Shobande and Akinbomi Futur Bus J 2020, 6(1):11 https://doi.org/10.1186/s43093-020-00019-8 Future Business Journal

RESEARCH Open Access Competition dynamics in Nigerian aviation industry: a game theoretic approach Olatunji Abdul Shobande1* and Mobolaji Daniel Akinbomi2

Abstract Background: This paper develops a game theoretic model that analyses the dynamics of competition among the leading domestic aviation frms in the Nigerian aviation industry. It probes the abilities of the prisoner dilemma to describe the subjective behaviour of the frms, which provide a yardstick for assessing the optimal competitive strate- gies available to the frm to survive the business environment. Results: The solution of the game provides diferent optimal competitive strategies for the frms. While fndings show that Aero Contractors placed more weight on fight pricing to survive in the industry, needed to retain non- pricing competitive strategy to remain the leading domestic aviation frm in . Conclusion: Based on our fndings, we conclude that if both frms stick to the optimal strategy, they would both share the market. Keywords: Firm strategy, Game theory, Duality, Aviation industry JEL Classifcation: L2, L11, C69, C70, C71

Introduction the efects of less regulation provided passengers with Te paper focuses on the Nigerian aviation industry, diferent choices in terms of price service options for dif- which has continued to experience historic changes, ferent routes. According to available analysis, the Nige- growth, and development. We provide evidence by apply- rian industry is still far from hitting the peak of ing the prisoner dilemma theoretic intuition to experi- competition milestone as may be expected, despite the ment with the competitive dynamics of the industry. remarkable transition experienced [2]. One major chal- We work with two leading aviation frms that serve as lenge often cited has been the inability to reconcile the the main drivers of the Nigerian aviation business with existing pricing strategies and customer protection [3]. the aim of investigating the various economic strategy Tis remains a huge concern and demands regulatory employed by the frms to navigate the dynamics of avia- response/intervention to avoid over exploitation of pas- tion business environment in which they operate. sengers while reassuring that prices are to some degree In recent pasts, there have been remarkable transfor- benefcial to the services. mations in the industry, which have infuenced In explaining the analysis of existing market structure economic efciency and the high degree of competition and providing yardstick for economic strategy and mana- noticed among operators. Interestingly, the deregulation gerial decision of frm, in order to provide service deliv- and liberalisation of the sector also contributed in moti- ery to passengers without monopolistic tendency of the vating new entry of frms into the sector [1]. However, frms, this study examines the efect of price charges on passengers’ patronage among two leading airline opera- tors in the Nigerian aviation industry. Specifcally, the *Correspondence: [email protected] objectives are to: (1) determine the best strategy to adopt 1 Business School, University of Aberdeen, Block C, Room F02, Edward Wright Annexe, Aberdeen AB23 3RX, UK by Arik Air and Aero Contractors in surmounting identi- Full list of author information is available at the end of the article fed challenges. Te strategy can either be a price or an

© The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativeco​ ​ mmons.org/licen​ ses/by/4.0/​ . Shobande and Akinbomi Futur Bus J 2020, 6(1):11 Page 2 of 8

output, since frms compete on price and non-price vari- on most domestic trunk routes. Te open skies policy ables (2) determine mathematically, the payofs from the delivered yet another liberalisation policy adopted to best strategy that will be chosen by each frm. increase competition and growth of the industry in Nige- Te paper also aims at providing three important con- ria. Te open skies policy had as its core the unrestricted tributions to both theoretical and empirical understand- access of airlines to diferent destinations. Even though ing of the nature and structure of competition in the the domestic airlines in Nigeria are plagued by capac- aviation market. First, the paper develops a game theory ity challenge and poor service delivery, we argued that based on linear programming in the analysis of the exist- strategic approach to overcoming these identifed issues ing competition and market structure in the Nigerian avi- should be taken if the domestic airlines will survive the ation industry. Te approach provides the yardstick for harsh operating environment. Tus, this study employs evaluating the economic strategy adopted between the the technique of strategic decision