Abstract

This paper examines a general model of contract in multi-period settings with both external and self-enforcement. In the model, players alternately engage in contract negotiation and take individual actions. A notion of contractual equilibrium, which combines a bargaining solution and individual incentive constraints, is proposed and analyzed. The modeling framework helps identify the relation between the manner in which players negotiate and the outcome of the long-term contractual relationship. In particular, the model shows the importance of accounting for the self-enforced component of contract in the negotiation process. Examples and guidance for applications are provided, along with existence results and a result on a monotone relation between “activeness of contracting” and contractual equilibrium values.

Highlights

  • Many economic relationships are contractual, in that the parties negotiate and agree on matters of mutual interest and intend for their agreement to be enforced

  • I discuss various alternatives in the analysis of contract negotiation and I define a notion of contractual equilibrium that combines a bargaining solution with incentive conditions on the individual actions

  • The selection of self-enforced and externally enforced components of contract entail the same basic ingredients—in particular, the notion of a disagreement point and relative bargaining power. These ingredients are more nuanced for self-enforcement than for external enforcement, because the implications for self-enforcement depend on how statements made during bargaining affect the way in which the players coordinate on individual actions later

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Summary

Introduction

Imagine that the parties are negotiating at the beginning of the second period, in the contingency in which they had selected mhh = mhl = ( 9, 9), mlh = ( 1, 1), and mll = (0, 0) in the first period (recall the description of Alternative 3 in the Introduction). Call the second period selections mhh , mhl , mlh , and mll. For any vector y = (y1 , y2 ) with y1 + y2 16, there is a specification of transfers such that (high, high) is a Nash equilibrium, 17 + mhh 1 + mhh 1 = y1 , and 2 = y2.

MW Example
Relation to the Literature
Outline of the Paper
Contractual Elements in an Ongoing Relationship
BoS Example
Modeling Contract Negotiation and Activeness
Bargaining Protocols
Equilibrium Conditions and Activeness Refinements
Example
Cooperative-Theory Representation
Representation of Contractual Activeness
Benchmark Solutions
Contractual Relationships
Formal Description of the Game with Joint Actions
Contractual Equilibrium
Analysis of Examples
A Sequence of Stage Games with Contracting
Activeness and Monotonicity
Conclusions
Bargaining Protocol Example
Finite Except for Spot Transfers
Relationships that are Finite Except for Contingent Transfers
Existence Results
Proof of Theorem 3
Proof of Theorem 4
Other Proofs

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