Bibliometric research of the Pay-What-You-Want Topic

Pay-What-You-Want (PWYW), is a pricing strategy increasingly applied in many different industries, both profitable and not. This study aims to identify influential cited works in PWYW research, determine the current status, and indicate the extent to which influential works have shaped the field addressing this concern, a set of bibliometric analyses conducted in this paper. The analysis was carried out on 136 research papers published between 2009 and 2022 have been analyzed based on Web of Science Core Collection (WoS) results. In order to identify the most cited authors and works, the co-citation analysis was applied. To scrutinize the intellectual structure of the field, bibliometric coupling was applied, to show the network structure of the themes, co-word analysis was applied. Building upon the results, this study suggests future research paths.


Introduction
In today's markets where competition is increasing day by day, companies apply alternative price strategies to stay competitive. Since Kim, Natter, and Span first introduced the Pay-What-You-Want (PWYW) concept in 2009, it has been applied by many companies and researched by global scholars. As a pricing strategy PWYW allows customers to pay any price, including zero, while not allowing the seller to withdraw the offer (Kim et al. 2009). Even though the possibility of zero payment, research proved that the PWYW pricing system is profitable (Chen et al. 2017).
Research on PWYW mainly focuses on the factors that cause non-zero payments. We have evidence from altruism (Böhm and Regner 2013), gender (Rennung and Göritz 2016), contribution to the social responsibility of the seller , fairness, income (Gneezy et al. 2012), satisfaction (Schons et al. 2013), lower price sensitivity (Kim et al. 2009), and contributing to a charity purpose through the purchase (Gneezy et al. 2012), are among buyer-related factors that impact payment magnitude. It is also well known that several seller characteristics explain non-zero payments, including monopoly status (Chao et al. 2015), organizational reputation (Hofmann et al. 2020), sharing revenues with a charity (Stel et al. 2008), and offering a minimum price.
There are two streams of research on the predictors of non-zero payments under the PWYW strategy, including consumer and seller-related factors. For example, across three experiments, Gneezy et al. (2012) found that identity and self-image concerns are essential predictors of payment amount under PWYW. Evidence also showed that avoiding guilt, a sense of fairness, customer satisfaction, and income impact customer behavior (Kunter 2015). The personal relationship is also effective on the payment amount. In a laboratory experiment, Hofmann et al. (2020) found that customers pay more when they closely know each other and are observed by someone else. Similarly, Roy and Das (2022) found that external influence with the low arousal music affects PWYW payment magnitude positively, and high arousal music motivates customers negatively in terms of higher payment.
The study structurally consists of the following stages. In "Methodology" section, the methodological aspect of the article is explained. Specifically, the study's research questions, the bibliometric method, and the protocol followed in applying this method are included. "Results" section presents the analysis results and the science mapping of the literature about PWYW. It specifically includes the results of co-citation, bibliographic coupling, and co-word analysis. Finally, in "Conclusions" section, the point of the study that deserves particular interest and the conclusions of the analysis will be made. Specifically, potential areas for future research on the issue of PWYW will be discussed.

Pay What You Want
The PWYW pricing strategy is profitable. In their studies, Chao et al. (2019) in which they investigated the effect of identifying any minimum payment requirement, compared two pricing strategies (uniform pricing and PWYW pricing) and found that the firm using the PWYW system also made a profit, even though the firm using the fixed price made more profit than the firm using the PWYW pricing.
Research shows that demographic factors also matter in the payment amount. Santana and Morwitz (2021) discussed the role of gender on payment amount, and throughout four studies, they found that women pay more than men. Product type is an influential factor in the payment amount. Weistein et al. (2019) investigated how a reference price affects the PWYW payment amount in hedonic and utilitarian product types. They found that in the absence of a reference price, the amount of payment increased in hedonic products, while the amount of payment decreased in utilitarian products. Payment visibility, time, or price recommendation are also adequate for the payment amount. Christopher and Machado (2019) studied four influential factors (price visibility, payment recipient, payment time, and price recommendation) in the payment amount of the PWYW pricing system through consumers' prosocial and self-interest motives. In certain product types, membership is an influential factor in payment amount; Gravert (2017) identified that members of a book store pay more than non-members.
It is striking that studies on PWYW are applied in different fields (Cui and Wiggins 2017;Kukla-Gryz and Zagórska 2017;Mendoza-Abarca and Mellema 2016;Narwal and Nayak 2019;Schröder et al. 2015). This differentiation makes it challenging to look at the field from a general perspective. This study addresses this issue by an in-depth examination of studies related to the field with the help of bibliometric analysis.
Bibliometric analysis reveals a general view of the studies that have been done and published on a subject or concept (Baumgartner and Pieters 2003;Fereira et al. 2014). Moreover, bibliometric methods mapping the data obtained from scientific databases, reveal the structural situations in the related field (Boyack and Klavans 2010).