in the context of game frms to survive their business environment. Second, the theory to obtain the optimal strategy for the survival of outcome of the experiment provides various managerial the Nigerian aviation frms, namely Arik Air and Aero strategies that can be adopted by management of these Contractors. In view of this, the problem addressed in frms to improve their service delivery and maximise pas- the study is, how will competitors determine the opti- senger patronage. Tird, the innovative part of the paper mal strategy to employ in order to remain competitive is the ability to reconcile the growing misconception that and survive the turbulent-cum-harsh operating/business regulation often result to inefciency and high cost of environment? Tis remains unsolved in the aviation lit- doing business in Nigeria. Te result shows that the exist- erature within the Nigerian context. It is this lacuna that ing system seems rigid and encourages exploitation of this study seeks to fll. passengers as the operators rely on pricing strategy as a measure to motivate customer. Tis is also blamed for the Hypothesis development poor service delivery experienced in the industry. Tus, In light of the above, two hypotheses were tested for this the need for proactive economic policy that will reassure study: customer protection and efcient service delivery can- not be ignored in the context of the Nigerian aviation Hypothesis 1 Does pricing behaviour determine pas- industry. senger patronage among the leading airline frms in Nigeria? Background and hypothesis development Background Hypothesis 2 What is the optimal competitive strategy Historically, competition in the Nigerian aviation indus- available to each frm to remain competitive in the avia- try can be traced to the pre- and post-independence eras. tion business environment? Te pre-independence development in the industry was occasioned by riotous feud between the British colo- For each hypothesis to be valid, the efect of pricing nial administration and the people of city in 1925, behaviour must refect the gain of each frm over its com- while the post-independence development saw that the petitor. Hence, to test the degree of competition among Federal Government buy out other shareholders of Nige- the leading aviation frms in Nigeria, we must compare rian Airways thereby making the airline wholly owned by the price behaviour and passengers’ patronage with its the Nigerian government. At this time, the airline had a existing output. On the other hand, we tested the ability monopoly for providing domestic services in Nigeria [2]. of the frms to cope within their business environment by It was also the national fag carrier for international ser- checking the optimal strategy it can adopt to improve its vices along the West African coast, and the USA. market share through efcient price service options. Te need for further transformation of the country’s air Te rest of the paper is organised as follows: the next transport services led to the eventual deregulation of the section presents the review of related literature and industry by the government [4, 5]. Tis action signalled methodology, followed by the last section, which con- unrestricted competition among the operators leading to cludes the paper with some policy implications of our the proliferation of small airline companies in Nigeria. fndings. In pursuance of the deregulation policy of the aviation industry, about 25 private airline operators were licensed Review of related literature in the early to contribute to the development of the In this section, we discuss the various theoretical under- industry. Te emergence of private airline operators suc- pinning and empirical arguments surrounding pricing cessfully broke the state monopoly (i.e. the Nigerian Air- behaviour and drivers of competition in the aviation ways) as they continue to run commercial air operations industry. Shobande and Akinbomi Futur Bus J 2020, 6(1):11 Page 3 of 8

Theoretical framework management and lack of organisational culture (Chen Te game theory is adopted to analyse competition et al. [28]; Yang and Dixon [29]). Chen et al. [28] rea- between Arik Air and Aero Contractors. One fre- soned that some frms fail to contest their position quently cited example of descriptive use of game theory in their respective industry due to poor management is the prisoner’s dilemma game [3, 6–10]. Te prisoner’s capacity and other organisational factors. Luo et al. [30] dilemma game is one of the classic examples of non- observed that organisational culture and the attitude of cooperative game in static form. In this game, there are management to compete are simultaneous factors that two players and each player have one turn, and the turns could juxtapose the level of success or failure that a frm are simultaneous. Te essential