On the role of outside options in wage renegotiation

• Date: 01 October 2018
• Author: Fengjiao Chen,Duozhe Li,Chiu Yu Ko
• Published date: 01 October 2018
• DOI: http://doi.org/10.1111/jems.12245

792 © 2018 Wiley Periodicals, Inc. wileyonlinelibrary.com/journal/jems J Econ Manage Strat. 2018;27:792–803.

Received: 11 August 2017 Revised: 16 January 2018Accepted: 31 January 2018

DOI: 10.1111/jems.12245

ORIGINAL ARTICLE

On the role of outside options in wage renegotiation

Fengjiao Chen1Chiu Yu Ko2Duozhe Li1

1Chinese Universityof Hong Kong,

Hong Kong (Email: jocelyncfj@gmail.com;

duozheli@cuhk.edu.hk)

2National Universityof Singapore, Singapore

(Email: kochiuyu@nus.edu.sg)

Fundinginformation

HongKong Research Grants Council,

Grant/AwardNumber: General Research

Fund/ProjectNo. CUHK450011; Singapore

Ministry of Education, Grant/AwardNumber:

AcademicResearch Fund Tier 1 Fund/Project

No.FY2014-FRC4-001

Abstract

We study a game-theoretic model of wage renegotiation. A worker, after receiving a

superior outside offer, initiates a wage renegotiationwit h his current employer.During

the renegotiation, whenever a proposal is rejected, the worker decides whether to opt

out. When the two parties are sufficiently patient, any wage levelbetween the outside

offer and the entire net surplus can be sustained in equilibrium. Opting out may also

arise in equilibrium. This result is in stark contrast to existing studies, in which the

outside option is sometimes a credible threat, but is never exercised in equilibrium.

1INTRODUCTION

Outside options play an important role in wage bargaining. Casual observations suggest that a worker with an outside option

is often in an advantageous position in forcing his or her employer to concede. Nonetheless, we also observe that negotiation

sometimes breaks down and the worker takes up the outside option. The reversescenario ar ises when a firm possesses an outside

option. Carpenter and Rudisill (2003) document how Volvo Trucks North America exploited the outside option of moving to

Mexico from Virginia to forcethe United Auto Union to concede to significantly reduced wages; they also report that Halliburton

exercised the outside option of moving from Maryland to Mexico after the firm's offers were rejected. Why did the firm succeed

in the former case in forcing a concession from the union but not in the latter? A satisfactory explanation calls for a closer look

at the strategic role of outside options in wage bargaining.

This paper studies a game-theoretic model of wage renegotiation between a worker and his firm after the worker obtains

an outside offer.1The term renegotiation is used because we consider the situation where the two parties have a preexisting

wage contract. The workeris producing per iodic revenueof a fixed amount for his firm, whereas the firm is paying him the wage

specified in the existing contract in each period before the renegotiation concludes with a new contract. During the renegotiation,

the two parties alternate in proposing of wage contracts, which the responding party is free to accept or reject. The acceptance of

a proposed wage concludes the renegotiation with a new contract. Upon either party's rejection, the worker must decide whether

to opt out. If the worker opts out, the renegotiation is over; from that period onward, the worker receives his outside offer and

the firm earns a smaller profit from hiring a replacement worker. Otherwise the current contract is enforced in this period and

the renegotiation continues.

We first show that when the outside offer is no less than the current wage, the worker not only can get the firm to match the

outside offer, but the worker can also exploit the outside offer to substantially improve his bargaining position. The worker can

even get the entire net surplus (the total net surplus of the profit over the cost of hiring a replacement). In fact, any wage level

between the outside offer and the entire net surplus can be sustained in an equilibrium with immediate agreement.

Through a wage expectation cycle, the workerleverages an outside offer well beyond its face value. When the worker expects

to accept the firm's outside offer-matching proposal in the next period, opting out after his current demand is rejected becomes

a credible threat. Hence, the worker will demand the entire net surplus, which will be accepted by the firm. Starting from there,

using backward induction, we can establish a decreasing sequence of wageexpectations: although he anticipates t hat int he next

period, he will be granted a certain wage greater than the outside offer, the worker will not opt out. This implies that he is willing

to settle for a lower wage in the current period. When the wage expectation approaches the outside offer, it eventually becomes

optimal again to opt out after a rejection, which gives the worker the power to make a take-it-or-leave-it offer. This closes the