Evolutionary Behavior of Supply Chains: Altruism or Fairness Caichun Chai*

Transcription

1 Advances in Economics Business Management Reseach volume 16 Fist Intenational Confeence on Economic Business Management (FEBM 2016) Evolutionay Behavio of Supply Chains: Altuism o Fainess Caichun Chai* * School of Management Engineeing Nanjing Univesity Nanjing China Coesponding autho: Caichun Chai PhD Cidate caichunchai@hotmailcom Abstact Basing on the individual behavio pefeences we analyze the evolutionay stable stategies of supply chains whee each chain consists of one manufactue one etaile Thee ae many manufactues etailes in the economic system A etaile a manufactue inteact with each othe omly A manufactue o etaile has two behavioal pefeences: fainess concen altuism concen We get the evolutionaily stable stategies unde linea dem nonlinea dem By analyzing the evolutionay stability of Nash equilibium is distinct unde dieent dem types The evolutionaily stable stategies of the manufactue etaile depend on thei pefeence paametes Keywods: evolutionay stable stategy; pefeence; fainess; altuism; selfishness 1 Intoduction In the expeimental economics objectives often show non-selfish behavio such as fainess altuism etc Fainess implies that goods o esouce should be distibuted by a peceived appopiateness in a society goup o oganization in economics While altuism efes to the behavio by an individual that inceases the fitness of anothe individual even this behavio may decease the fitness of the acto Fainess is a popula topic in the behavio eseach fo instance some scholas find that thee is a stong feelings of fainess about the poducts pice fo the consumes12 hence consumes ae unwilling to buy a poduct in a monopoly pice because they feel it is unfai Anothe example has been found in the fim s wage setting fo the wokes1345 which explain why some employes choose to cut down the numbe of pesons employed athe than cut the wage of thei wokes The study of altuistic behavio is anothe popula topic in the behavio economics The altuistic behavio of poposes in the Ultimatum game6789 the act of giving in the public goods1011 has been studied fo many yeas The investigation of non-selfish behavio especially fainess altuism has attacted many scholas in biology mathematics economics etc The study in supply chain management the dynamics of individual pefeence has been paid moe moe attention ecently T H Cui et al 12 investigated the ole of fainess in the channel coodination K M Amaeshi et al13 S Pa14 G E Goeing15 C F Hsueh16 D Ni et al17 consideed the ole of social esponsibility pefeence in a supply chain G E Bolton A Ockenfels18 E Feh K M Schmidt19 G Chaness E Hauvy20 studied the eect of fainess altuism ecipocity on the stategy of playes in the dieent games E Dekel et al 21 H Beste W Güth22 J C Ely O Yilankaya23 E A Ok F Vega-Redondo24 Y Shiata25 analyze the evolutionay dynamics of the geneal Copyight 2016 the Authos Published by Atlantis Pess This is an open access aticle unde the CC BY-NC license ( 83

2 Advances in Economics Business Management Reseach volume 16 individual s pefeence Howeve these papes few combine the two fields to examine the eect of pefeence on the dynamics of supply chains Ou pape is dieent with the existing liteatue at two points Fist we study the dynamics of playes stategies in the long tem athe than one-shot game focus on the evolutionay stability of manufactues etailes stategies in the supply chains Second we study the evolution of stategies with fainess altuism pefeences unde dieent dems analyze the eects of individual pefeences dem type on the evolutionaily stable stategies 2 Model analysis We assume that thee ae many (a suiciently lage numbe of) manufactues etailes in the maket They match omly to play a two-peson manufactue Stackelbeg game Let the unit wholesale pice be w the selling pice be p The manufactue the etaile have two pue picing stategies: fainess concen altuism concen 21 Mathematical models In this section we examine the eects of fainess concen altuism concen on a channel with one manufactue one etaile If a playe caes about fainess he maximizes his utility that includes two pats: one is monetay payo the othe is the disutility due to inequity If he is altuism concen he maximizes the combination of his pofit the pofit of his opponent Assuming the maket dem is given by only the manufactue incus a unit poduction cost c (0<c<1) in this channel We use to denote the pofits of the manufactue the etaile in this supply chain espectively Fist if only the etaile concens fainess the manufactue is altuistic Then the etaile will maximize a utility function that accounts fo the etaile s monetay payo as well as his concen about fainess when setting his pice We can wite p ( w p) + f ( w p) u= ( w p ) whee f ( w p) is the disutility due to inequity We model fainess as inequity avesion as in E Feh K M Schmidt19 The algebaic fom is α f 0 is the fainess paamete of etaile fom disadvantage pofit is the fainess paamete of etaile fom advantage pofit the paametes imply the degee of fainess fo etailes Similaly we can define the degee of fainess fo manufactues As the mention in T H Cui et al 12 although the distibutive fainess has much moe substance than a simple mathematic epesentation hee can captue we believe that this fomulation stikes a easonable balance between modeling tactability behavioal complexity When the pofit of the manufactue is highe than the pofit of the etaile the equilibium pofit of the manufactue is always less than that one of the etaile if the etaile is fainess concen Hence in this section we only conside this case that the etaile s pofit highe than m So fo a fainess concen manufactue etaile the the manufactue s ie ππ optimization poblems ae 84