elements of simultane- attains. Some scholars called attention to how long-term ous play are that each player moves without knowing the development and strategic management drive competi- move of the other. Each player has two possible strate- tion among frms [31–34]. Wang et al. [31] contend that gies—to maintain innocence or to cravenly confess. If organisations with knowledge sharing skills and man- both players maintain innocence, they will increase their ager’s training capabilities are more likely to survive the payofs. However, if they are induced with a promise of pressure of competition. Dorn et al. [35] promoted the few years in jail by confessing, then the payofs might be stance that the structure, strategy and policy operated reduced. Te implication of prisoner’s dilemma to frms by an organisation are some of the predetermined fac- in competitive industry is to maintain current strategy tors that keep shaping and reshaping the nature of the that gives each player maximum payofs. organisation’s behaviour towards competition. Further In view of this, in any game of analysis, linear program- on the debate of organisation and motivators of competi- ming has been found mathematically to provide optimal tion, other scholars argued for interpersonal relationship solution to the players (Afrousheh et al. [11]; Cong et al. and corporate identity as major movers of frm’s competi- [12]; Zimmermann et al. [13]; Andrews et al. [14]), his- tion, especially in the aviation industry [36–39]. Ceptu- torically, ideas of linear programming inspire many basic reanu et al. [40] concluded in their work that competitive concepts of optimisation theory such as duality, decom- performance has signifcant implication on the overall position and importance of convexity and its generalisa- benefts and outcome of the organisation’s performance/ tions [15, 16]. In addition, it is useful in modelling issues sustainability. of planning, routing, scheduling, allocation and design. In German, Barry and Nienhueser [41] examined the An evaluation of 500 largest frms in the world showed low-cost airline industry and reported that competitive that 85% of them have used linear programming [11, 17– pressure stemming from European aviation demand for 20]. It is in the light of this that this current study utilised low-cost travelling is major driver of competition in the linear programming algorithm in fnding the optimal German aviation industry. strategy and the payofs emanating from such optimal In the USA, Velu [42] examined the level of dominance strategy for the two selected frms in the Nigerian domes- in frms and drivers of competition. He argued that the tic aviation sector. degree of innovation experienced within the system was major contending factor that determined competition in the US economy. Empirical literature In the Polish economy, Klimas [43] identifed the gap in Early literature has made reasonable eforts to build competition in the Polish aviation industry and suggested diferent models that explain nature, strategies, and that organisational culture and orientation are key driv- behaviour of frms to cope with their environment. For ers of competition in the industry. instance, Bell [21] once argued that a frm’s managerial In India, Singh [44] measured the competitive service asset is a key driver of competition in any industry. Chen quality performance of aviation frms and provided evi- et al. [22] in their study postulated that market compe- dence that traveller’s rate was a major driver of compe- tition and internal governance are critical for assessing tition among frms in the Indian aviation industry. Te competition in Taiwan. Sanjo [23] suggested that the cap- author further stressed that the aviation industry in India ital based on a frm and the business location is critical has undergone rapid transformation with the liberalisa- for competition. Further on competition, some studies tion of the sector leading to increase in cost, tight proft claimed that the degree of the frm’s orientation is crucial margins, and increasing competition among airlines. in surviving the dynamic competitiveness in the face of Tus, an airline’s success depends heavily on its ability to uncertain and highly challenging business environment retain old customers and attract new ones. [24–27]. In Korea, Park et al. [45] investigated whether and how Recent studies attributed consistent failure and poor service quality and corporate social responsibility (CSR) performance of businesses across the globe to poor signifcantly afect behavioural intention of customers Shobande and Akinbomi Futur Bus J 2020, 6(1):11 Page 4 of 8

