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Symmetry in Bargaining & Efficient Contracts Under Asymmetric Information

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Research Paper

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Symmetry in Bargaining

  • Efficient Contracts under Asymmetric Information

Studies in Microeconomics

5(2) 1–11

© 2017 SAGE Publications

India Pvt. Ltd

SAGE Publications sagepub.in/home.nav DOI: 10.1177/2321022217713094 http://mic.sagepub.com

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Arijit Sen1

Abstract

This paper shows that in a Spencian agency model, contract determination through alternating-offer bargaining can generate efficient outcomes. This result holds in parameter regimes in which the screening equilibrium (where the uninformed principal makes a take-it-or-leave-it offer to the agent) and the signalling equilibrium (where the informed agent makes a take-it-or-leave-it offer to the principal) both predict inefficient contracts. More generally, this paper clarifies that in negotiations under incomplete information involving interdependent values, symmetry in the bargaining protocol can limit the extent of allocation inefficiencies and can lead to ex post efficient agreements.

Keywords

Alternating-offer bargaining, interdependent values, screening, signalling

Introduction

The presence of information asymmetries in economic interactions leads to inefficient outcomes—this has been a central message of a large literature in information economics that began with the seminal papers of Akerlof (1970), Spence (1973) and Rothschild and Stiglitz (1976). While many related papers identify the nature of outcome inefficiencies as a function of the structure of infor-mation asymmetries (e.g., independent vs. interdependent values), the underlying message may have found its clearest exposition in Myerson and Satterthwaite (1983) where it was proved that in the presence of hidden information, not all gains from trade will be realized in situations where the existence of gains from trade is not common knowledge ex ante.

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1Indian Institute of Management Calcutta, Kolkata, India.

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Corresponding author:

Arijit Sen, Indian Institute of Management Calcutta, Kolkata 700104, India.

E-mail: arijitsen@iimcal.ac.in


2        Studies in Microeconomics 5(2)

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But subsequent to that paper, two important contributions by Cramton, Gibbons and Klemperer (1987) and McAfee (1991) highlighted the following issue: It is the co-existence of information asymmetries and other ex ante asymmetries among traders that generate allocation inefficiencies. The first paper shows that if ex ante property rights over an indivisible good are symmetrically distributed over a group of economic agents who have incomplete information about each other’s valuations of the good, then one can design an efficient allocation mecha-nism. The second paper establishes a similar result in a scenario where a good can be traded in continuous quantities, and where each agent might be either a buyer or a seller depending upon her realized private information.

These papers indicate that in contract negotiations under incomplete informa-tion, symmetry in the status quo (i.e., default) allocation can help alleviate the problem of inefficient trades. This insight finds a comprehensive exposition in a recent paper by Segal and Whinston (2011). The following statement in McAfee (1991) nicely summarizes the main conclusion of this set of papers: ‘inefficiency does not spring from asymmetric information, but asymmetric information in conjunction with an ex ante asymmetry’.

Note, however, that the ex ante symmetry that the aforementioned papers focus on is regarding the status quo allocation. That leaves open the following question: What will be the nature of negotiated outcomes under incomplete information if the bargaining protocol (rather than the default trade) is reasonably symmetric? The current paper addresses this question and shows that even with regard to the bargaining process, a similar result holds: A more symmetric contract negotiation protocol can lead to an efficient agreement under incomplete information involv-ing interdependent values, in scenarios where asymmetric bargaining protocols would not.

Specifically, we study an interdependent values agency model under hidden information a la Spence (1973), where the agent has private information regarding the total surplus that can be created in the relationship and the principal cares directly about the agent’s private information. In the extant literature, such agency relations have been predominantly analyzed under two asymmetric bargaining protocols: In the screening models, it is posited that the uninformed principal makes a take-it-or-leave-it offer to the agent, while signalling models study the case where the informed agent makes a take-it-or-leave-it offer to the principal.1 The literature then delineates the allocation inefficiencies that arise given such extreme allocation of bargaining power between the two parties.

In contrast, this paper considers the following negotiation structure: Contracts are determined in an infinite-horizon alternating-offer bargaining game, where offers and counter-offers can be made arbitrarily quickly, and where each player can propose a menu of contracts every time it is her turn to make an offer. This bargaining structure captures the following features that may be considered desirable in modelling many real-world negotiations: (a) the extensive form provides minimal pre-commitment ability to the players; (b) the bargaining powers of the players are quite symmetric; and (c) the uninformed player has the ability to screen the private information of the informed player (by offering a


Sen

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menu of contracts), while the informed player can signal his private information by his own offers.

In such a contract negotiation game, we show that when the production and cost functions satisfy a set of parameter restrictions, there exists a pure-strategy Perfect Bayesian Equilibrium (PBE) whose outcome is immediate agreement on a contract that is ex post efficient, given the agent’s realized private information. This outcome is distinct from the ex post inefficient outcomes that arise in the screening and signalling equilibria under the same set of parameter restrictions. Further, the bargaining equilibrium does not require any unreasonable off-equilib-rium beliefs; the equilibrium survives (a weaker version of) the perfect sequential equilibrium (PSE) refinement of Grossman and Perry (1986 a, b).2,3

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