3 Advances in Economics Business Management Reseach volume 16 espectively Let the fist ode patial deivative equal zeo we get the fist ode condition Fom the indiect calculation it is easy to veify that when the fist ode patial deivative at point than zeo when the fist ode patial deivative at point ie it is unimodal in p Thus this is a unique utility at the point manufactues can get thei maximal utility Thus we get the equilibium wholesale pice such that at this point o is less than zeo such that etailes can get the maximal Similaly we can get thee exists a unique m is tue let ensue ππ is lage maket pice is espectively In ode to we get the equilibium pofits of manufactue etaile ae Othewise Similaly unde the assumption we get the equilibium pofits fo the manufactue etaile as Table 1 Hee 0 βα βf 10 αα αf 1 β a a a denote the degees of altuism fo manufactues etailes; βf αf denote the degees of fainess fom disadvantage pofit fo manufactues the degee of fainess fom advantage pofit fo etailes espectively The supescipts f a denote the stategy fainess altuism the fist one is the stategy of manufactues the second one is the stategy of etailes Subscipts m denote the pofits of manufactues etailes When we can similaly analyze the dynamics of the supply chain 22 Evolutionay analysis We assume the pinciple of an individual choose his stategy is the stategy that gets a highe pofit has the highe pobability to be chosen in the futhe inteaction The change of the shaes of the manufactue etaile using altuistic stategy satisfy the eplicato dynamics Let x denote the shae of manufactues using altuistic stategy y denote the shae of etailes using altuistic stategy then shaes of manufactue etaile using fai stategy ae espectively Two-tuple (x y) means that thee ae manufactues with popotion x using stategy altuism etailes with popotion y using stategy altuism Thus basing on the eplicato dynamics the stability of the dieential equation we get the esults as follows 85

4 Advances in Economics Business Management Reseach volume 16 Table 1 - The equilibium pofits of the manufactue etaile in the one-shot game 86

5 Advances in Economics Business Management Reseach volume 16 Poposition 1 (1) When is small (less than 1/5) the point (0 0) ie the stategy (fainess fainess) is an evolutionaily stable stategy; (2) When is elative lage ( ) the equilibium (0 1) ie stategy (fainess altuism) is an evolutionaily stable stategy; (3) When elative lage ( is ) the equilibium (1 1) ie stategy (altuism altuism) is an evolutionaily stable stategy; (4) When is small (less than 1/4) the equilibium point (1 0) ie stategy (altuism fainess) is an evolutionaily stable stategy The poof is a staightfowad computation Fo descibing the dynamics of Poposition 2 we give Figs 1-4 as follows whee c=1 Fig 1 - The potait of Poposition 2(1) ) ( Fig 2 - The potait of Poposition 2(2) ( ) 87

6 Advances in Economics Business Management Reseach volume 16 Fig 3 - The potait of Poposition 2(3) ( ) Fig 4 - The potait of Poposition 2(4) ( ) Fom Poposition 1 Figs 1-4 the fou stategy pofiles: two symmety stategy pofiles two asymmety stategy pofiles specially both manufactue etaile use stategy altuism o fainess manufactues use stategy fainess etailes use stategy altuism manufactues use stategy altuism etailes fainess may be evolutionaily stable stategy depend on thei pefeence paametes When the degee of fainess to the manufactue is high the manufactue should use altuistic stategy; coespondingly when the degee of fainess fo the etaile is high then he should use altuistic stategy The degee of the etaile is elatively low when the degee of altuism to the manufactue is elative high the manufactue should use fai stategy when the degee of altuism to the manufactue is elatively low he should use altuistic stategy The evolutionay stability of stategy depends on the elative values of individual pefeence paametes 3 The impact of dem type Fo analyzing the eect of dem type on the evolutionaily stable stategies in the supply chain we discuss the case that the dem is a linea function of pice in this section Assuming the dem is given by we study the evolutionaily stable stategies 31 Equilibium outcomes unde linea dem function in the one-shot game Fist we conside the case that the pofit of the manufactue is highe than the etaile s So in the case whee the manufactue is an altuist the etaile caes about fainess the optimization poblems of the manufactue etaile ae espectively Hee Fom denotes the degee of altuism of the manufactue we get the second ode condition is tue Similaly we can get the second ode condition fo also is tue Thus we obtain the equilibium outcomes of manufactues etailes in the one shot game The specific outcomes ae shown in Appendix Basing on the calculation we get five payo matices depend on the values of the pefeence paametes We focus on one case in ou pape the othes can be analyzed using the simila 88