to use or not to use an airline, through customer satis- We assumed that frms select their strategies on the faction survey among South Korean airline service pro- basis of probability. Let p1, p2, …, pm be the probabili- viders. Tey explored an integrated research model and ties with which frm I will employ each of its n strate- 0 ≤ ≤ 1 = 1, , n = 1 provided evidence that economic, social, and environ- gies, where pi (i ... n) and i=1 pi . mental responsibilities, as well as in-fight service quality, We assumed that some random process is employed by signifcantly determined customers’ satisfaction. Again, frm I to select a particular strategy and the strategy so they concluded there were notable connections between chosen corresponds to the selected number. A random customer satisfaction and behavioural intention to use. number selected does not give frm II the opportunity to Adler and Hanany [46] compared aviation markets anticipate frm I’s choice even if she knows frm I’s prob- under conditions of competition, code sharing contracts abilities. Firm II can randomise its strategy selection by and anti-trust immune alliances, assuming that demand assigning the probabilities x1, x2, …, xn to its strategy, 0 ≤ ≤ 1 = 1, , n = 1 for fights depends on both fares and the level of fre- where xi (i ... n) and i=1 xi . quency ofered. Using a hybrid competitive/cooperative Te probabilities, which the frms selected employed, game theoretic framework, we showed that the stronger are defned as optimal if: the inter-airline agreement on overlapping routes, the n higher the producer surplus. We also demonstrated that ≥ = 1, ..., bijxi Vi n (1) under asymmetric and uncertain demand, code sharing i=1 on parallel links might be preferable to competitive out- comes for multiple consumer types. n ≤ = 1, ..., Alderighi et al. [47] examined the price setting behav- cijxi Vi m (2) iour of full-service airlines in European passage aviation i=1 market. Te authors developed a model of airline com- petition, which accommodates various market structures where V is the value of the game. Equation 1 states that and provided evidence that competition in the avia- frm I’s expected profts is at least as great as V if frm II tion market in Europe was measured by price behaviour employs any of its pure strategies with a probability of among the aviation frms. one. In all the paper reviewed above, a crucial sustained A fundamental theory of game theorem states that a assumption is that competition remains the paramount solution that satisfes Eqs. (1) and (2) always exists, and for frm to survive their business environment. However, that V is unique. If both frms select their strategies on it is unclear whether increase or decrease in competition a probabilistic basis, frm I’s expected proft, E1 is deter- can improve customer patronage and reassure greater mined from Eq. (1) as: output. In particular, majority of the studies seems silent n n 1 = ≥ on the nature and pattern of competition that can be Q bijpixi V (3) used in the aviation industry. For instance, some studies i=1 i=1 claimed that uncertainty in demand can make it impos- Firm II’s expected loss, E2 is determined from Eq. (2) sible for frm to compete [46]. Other studies argued that as: price setting behaviour are drivers of competition [47]. n n Tus, the lack of consensus among scholars on whether Q2 = cijpixi ≤ V pricing behaviour or demand uncertainty are the drivers (4) j=1 i=1 of competition motivate further re-examination of this link. One common feature among these studies, however, Te middle term in Eqs. (3) and (4) is identical. Tat is the heavy reliance on the game theoretical approach. is frm I’s expected proft equals frm II’s expected loss. Te combination of game theory and linear program- Combining Eqs. (3) and (4) yields V ≤ Q1 ≤ Q2 ≤ V. ming were used to aid the analysis of this present study Tis proves that Q1 = Q2 = V. Tese relations state that too. the expected outcome is the same for the two frms if both employ their optimal probabilities. Research method By converting their games into linear programming format, optimal strategies for the two frms and the value We worked with the empirical strategy of Ignatius et al. for the game can be determined. First, we consider cases [48] and Straub and Schaefer [18] to determine the opti- in which the value of the game is positive. Tat is V > 0. mal strategy and the payofs from such strategy so chosen From the backward induction game, we analysed the by the two frms—Arik Air and Aero Contractors, which optimal strategies starting from frm II.We defne the var- are the leading domestic aviation frms. iables for frm II as: Shobande and Akinbomi Futur Bus J 2020, 6(1):11 Page 5 of 8

