGAINING UNDER UNCERTAINTY AND THE EFFICIENCY PROBLEM

• INCENTIVE-COMPATIBLE PRICING PROCEDURES: IMPOSSIBILITY AND POSSIBILITY RESULTS

• CONCLUSION

• REFERENCES

Chatterjee and Samuelson (1987) recently examined a noncooperative game-theoretic bargaining model with two-sided incomplete information and an infinite horizon. Results were obtained from the model with the help of restrictions on agents' strategies. This paper examines the model without these restrictions. By doing so, we will gain some insight into whether these results are robust, in the sense that they do not depend upon the special structure of the model, and hence, might provide useful theoretical foundations for applied work. We find that the basic results generalize. As with the restricted model. we find an equilibrium in which bargaining will proceed for a finite but endogeneously determined number of stages. A terminal condition on the equilibrium sequence of agents' beliefs determines the properties of the equilibrium and allows comparative static results to be obtained. These include the finding that agents are more likely to capture a large share of the potential gains from bargaining if they exhibit characteristics that can be readily interpreted as giving them more bargaining power. Unlike the restricted model, this equilibrium is not unique, though we argue that it is plausible.