Methodology
Since PWYW is a profitable payment system (Chao et al. 2019), it can assume that this pricing mechanism can be a critical strategy for many organizations. For actors who want to use/research this pricing system, the existing studies in the field of PWYW must first be determined. Then, it should be stated what the intellectual structure and emerging literature trends are, and finally, what kind of work can do to improve the PWYW payment magnitude in the future. Since no literature analysis or reviews on the field has conducted to date, this study aims to contribute to this gap by asking the following research questions.
• RQ 1 What is the current publication trend, most influential articles, and journals in PWYW? • RQ 2 What is the intellectual structure of current research? • RQ 3 a. What are the themes associated with a particular line of research? b. What are the potential areas for future research?
Based on the research questions, a bibliometric analysis will be conducted. The bibliometric analysis uses for interpreting unstructured data and mapping out how these areas have evolved (Verma and Gustafsson 2020). In this way, it provides information for researchers and users who want to learn in the field of PWYW to look at the field from a general perspective and learn about new research areas (Donthu et al. 2021).
This study collects and analyzes bibliometric data on PWYW studies for review. For this purpose, the SPAR-4-SLR protocol was used (Paul et al. 2021).
In the first step of the search, the phrase "pay what you*" was used. The search was conducted among author keywords, keyword plus, titles, and abstracts; 1074 results were listed. Keywords alone could be used for the search, but some journals do not contain keywords in their publications. Each author carefully examined the relevant literature publications to identify the keywords that allowed the research to be carried out. Then with the keywords "pay what you want" or "pay as you wish" or "pay as you like" or "pay what you will" or "pay as you will" or "pay what you can" or "name your own price", the search reconducted. In order to increase the validity of the terms (Chabowski et al. 2013), the exact search was carried out by all authors with an unbiased eye.
In order to reach the complete results with the keywords, both Scopus and WoS databases were examined. Similar results were obtained in both databases. However, there were too many unrelated publications among the results from the Scopus database. WoS database was used because it would make the data more reliable. Additionally, the WoS core collection is a very comprehensive database for researchers (Baier-Fuentes et al. 2021), due to its ability to present data from many databases, such as SSCI (the Social Sciences Citation Index), SCIE (the Science Citation Index Expanded the Science Citation Index Expanded), ESCT (the Emerging Sources Citation Index). It has been used as a data source in many studies until today (Adler and Sarstedt 2021;Ghorbani et al. 2021;Kumar et al. 2019;Li et al. 2019;Rathi et al. 2022).
The results have limited the types of documents to articles, review articles, and early access. Since "Pay What You Want" was first used as a term by Kim and his colleagues in 2009, publications from 2008 and earlier years were subtracted from the results (See Fig. 1).
The research was carried out through publications in English. Since PWYW is a pricing system, results are limited to categories on this issue. Categories such as medicine, engineering, etc. were omitted from the results (See Fig. 2).
Results were double-checked by each author. Because some publications may be featured more than once, or there may be problems with authors' names. The authors' names, titles, and abstracts in the results were checked one by one to eliminate these possibilities. Then, data ready for analysis was obtained.
Articles, review articles, and early access were included in the study, and other publication types were excluded from the results. Articles are included because they have considered with the peer review system (Kumar et al. 2022;Paul et al. 2021).
A bibliometric analysis approach was adopted for the analysis of the 136 results obtained. The bibliometric analysis approach is frequently used by researchers (Ellegaard and Wallin 2015) in systematic reviews in the fields of business Figure 1 Procedure of the study based on the SPAR-4-SLR Protocol.