7 Advances in Economics Business Management Reseach volume 16 method We get payo matix when βa (1 + aa f )(1 2 f ) aa f +2 f 0 a a β a < 1 as Table 2 Table 2 - The mateial payo with altuism fainess M R altuism altuism π maa π aa fainess π mfa π fa fainess π m π π m π Whee α f β f ae the fainess paametes of the etaile manufactue espectively a β ae the altuism paametes of the etaile manufactue espectively The supescipts f a denote the stategy fainess altuism the fist one is the stategy of manufactues the second one is the stategy of etailes Subscipts m denote the equilibium pofits of the manufactue etaile a 32 Evolutionaily stable stategy unde linea dem function In this subsection we analyze the evolutionay stable stategies Let manufactues who ae altuism concen concen we get the eplicato dynamics a be the faction of be the faction of etailes who ae altuism (1) By calculating we have the esults ππ sgn(ππ is m m m m ) depends on the value of β a If the value of β a is small then positive; if the value of β a is lage ππ is negative And basing on the Figs 5-10 we m m fa aa see that ππ ππ ae negative m 0020 m a 0005 Fig 5- ππ m m vesus α f βf with β a = 04 Fig 6- ππ vesus m m βa β f 03 = α f 048 with= 89

8 Advances in Economics Business Management Reseach volume 16 fa a Fig 7- vs αf βf fa Fig 8- ππ vs with aa aa βf with= = α f aa Fig 9- ππ vs aa βa with α f = f aa Fig 10- ππ vs α f with Hence we have esults as below basing on the numeical simulation Poposition 2 The points (0 1) (1 1) ae unstable While the point (0 0) is asymptotically stable as the value of β a is lage the point (1 0) is asymptotically stable as the value of β a is small Fom Poposition 2 we know that if the manufactue does not cae a lot about altuism then he decides his wholesale pice by maximizing his function of altuism the etaile decides his maket pice by maximizing his fai utility is the evolutionay stable stategy; if the manufactue caes a lot about altuism then the stategy pofile whee both manufactue etaile decide thei pices by maximizing the function of thei fai utilities is the evolutionay stable stategy 33 The impact of dem type on evolutionaily stable stategy In the above analysis we get the evolutionaily stable stategies of manufactues etailes unde linea dem non-linea dem Fom the Popositions 1 2 although the conditions of paametes to the evolutionaily stable stategies ae independent of the dem paametes the esults ae distinct unde dieent dem type Unde the non-linea dem when the etaile is fainess concen the equilibium pofit of manufactues is always less than the equilibium pofit of etailes the equilibium outcomes in the one shot game unde linea dem ae iche than those unde non-linea dem 90

9 Advances in Economics Business Management Reseach volume 16 Basing on Poposition 2 when the degee of altuism of the manufactue is high he chooses the fai stategy when the degee is elative low he chooses the altuistic stategy Those esults ae simila to those in Poposition 1 Howeve in Poposition 2 etailes always use fai stategy unde linea dem while accoding to Poposition 1 unde non-linea dem when the degee of fainess of etailes elatively high etailes use stategy altuism is a bette stategy in the long tem inteaction The possible eason is that if the etaile caes about fainess vey much the disutility fom inequity will hut his benefit Futhemoe fom Poposition 1 Poposition 2 the stategy pofile that both the manufactue the etaile use stategy altuism can be an evolutionaily stable stategy unde non-linea dem while the esult is not tue unde linea dem Hence though the conditions of individual pefeence paametes that satisfy the evolutionaily stable stategies do not depend on the dem function diectly the dem type is an impotant facto to the evolutionaily stable stategies of the manufactue the etaile 4 Conclusions In this pape we analyze the evolutionay stable stategy in the supply chain consists of many manufactues etailes We assume that each manufactue o etaile has two kinds of stategies to choose: fainess altuism We get that the evolutionay stable stategy depends on the values of fainess o altuism paametes Futhemoe the maket dem also fects the stategy choice of manufactues etailes Howeve we get some esults about individual s pefeence fainess o altuism by numeical examples next we will continue to analyze the situation completely Acknowledgment Thanks fo the suppot of NSF( ); Univesity Scientific Reseach Innovation Plan of Jiangsu (KYLX_0063); Outsting Talent Fund of Anhui (2013SQRL030ZD) Refeences 1 D Kahneman J L Knetsch R Thale Fainess as a constaint on pofit seeking: Entitlements in the maket The Ameican Economic Review 76 (1986) M Rabin Incopoating fainess into game theoy economics The Ameican Economic Review 83 (1993) R M Solow On theoies of unemployment Ameican Economic Review 70 (1980) J Agell P Lundbeg Theoies of pay unemployment: Suvey evidence fom Swedish manufactuing fims Scinavian Jounal of Economics 97 (1995) C M Campbell K Kamlani The easons fo wage igidity: Evidence fom a suvey of fims Quately Jounal of Economics 112 (1997) R Slonim A E Roth Financial incentives leaning in ultimatum maket games: An expeiment in the Slovak Republic Econometica 66 (1997) R H Thale The ultimatum game Jounal of Economic Pespectives 2 (1988)

