Optimal pricing contracts and level of information asymmetry in a supply chain

• Date: 01 September 2018
• DOI: http://doi.org/10.1111/itor.12237
• Published date: 01 September 2018

Intl. Trans. in Op. Res. 25 (2018) 1583–1610

DOI: 10.1111/itor.12237

INTERNATIONAL

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IN OPERATIONAL

RESEARCH

Optimal pricing contracts and level of information

asymmetry in a supply chain

Jian-Cai Wanga, Liu Yangb, Yao-Yu Wangc∗and Zhaohua Wanga

aSchool of Management and Economics, Beijing Institute of Technology, Beijing, P.R. China

bBusiness School, University of International Business and Economics, Beijing, P.R. China

cDongwu Business School, Soochow University,Suzhou, P.R. China

E-mail: mswangjc@gmail.com [J.-C.Wang]; amyangliu@gmail.com; wangyaoyu@suda.edu.cn[Y.-Y. Wang];

wangzhaohua@bit.edu.cn [Z. Wang]

Received 25 May2015; received in revised form 9 October 2015; accepted 30 October 2015

Abstract

This study considers a stylized supply chain model consisting of a dominant supplier and a buyer, in which

the latter possesses superior knowledge of his private cost information. The supplier’s imperfect knowledge

about the buyer’s cost is denoted by a subjective distribution. By assuming that the distribution is uniform,

we first derive the explicit expressions of the optimal equilibrium outcomes of two contract formats offered

by the supplier,the simple price-only contract and sophisticated menu of contracts, respectively. Based on the

optimal results,we continue to investigate howthe supplier’s expected profit varieswith the level of information

asymmetry, which is measured by the variance of the supplier’s subjective distribution. Our findings indicate

that the supplier’s expected profits initially decrease and then increase as the supplier’s knowledge of the

buyer’s cost becomes increasingly uncertain. That is, if the supplier could choose the level of information

asymmetry, she would prefer a symmetric case (with the variance being zero) or a totally asymmetric case

(with the variance being as high as possible). Numerical experiments demonstrate that our result still holds

when we take into account such distributions as a truncated gamma and normal, and a fixed support of the

distribution function instead of a moving support.

Keywords:supply chain management; contract; information asymmetry; cutoff level policy

1. Introduction

A supply chain typically consists of several independent companies operating on their own in-

terests, and supply chain inefficiency occurs when these companies’ objectives are not aligned

(Cakanyildirim et al., 2012). Nowadays, much research has been conducted on how a dominant

“upstream” player can design a “channel coordinating” contract to benefit herself and/or improve

the overall performance of the whole supply chain (see, e.g., Pasternack, 1985; Tsay, 1999; Cachon,

2003; Chen et al., 2006; Wang et al., 2012b; Yan, 2015; among others). However, an effective design

∗Corresponding author.

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1584 J.-C. Wang et al. / Intl. Trans. in Op. Res. 25 (2018) 1583–1610

of such contracts typically requires the dominant designer to know accurately the magnitudes of

key system parameters (Cachon and Lariviere, 2001; Wanget al., 2008). Unfortunately, information

asymmetry issues always exist in a contractual relationship, that is, one player knows something

that another does not. Given the information asymmetry situation, one intuitively expects that

the dominant player wants to keep the level of information asymmetry as low as possible. Is this

always the case? Do the contract formats have an effect on the dominant player’s preference on the

level of information asymmetry? Most of earlier studies focus on the optimal contract design in a

Stackelberg game framework “where the level of information asymmetry between players is given,”

and/or examines the value of information under various supply chain contracts, but these studies

do not explore the effect of the level of information asymmetry on the profits of the involved players.

This study intends to fill the literature gap by providing answers to these questions.

To this end, we consider a stylized supply chain setting with a dominant supplier (upstream

player, a female) selling products through a buyer (downstream player, a male) who possesses

superior downstream cost information. The supplier’s imperfect knowledge about the downstream

cost is denoted by a prior distribution. The Stackelberg game model is used for formulating the

sequent events, that is, the supplier first offers either a simple price-only contract or a sophisticated

menu of contracts,and the buyer responds by placing an order and setting the retail price or choosing

one item from the menu. We first derive the explicitexpressions of the optimal equilibrium solutions

for the two contracts, and then further investigate the effect of the level of information asymmetry,

which is measured by the standard deviation (or variance) of the supplier’s prior distribution about

the downstream cost, on the supplier’s expected profits. Ebrahim-Khanjari et al. (2012, 2014) also

take the variance of a prior distribution as a measure for the level of information asymmetry or

informationaccuracy. Webegin with the assumption that the asymmetric information is “uniformly”

distributed to derive analyticalresults. The main results of our study indicate thatthe supplier prefers

the variance being zero or as high as possible. That is, the supplier prefers two extreme cases: either

she knows the buyer’s cost deterministically or she is in sheer ignorance of the downstream cost

information. Moreover, we show that the contract format has no significant effect on the supplier

preference pattern by comparing the results between the price-only contract and menu of contracts.

As we know that a uniform distribution has a thick truncated right-hand tail and its coefficient of

variation is limited with a maximum of only 0.577. In order to test the validity of our conclusions,

we also conduct numerical experiments under a “truncated gamma distribution” in Section 4, and

demonstrate that the aforementioned results are still valid with a range of numerical examples.

Similarly, the contract format does not have impact on the supplier’s preference pattern.

The rest of the paper is organized as follows. We conduct a literature review in Section 2.

Section 3 provides a description of the model assumptions and justifications. Section 4 presents

the optimal solutions and relevant analysis for each contract considered using a moving support of

the distribution functions. In particular, Sections 4.1 and 4.2 present the explicit expressions of the

optimal solutions for the price-only contract and menu of contracts, respectively, and investigate

the impacts of the level of information asymmetry on the supplier’s expected profit. A comparison

is made between the corresponding results under the two contract formats, and it is shown that

the contract format does not have effect on the supplier’s preference pattern. Section 4.3 provides

an explanation to the counterintuitive results. In Section 5, we test our conclusions under a fixed

support of the distribution functions and compare the results with those of Corbett et al. (2004).

Section 6 concludes and discusses some relevant observations in earlier research.

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2015 The Authors.

International Transactionsin Operational Research C

2015 International Federation of OperationalResearch Societies