inequity aversion in screening contracts: experimental evidence and model analysis

Inequity aversion in screening contracts: experimental evidence and model analysis

IFORS, 15th July 2014, Guido Voigt

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G. Voigt –Magdeburg,

Agenda

• Motivation• Model• Supply chain performance• Outlook and discussion

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G. Voigt –Magdeburg,

Asymmetric information in supply chains

• Asymmetric information (may) deteriorate supply chain performance ….

• …. evolve in many supply chain interactions

– Joint lot-sizing (holding costs- and/or fixed costs)

– Pricing decisions (production costs, end-customer demand)

– Capacity decision (backorder costs, investment costs)

• Solution concept: Screening contracts

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G. Voigt –Magdeburg,

Screening contracts: Basic Idea

Supplier (uninformed)Low cost buyer

High cost buyer?Contract “low”

Contract “high”

Buyers: Profit maximizer

Empirical: Buyers are insensitive to

small payoff differences

Research questions:• Impact on Supply Chain Performance ?• Behavioral robust contract design ?

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G. Voigt –Magdeburg,

Agenda

• Motivation• Model• Supply chain performance• Outlook and discussion

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G. Voigt –Magdeburg,

Model

• B asks S for smaller lot-sizes q– B: lower inventory holding costs (h /2 * q)– S: higher fixed costs ( f * d / q )

• B: may switch to alternative supplier (costs: R) – S does not know the buyer‘s actual benefit (h)– … but has to lower wholesale price ( w ) to induce

higher order sizes

Supplier (S) Buyer (B)

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G. Voigt –Magdeburg,

Classical Screening Model

• Probability distribution pi w.r.t. holding costs hi, i=1,…,n; h1<h2<…<hn

• Screening idea: One contract Ai = < qi, wi > for each possible holding cost realization hi

, 1

1 1

max ( ) . .

, 1,..., 12 2

2

i i

nw q S i ii

i

i ii i i i

nn n

fE P p d w s tq

h hw d q w d q i n

hw d q R d

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Example for 3 holding cost levels - low (l), med (m), high (h)

ql= 400 wl= 9,83qm= 189 wm= 10,89qh= 129 wh= 11,78

Buyer's cost ql, wl qm, wm qh, wh Alternative

hl 1183 1183 1243 1500

hm 1583 1371 1371 1500

hh 1983 1560 1500 1500Supplier‘s profit 783 666 558 0

2 2l l

l l m mh hw d q w d q

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G. Voigt –Magdeburg,

Experimental results – Classical screening contracts

• Inderfurth et. al (2012):

• Profit maximum ≈ 70%

• Near profit maximum (10 cent difference) ≈ 26%– Huge cost effect on supply chain performance

• Other ≈ 4%

ql, wl

qm, wm

qh, wh

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G. Voigt –Magdeburg,

Inequity aversion

• Buyer hi not inequity averse with probability αi <wi,qi>

• Buyer hi is inequity averse with probability (1-αi) <wi+1,qi+1>

• „Empirical“ objective function:

, 111

max ( ) 1i i

nw q S i i i i ii

i i

f fE P p d w wq q

• Supplier does not exhibit inequity aversion if it is too costly• Frequency αi depends (linearly) on payoff difference ti between

alternatives

1 1, 1,..., 12 2

i ii i i i i

h hw t d q w d q i n

Slack

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G. Voigt –Magdeburg,

Behaviorally robust Principal-Agent model

• (OR) Challenge: Objective function not anymore concave,… but uni-modular for linear α(ti)

• Note: „Bunching“, i.e., qi=qi+1, occurs more frequently – derivation of optimal contract much more complex

, , 111

1 1

max ( ) ( ) 1 ( )

. .

, 1,..., 12 2

2

i i i

nw q t S i i i i ii

i i

i ii i i i i

nn n n

f fE P p d t w t wq q

s th hw t d q w d q i n

hw t d q R d

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G. Voigt –Magdeburg,

Buyer's cost ql, wl qm, wm qh, wh Alternative

hl 1072 1106 1138 1500

hm 1472 1289 1289 1500

hh 1872 1471 1440 1500Supplier‘s profit 672 578 532 0

Behaviorally robust contract

ql= 400 wl= 8,72 tl= 0,35qm= 183 wm= 10,15 tm= 0qh= 151 wh= 10,62 th= 0,6

ql= 400 wl= 9,83qm= 189 wm= 10,89qh= 129 wh= 11,78

„Classical“ contract parameters

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G. Voigt –Magdeburg,

Agenda

• Motivation• Model• Supply chain performance• Outlook and discussion

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G. Voigt –Magdeburg,

Supply chain performance

Fraction of strictly profit maximizing buyers

Classical screening benchmark

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G. Voigt –Magdeburg,

Supply chain performance

Fraction of strictly profit maximizing buyers

Classical screening benchmark

Classical contract parameters

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G. Voigt –Magdeburg,

Supply chain performance

Fraction of strictly profit maximizing buyers

Classical screening benchmark

Classical contract parameters

Behavioral robust contract parameters

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G. Voigt –Magdeburg,

Summary, conclusion, and Outlook• Critical assumption in screening theory: strict profit

maximization• Neglecting behavioral irregularities leads to high performance

losses • Main contribution– Derivation (and solution procedure) for the optimal

„behavioral robust“ contract• Main limitation: linear dependency of αi and ti • Outlook: Experimental testing

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G. Voigt –Magdeburg,

Thanks!

guido.voigt@ovgu.de

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G. Voigt –Magdeburg,

Numerical example: 3 buyer types• wi irrelevant for supply chain performance

• Behavioral robust parameters: Order size– q2 is lower (less likely)– q3 is higher (more likely)

+-

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G. Voigt –Magdeburg,

Relevant Literature• Probablistic choice models* and type dependent decision errors**:

– The higher the profit of an alternative, the higher the probability that the alternative is chosen (not supported by experiments)

– <wi,qi> ↔ <wi+1,qi+1> (not supported by experiment)

• Increase pay-off differences between alternatives

– Closest to the underlying work

– Only for the case of 2 types (many aspects not addressed)

– Restrictive assumption on „decision error“ (monotone hazard rate)

* Basov and Danilkina (2006) and Basov (2009), ** Basov and Mirrless (2009)

*** Laffont and Martimort, 2002 (Textbook)

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G. Voigt –Magdeburg,

Parameters numerical example

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Complete set of profit/cost impact – Behavioral robust contract

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G. Voigt –Magdeburg,

Impact of bunching (1/2)

0.1

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G. Voigt –Magdeburg,

Impact of bunching (2/2)

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References• Inderfurth, K.; Sadrieh, A. and Voigt, G. (2012) The Impact of

Information Sharing on Supply Chain Performance in Case of Asymmetric Information. Forthcoming in Production & Operations Management

• Basov, S. (2009) Monopolistic Screening with Boundedly Rational Consumers, The Economic Record, 85, pp. S29-S33

• Basov, S. and Danilkina, S. (2006). Quality and product variety in a monopolistic screening model with nearly rational consumers, Proceedings of the 35th Australian Conference of Economists, pp. 1-21, http://www.business.curtin.edu.au/files/Basov_Danilkina.pdf

• Laffont, J.-J. and Martimort, D. (2002) The theory of incentives: The Principal-Agent Model. Princeton University Press, Princeton/New Jersey