xi Table 2 Approximated fgure on air fare and passengers’ X = j = 1, ..., n j V (5) volume. Source: Researchers (2019) Companies Objectives By defnition, Average air fare Passengers’ 1 volume = X1 + X2 +···+X V n (6) Arik Air 47 19 It is expected that frm II will make its maximum expected Aero Contractors 12 18 loss as1 small as possible, or equivalently, it desires to make V as large as possible. Te linear programming equivalent is to fnd values for Xj ≥ 0 j = 1, ..., n which have a linear programming problem for Arik Air solution. maximises Eq. (6) subject to Here, X1 represent airfare and X2 represent passengers’ vol- + +···+ ≤ 1 = 1, , xi1X1 xi2X2 xinXn i ... n (7) ume and let V be the value of the game. Arik Air solution Sources and measurement of data Max. X0 = X1 + X2 Te data used to estimate this model are annual sec- S.t. 47X1 + 19X2 ≤ 1 ondary data obtained from the Nigerian Civil Aviation 12X1 + 18X2 ≤ 1 Authority (NCAA) based on the existing records of Arik Air and Aero Contractors. Annual data on Arik Air and Putting the LPP into standard form, we have Aero Contractors on airfare and passengers’ volume Max. X0 = X1 + X2 (as the measure of output) are utilised. A linear pro- S.t. 47X1 + 19X2 + S1 = 1 gramming model is developed to determine an optimal 12X1 + 18X2 + S2 = 1 resource strategy, and the model is used to select the best , , , ≥ 0. strategy between airfare and output proxied by passen- X1 X2 S1 S2 gers’ volume and payofs from each strategy. Solving using the simplex method gives Te airfare used covered both the economy class and business class. We do not make distinction between X1 = 0; X2 = 1 19; X0 = 1 19 the economy class and business class, as classes’ fares = 1 are totalled and averaged. Te passengers’ volume as a Te value of the game can be obtained as V X0 . 1 measure of output is totalled from January to December V = 1/ 19 = 19 . Te required probability is of 2014. Te periodicity is based on constraints in data 1 19 X2 = X2 X0 = 19 × 1 = 1. availability and motivation discussed in the introduction. Aero Contractor’s solution Linear Programming Solver (LPS), version 1.11.1, was We can solve Aero’s problem by frst converting it into used to simulate the model. linear programming problem (LPP). Aero minimisation Experimental results problem is dual of Arik maximisation problem, and by extension the duality theory, the conversion is as follows. In this section, we present the outcome of our experi- Let y1 be the fight price and y2 be the passengers’ volume mental results and discussions, which allow us to decide and V the value of the game. regarding the future prospect of these organisations. By duality theory, we have Following the data obtained from the NCAA, we can draw tables to represent the value as follows (Table 1): Min. y0 = y1 + y2 Table 2 shows the entries of the extracted dataset in the S.t 47y1 + 12y2 ≥ 1 matrix form based on row and column. Tis permits us to 19y1 + 18y2 ≥ 1 y1, y2 > 0 Table 1 Airfare and passengers’ strength of Arik Air Apply simplex method to the dual problem to solve the and Aero Contractors. Source: Researchers (2019) minimisation problem. Introducing slack variables and Companies Objectives rearranging the objective function, we have Average air fare Passengers’ strength

Arik Air 47,057.68 1,987,691 Aero Contractors 12,898.72 1,833,292 Shobande and Akinbomi Futur Bus J 2020, 6(1):11 Page 6 of 8

Max. y0 = y1 + y2 Nigeria (for domestic route), and they account for 73% S.t 47y1 + 12y2 = 1 of total airlines’ preferences. Obviously, the study favours 19y1 + 18y2 = 1 Aero Contractors because of its afordable pricing, high y1, y2, S1, S2 ≥ 0 safety standards, good quality services, large number of travel destinations, good records for timeliness for fight Putting LLP in standard form, we have departure, and efective communication of information on gate changes. Furthermore, the afordable pricing is 47y1 + 12y2 + s1 = 1 worth mentioning here. Tis is consistent with the result 19 + 18 + = 1 y1 y2 s2 obtained in this study. y1, y2, S1, S2 ≥ 0 Conclusion By solving the1 LPP, the following1 results were obtained. Tus, y1 = 19 , y2 = 0 , y0 = 19 . Te value of the Te main aim of this paper is to describe the subjective V = 1/y0 = 19 behaviour of frms in the Nigerian aviation industry. We game is obtained as . Te1 required19 prob- ability is obtained as Y1 = y1 y0 = 19 × 1 = 1 , employed a game theoretic and optimisation technique Y2 = y2 y0 = 0. to measure the degree of competition in the industry. We considered the strategies of the players based on price charges on airfare and passengers’ volume to proxy each Discussion of results frm’s output in the aviation industry. Our experimen- Tis study examined the application of game theory in tal results indicated that competition in the Nigerian analysing competition in the Nigerian aviation industry aviation industry is driven by customer patronage and by focusing on Arik Air and Aero Contractors as the basis price charged by airline frms. Tus, we concluded that of analysis. Te results obtained using simplex method of game theory approach anchored on the linear program- linear programming and duality theory