【文献阅读】Fairness and Channel Coordination

Brief Summary:

This paper investigated how fairness affect channel coordination in a conventional dyadic channel on the basic conception of disadvantageous and advantageous inequity. The result shows that the manufacturer can use a simple wholesale price to achieve both the maximum channel profit and the maximum channel utility.

Background:

1. Motivation:

1. From academic perspective: Fairness plays an important role in developing and maintaining channel relationships.
2. From industrial perspective: channel members care about fairness in transactions in ”a richer real-world environment”.

1. Past theoretical models on channel issues:

1. The manufacturers’ choice on channel structure
2. The channel coordination role of pull promotion & quantity discounts in dyadic channel
3. The mechanisms for channel coordination to align franchise interest and to achieve customer satisfaction in the context of demand uncertainty and heterogeneity.
4. In a competitive context
5. Use a reference-dependent approach to study double-marginalization problem in dyadic channel

1. A brief introduction on the study

Modeling:

1. Bare-bones model

Assumptions：

1. 1 manufacturer vs 1 retailer in the conventional distribution channel facing the same demand
2. Cournot competition：Dp=a-bp (b>0)
3. Sequence of the events: Firstly, the manufacturer sets her wholesale price; Then, the retailer sets its price
4. Objective function:

 max Πc (the Channel ‘s whole profit)

max Π (the manufacturer’s profit)

max π (the retailer’s profit)

 

1. Only retailer is fair-minded:

1. On the basic assumptions of conventional distribution channel
2. Retailer’s objective function changes into utility function:

max uw,p=πw,p+fr(w,p)

In which, profit function πw,p=p-wDp=(p-w)(a-bp)

Equity function is to measure the retailer’s inequity, combined with disadvantageous and advantageous inequity

frw,p=-αmaxγΠw,p-πw,p,0-βmaxπw,p-γΠw,p,0

In which, 0<β≤α<1, and the retailer perceives its monetary payoff relative to the manufacturer’s profit, thus the retailer’s monetary payoff is described as follows: γΠw,p=γ(w-c)D(p), in which the parameter γ>0.

1. In order to solve the problem, we firstly derive the retailer’s optimal decision conditional on the retailer’s monetary payoff being either lower or higher than his equitable payoff. Second, the optimal solutions from both cases are compared to determine the retailer’s global optimal solution.
2. The manufacturer’s wholesale price and profit are optimized on Retailer’s response function p(w).
3. Sub-conclusion: ①The manufacturer can coordinate the fair channel, both in terms of achieving the maximum channel profitability and in terms of attaining the maximum channel utility, with a constant wholesale price w.②When a fair channel is coordinated through a constant wholesale price, the retailer perceives no inequity. Therefore, a constant wholesale price as a channel coordination mechanism can help to foster an equitable channel relationship.

 

 

1. Both manufacturer and retailer are fair-minded

1. On the basis of Model 2, the manufacturer is also fair-minded and she considers μπ as her fair payoff whereμ>0
2. The manufacturer’s objective function also changes into utility function:

max UX,p=ΠX,p+fm(X,p)

Where X is the manufacturer’s decision variable and the equity function is as follows:

fmX,p=-α0maxμπX,p-ΠX,p,0-β0max⁡{ΠX,p-μπX,p,0}

In which 0≤β0≤α0<1 and Model 2 is a special case with α0=0 β0=0.

1. The equity-capable channel payoff (ECCP): Πc refers to the channel’s summary profit

ECCP=γ1+γΠc+μ1+μΠc=μγ+μ+γ+μγμγ+μ+γ+1Πc

Acrimonious channel: ECCP>Πc μγ>1

Harmonious channel: ECCP≤Πc  μγ≤1

1. The key to this model is not to solve the optimal wholesale price but to check whether the current wholesale price is still optimal for the manufacturer when she herself cares about fairness.
2. Sub-conclusion: The manufacturer’s concern for fairness will not affect the maximization of either channel profit or channel utility unless she is very averse to her own disadvantageous inequality.

 

Conclusions:

1. Because of fairness concerns, the retailer has an incentive to an equitable outcome in channel interactions, and channel coordination can be achieved using a constant wholesale price.
2. An equitable channel relationship may be an exception rather than a norm, especially when all channel members are fair-minded.

 

Limitations and future research:

1. We take for granted that the concerns with fairness displayed by a firm’s managers are an automated, nonstrategic behavior. Future work can explore the strategic manufacturer manager’s behavior.
2. We do not examine how imperfect information may affect channel interactions in the presence of fairness concerns. Future work can incorporate information sharing into the model.
3. We analyzed a simple dyadic channel. Future work can generalize the analysis into n-stage channel.