10 Advances in Economics Business Management Reseach volume 16 8 C Camee R H Thale Ultimatums dictatos mannes Jounal of Economic Pespectives 9 (1995) W Güth R Schmittbege R Tietz Ultimatum bagaining behavio-a suvey compaison of expeimental esults Jounal of Economic Psychology 11 (1990) G S Becke Altuism egoism genetic fitness: Economics sociobiology Jounal of Economic Liteatue 14 (1976) J Andeoni Pivately povided public goods in a lage economy: The limits of altuism Jounal of Public Economics 35 (1988) T H Cui J S Raju Z J Zhang Fainess channel coodination Management Science 53 (2007) K M Amaeshi O K Osuji P Nnodim Copoate social esponsibility in supply chains of global bs: A bounday less esponsibility? Claifications exceptions implications Jounal of Business Ethics 81 (2008) S Pa Coodination of a socially esponsible supply chain using evenue shaing contact Tanspotation Reseach Pat E 67 (2014) G E Goeing Copoate social esponsibility maketing channel coodination Reseach in Economics 66 (2012) C F Hsueh Impoving copoate social esponsibility in a supply chain though a new evenue shaing contact Intenational Jounal of Poduction Economics 151 (2014) D Ni K W Li X Tang Social esponsibility allocation in two-echelon supply chains: Insights fom wholesale pice contacts Euopean Jounal of Opeational Reseach 207 (2010) G E Bolton A Ockenfels ERC: A theoy of equity ecipocity competition The Ameican Economic Review 90 (2000) E Feh K M Schmid A theoy of fainess competition coopeation The Quately Jounal of Economics 114 (1999) G Chaness E Hauvy Altuism equity ecipocity in a gift-exchange expeiment: An encompassing appoach Games Economic Behavio 40 (2002) E Dekel J C Ely O Yilankaya Evolution of pefeences Review of Economic Studies 74 (2007) H Beste W Güth Is altuism evolutionaily stable? Jounal of Economic Behavio & Oganization 34 (1998) J C Ely O Yilankaya Nash equilibium the evolution of pefeences Jounal of Economic Theoy 97 (2001) E A Ok F Vega-Redondo On the evolution of individualistic pefeences: An incomplete infomation scenaio Jounal of Economic Theoy 97 (2001) Y Shiata The evolution of fainess unde an assotative matching ule in the ultimatum game Intenational Jounal of Game Theoy 41 (2012)

11 Advances in Economics Business Management Reseach volume 16 Appendix The computation of the equilibium outcomes unde linea dem Fist we conside that the manufactue is an altuist the etaile caes about fainess the objective functions of the manufactue etaile ae By calculating we have the equilibium is And the pofits ae When the manufactue caes about fainess the etaile is an altuist then the objective functions ae espective By calculating we obtain the equilibium ae And when ie β f > 2 > 1/ aa o β f < 1 + 3a a (3 + aa a )(1 + a ) the equilibium pofits ae Othewise w fa = w p fa = 2a + b(1 + a a ) b(3 + 2a a ) fa fa = = ππ m (a bc) 2 (1 + a a ) b(3 + a a ) 2 So the pofit of the manufactue the etaile ae espectively 93

12 Advances in Economics Business Management Reseach volume 16 Similaly when both the manufactue etaile ae fainess concen the pofit of manufactue etaile ae as follows When both the manufactue etaile ae altuism concen the pofits of the manufactue etaile ae espectively Similaly we can get the equilibium outcome when the pofit of etailes highe than that one of manufactues 94