showed that Arik ming has helped to describe the responses of the play- Air should place more weight on the strength of its pas- ers and that the optimal strategy of both frms examined senger as this gives a probability value of 1 (one), while increased customer’s patronage by manipulating airfares no weight should be placed on fight price as this gives based on varied time factor to enable them survive the a probability value of zero. If followed, this will give an competition in the industry. optimal beneft value of #19 million. In particular, Arik Air should place more weight on Te solution for Aero Contractors is obtained by dual- retaining its passengers through other product features ity theory. Te result of the analysis showed that for opti- other than price. If followed, it will give the frm a payof mum performance, Aero Contractors should place more of 19 million Naira, while Aero Contractors should place weight on fight price as this gives a probability value of more weight on airfare. If followed, this will give the frm 1.00 and no weight be placed on passengers’ volume. If a payof of 19 million naira as obtained in the study’s followed, this will give an optimal beneft value of #19 analysis. In this case, they will share the market equally. million. We therefore recommend that Arik Air and Aero Con- Te implication of this study is that in spite of the tractors should use the result obtained in this research fact that Arik Air charged the highest fare as shown in work in their resource allocation and planning. Tis will Table 1; it yet controls the largest share of the domes- certainly yield encouraging benefts. Firms should engage tic aviation industry. Tus, non-price competition in a healthy competition by using game theory to deter- would serve to retain Arik Air’s largest share in indus- mine their saddle point and working constantly on that try. We can, therefore, infer that non-price competition point. is relevant in the aviation industry. However, the result Furthermore, the managerial implication of this study obtained for Aero Contractors showed that price matters is numerous. First, the positioning of our analysis clearly for the airline to determine its passengers’ strength. Ber- emphasised that price setting behaviour plays a pre- trand solution, would therefore, be appropriate for Aero dominant role in the hallmark strategy of the aviation Contractors as this would give a beneft value of 19 mil- frm in Nigeria. Te results further confrm that surviv- lion naira. Tus, we can conclude that if both frms stick ing the harsh business environment requires that avia- to the optimal strategy, they will both share the market. tion frms involve in various pricing practises such as As a departure from earlier studies, the uniqueness of price penetration, price skimming, and price discrimi- our result is in its general accord with the recent com- nation. Te motivation behind this pricing behaviour is petitive dynamics experienced in the Nigerian Avia- connected with dynamic market condition as well as the tion industry. Our study provided evidence that Aero environment where the frm operates. While manage- Contractors and Arik Air are the preferred airlines in ment can use pricing decision to output growth through Shobande and Akinbomi Futur Bus J 2020, 6(1):11 Page 7 of 8

price adjustment mechanism, additional service delivery 5. ICAO (2010) Order from Chaos: answering Haiti call ad contributing to its renewal. Int Civ Aviat Organ 65(5):347 to ensure that customer expectation are met must be 6. Pothos EM, Perry G, Corr PJ, Matthew MR, Busemeyer JR (2011) Under- given further considerations. Finally, we advise that price standing cooperation in the Prisoner’s Dilemma game. Pers Individ Dif behaviour can be a good strategy for competition, but 51(3):210–215. https​://doi.org/10.1016/j.paid.2010.05.002 7. Ellett L, Allen-Crooks R, Stevens A, Wildschut T, Chadwick P (2013) A para- care must be taken not to use excessive pricing to per- digm for the study of paranoia in the general population: the Prisoner’s suade customer as the consequences might have after- Dilemma game. Cogn Emot 27(1):53–62. https​://doi.org/10.1080/02699​ math efects during demand shock or changes in market 931.2012.68975​7 8. Meng X, Sun S, Li X, Wang L, Xia C, Sun J (2015) Interdependency enriches conditions (Additional fle 1: Table S1). the spatial reciprocity in prisoner’s dilemma game on weighted networks. Phys A Stat Mech Appl 442:388–396. https​://doi.org/10.1016/j.physa​ Supplementary information .2015.08.031 9. Gao J, Li Z, Liu Y, Wang L (2011) The efect of recommended role models Supplementary information accompanies this paper at https​://doi. in prisoner’s dilemma game. Phys A Stat Mech Appl 390(5):811–816. https​ org/10.1186/s4309​3-020-00019​-8. ://doi.org/10.1016/j.physa​.2010.10.048 10. Zhang C, Zhang J, Xie G, Wang L (2011) Efects of encounter in a popula- Additional fle 1: Table S1. Simulations. tion of spatial prisoner’s dilemma players. Theor Popul Biol 80(3):226–231. https​://doi.org/10.1016/j.tpb.2011.06.007 11. Afrousheh K, Makdisi Y, Kokaj J, Maraf M, Mathew J, Pichler G (2013) Abbreviations Collision induced modifcation of spectral lines in the frst autoionization CSR: Corporate social responsibility; NCCA​: Nigerian Civil Aviation Author- region of barium. Eur Phys J D 67(12):262. https​://doi.org/10.1140/epjd/ ity; LPP: Linear programming problem; LPS: Linear programming solver; US: e2013​-40542​-2 . 12. Cong R, Wu T, Qiu YY, Wang L (2014) Time scales in evolutionary game on adaptive networks. Phys Lett Sect A Gen At Solid State Phys 378(13):950– Acknowledgements 955. https​://doi.org/10.1016/j.physl​eta.01.041 The authors are grateful to the Nigerian Civil Aviation Authority for providing 13. Zimmermann M, Schopf D, Lütteken N et al (2018) Carrot and stick: A dataset used in this study. We also thank the editors and reviewers for their game-theoretic approach to motivate cooperative driving through social constructive comments. interaction. Transp Res Part C Emerg Technol 88(February):159–175. https​ ://doi.org/10.1016/j.trc.01.017 Authors’ contributions 14. Andrews DWK, Marmer V, Yu Z (2018) On optimal inference in the linear The authors contribute in the ratio 60–40%. Corresponding author (OA 60%); IV model. SSRN 10:457–485. https​://doi.org/10.2139/ssrn.31322​92 second author (MD 40%). MD analysed and interpreted the preliminary 15. Fu K, Chen Z, Sarker BR (2019) An optimal decision policy for a single- analysis and provided the review of the empirical literature. OA prepared the vendor single-buyer production-inventory system with leaning efect, introductory and methodological sections of the paper, and performed the fuzzy demand and imperfect quality. J Inf Optim Sci 40(3):633–658. https​ full empirical analysis of the paper. Both authors read and approved the fnal ://doi.org/10.1080/02522​667.2018.14270​26 manuscript. 16. Houssein EH, Hamad A, Hassanien AE, Fahmy AA (2019) Epileptic detection based on whale optimization enhanced support vector Funding machine. J Inf Optim Sci 40(3):699–723. https​://doi.org/10.1080/02522​ Not applicable. 667.2018.14536​71 17. Yu H, Tseng HE, Langari R (2017) A human-like game theory-based Availability of data and materials controller for automatic lane changing. Transp Res Part C Emerg Technol. This is available on request. 88:140–158. https​://doi.org/10.1016/j.trc.2018.01.016 18. Straub ER, Schaefer KE (2019) It takes two to tango: automated vehicles Competing interests and human beings do the dance of driving—four social considera- The authors declare that they have no competing interests. tions for policy. Transp Res Part A Policy Pract 122:173–183. https​://doi. org/10.1016/j.tra.2018.03.005 Author details 19. Gaynor MS, Kleiner S, Vogt W (2013) A structural approach to market def- 1 Business School, University of Aberdeen, Block C, Room F02, Edward Wright nition with an application to hospital industry. J Ind Econ 61(2):243–289 Annexe, Aberdeen AB23 3RX, UK. 2 Department of Economics, University 20. Sumathi P (2016) A new approach to solve linear programming prob- of , Lagos, Nigeria. lem with intercept values. J Inf Optim Sci 37(4):495–510. https​://doi. org/10.1080/02522​667.2014.99603​1 Received: 12 July 2019 Accepted: 26 February 2020 21. Bell GG (2005) Clusters, networks, and frm innovativeness. Strateg Manag Published: 21 May 2020 J 26(3):287–295. https​://doi.org/10.1002/smj.448 22. Chen A, Kao L, Lu CS (2014) Controlling ownership and frm performance in Taiwan: the role of external competition and internal governance. Pac Basin Finance J 29:219–238. https​://doi.org/10.1016/j.pacf​n.2014.04.007 References 23. Sanjo Y (2014) The role of frm ownership in policy competition for 1. Jimenez E, Claro J, de Sousa JP (2014) The airport business in a competi- foreign direct investment between asymmetric countries. Int Rev Econ tive environment. Procedia-Soc Behav Sci. 2014(111):947–954. https​://doi. Finance 35:110–121. https​://doi.org/10.1016/j.iref.09.009 org/10.1016/j.sbspr​o.01.129 24. Chin CH, Lo MC, Ramayah T (2014) Market orientation and organiza- 2. Oghojafor BEA, Alaneme GC (2014) Nigeria airways: the grace and grass tional performance: the moderating role of service quality. SAGE Open experience (a case study). Int J Bus Soc Sci 5(13):138–150 3(4):2158244013512664. https​://doi.org/10.1177/21582​44013​51266​4 3. Rousselière D (2019) A fexible approach to age dependence in organi- 25. Jönsson C (1981) Sphere of fying: the politics of international aviation. Int zational mortality: comparing the life duration for cooperative and non- Organ 35(02):273. https​://doi.org/10.1017/s0020​81830​00324​46 cooperative enterprises using a Bayesian generalized additive discrete 26. Horstmann N, Krämer J, Schnurr D (2018) Number efects and tacit col- time survival model. J Quant Econ 17:829–855. https​://doi.org/10.1007/ lusion in experimental oligopolies. J Ind Econ 66(3):650–700. https​://doi. s4095​3-019-00164​-0 org/10.1111/joie.12181​ 4. OECD (1999) Infrastructural development and regulatory reform in sub 27. Eceral TÖ, Köroğlu BA (2015) Incentive mechanisms in industrial develop- Saharan Africa: the case of air transport. In: OECD working paper no 154, ment: an evaluation through defense and aviation industry of Ankara. (154) Shobande and Akinbomi Futur Bus J 2020, 6(1):11 Page 8 of 8

Procedia-Soc Behav Sci 195:1563–1572. https​://doi.org/10.1016/j.sbspr​ 41. Barry M, Nienhueser W (2010) Coordinated market economy/liberal o.2015.06.192 employment relations: low cost competition in the german avia- 28. Chen MC, Cheng SJ, Hwang Y (2005) An empirical investigation of tion industry. Int J Hum Resour Manag 21(2):214–229. https​://doi. the relationship between intellectual capital and frms’ market value org/10.1080/09585​19090​35095​22 and fnancial performance. J Intellect Cap 6(2):159–176. https​://doi. 42. Velu C (2016) Evolutionary or revolutionary business model innova- org/10.1108/14691​93051​05927​71 tion through coopetition? the role of dominance in network mar- 29. Yang M, Dixon RK (2012) Investing in efcient industrial boiler systems in kets. Ind Mark Manag 53:124–135. https​://doi.org/10.1016/j.indma​ China and Vietnam. Energy Policy 40:432–437. https​://doi.org/10.1016/j. rman.2015.11.007 enpol​.2011.10.030 43. Klimas P (2016) Organizational culture and coopetition: an exploratory 30. Luo X, Slotegraaf RJ, Pan X (2006) Simultaneous role of cooperation. J study of the features, models and role in the Polish Aviation Industry. Ind Mark 70(April):67–80. https​://doi.org/10.1509/jmkg.70.2.067 Mark Manag 53:91–102. https​://doi.org/10.1016/j.indma​rman.2015.11.012 31. Wang H, He J, Mahoney JT (2008) Top management incentive compen- 44. Singh AK (2016) Competitive service quality benchmarking in sation and knowledge sharing in multinational corporations. Strateg airline industry using AHP. Benchmarking 23(4):768–791. https​://doi. Manag J 37(1):116–132. https​://doi.org/10.1002/smj.712 org/10.1108/BIJ-05-2013-0061 32. Bengtsson M, Kock S, Lundgren-Henriksson EL, Näsholm MH (2016) 45. Park E, Lee S, Kwon SJ, del Pobil AP (2015) Determinants of behavioral Coopetition research in theory and practice: growing new theoretical, intention to use South Korean airline services: efects of service quality empirical, and methodological domains. Ind Mark Manag 57:4–11. https​ and corporate social responsibility. Sustainability 7(9):12106–12121. https​ ://doi.org/10.1016/j.indma​rman.05.002 ://doi.org/10.3390/su709​12106​ 33. Squazzoni F, Jager W, Edmonds B (2014) Social simulation in the social 46. Adler N, Hanany E (2015) Regulating inter-frm agreements: the case sciences: a brief overview. Soc Sci Comput Rev 32(3):279–294. https​://doi. of airline codesharing in parallel networks. Transp Res Part B Methodol org/10.1177/08944​39313​51297​5 84:31–54. https​://doi.org/10.1016/j.trb.12.002 34. Squazzoni F (2014) The agent-based modeling approach through some 47. Alderighi M, Cento A, Nijkamp P (2012) Rietveld P (2012) Competition foundational monographs. Princ Appl Soc Phenom 55(4):827–840 in the European aviation market: the entry of low-cost airlines. J Transp 35. Dorn S, Schweiger B, Albers S (2016) Levels, phases and themes of coope- Geogr 24:223–233. https​://doi.org/10.1016/j.jtran​geo.008 tition: a systematic literature review and research agenda. Eur Manag J 48. Ignatius J, Tan TS, Dhamotharan L, Goh M (2018) Deregulation control 34(5):484–500. https​://doi.org/10.1016/j.emj.02.009 by mergers and acquisitions: a game theoretic analysis of the Chinese 36. Kim Y (1990) Prospects for Japanese-US trade and industrial competition. Airline Industry. Technol Econ Dev Econ 24(6):2277–2294. https​://doi. Asian Surv 30(5):493–504 org/10.3846/20294​913.2016.12664​10 37. Hahn JH, Kim SH (2016) Interfrm bundled discounts as a collusive device. J Ind Econ 64(2):255–276. https​://doi.org/10.1111/joie.12097​ 38. Noel MD (2018) Gasoline price dispersion and consumer search: evi- Publisher’s Note dence from a natural experiment. J Ind Econ 66(3):701–738. https​://doi. Springer Nature remains neutral with regard to jurisdictional claims in pub- org/10.1111/joie.12179​ lished maps and institutional afliations. 39. Hu W, Xiao J, Zhou X (2014) Collusion or competition? Interfrm relation- ships in the chinese auto. J Ind Econ 62(1):1–41 40. Ceptureanu SI, Ceptureanu EG, Olaru M, Vlad LB (2018) An explora- tory study on coopetitive behavior in oil and gas distribution. Energies 11(5):1–19. https​://doi.org/10.3390/en110​51234​