Assembling Identification
Domain: Pay what you want pricing system Research questions: 1. What is the current publication trend, most influential articles, and journals in PWYW? 2. What is the intellectual structure of current research? 3a. What are the themes associated with a particular line of research? 3b. What are the potential areas for future research? Source quality: Web of Science (WoS) Acquisition Search period: 2009 to 2022 Search keywords: "pay what you want" or "pay as you wish" or "pay as you like" or "pay what you will" or "pay as you will" or "pay what you can" or "name your own price" Total number of publications: n = 193 Arranging Purification Filtered language: English Filtered document type: Articles (151), Review Articles (4), Early Access (6) (Baker et al. 2020;Donthu et al. 2021).
In order to answer the research questions, the following bibliometric analysis were applied in this study; for RQ1, co-citation, for RQ2, bibliometric coupling, for RQ 3a, cooccurrence (= > co-word).
The research was conducted using one of the most commonly used software (Pan et al. 2018

Co-citation analysis
For research question 1, the most cited authors and most cited studies were identified by co-citation analysis. Cocitation analysis uses citation dynamics to link documents, authors, or journals (Zupic and Čater 2015).
In the study, co-citation analysis was performed on 136 articles about PWYW. It examined co-citation pairs among the most cited works, with three or more citations in analysis. The list of the most cited authors can be seen in Table 1, and the list of most cited studies can be seen in Table 2. Tables 1 and 2 show the most cited authors and researchers in the field of PWYW and express their contributions to shaping the field. It can be observed that the results obtained in Table 1 match those obtained in Table 2.
Although the issue of PWYW is relatively new, it is undeniable that quite research has been done until today. Considering the results, it stands out that the author who has done the most cited work is Kim (2009) and her colleagues' study (Kim et al. 2009) (see Table 1 and 2). Since Kim and her colleagues are the first scholars to mention the issue, this result can be expected. Additionally, three of her and her colleagues' works are included in the top list of the most cited articles (Kim et al. 2009(Kim et al. , 2014a. The second most cited author is Gneezy, A. in Table 1 and their work (in Table 2) still seems to influence the area (Gneezy et al. 2012). Gneezy has a powerful influence in the field, as her work with her friends in 2010 also ranks third in Table 2 (Gneezy et al. 2010).
Regner is the third most cited author in Table 1, and his study with Traxler (Regner and Traxler 2012) is ranked as the fourth most cited work in Table 2.
The Proceedings of the National Academy of Sciences include the second most cited article, Gneezy et al. (2012), which examined the role of identity and self-image on PWYW.
The third most cited work is in the Science; Gneezy et al. (2010) studied the issue of PWYW regarding social responsibility.
Overall, in Table 1, 28 authors listed were cited at least 19 times. In Table 2, 19 articles are listed which were cited at least 17 times. All these authors in Tables 1 and 2 have contributed to shaping the PWYW literature.  Table 3 shows the list of journals contributed to the field PWYW. According to Table 3, the journal with the highest number of articles on PWYW is the Journal of Business Research, with 13 articles. Journal Of Behavioral and Experimental Economics is the second in publications with 12 articles. After JBEE, the number of articles published by journals is halved. Journal of Revenue and Pricing Management and Management Journal are the third with the 6 articles.
There are some contradicts between most cited authors and most published journals. In Table 2, the work of Kim et al. (2009) is most cited in the Journal of Marketing, however there are two articles in this journal about the issue PWYW.
On the other hand, when Tables 2 and 3 evaluate together, there seems a balance in terms of citation. For example, the most frequently cited journal is the Journal of Business Research with three articles; Johnson and Cui (2013) worked on the external reference price for the payment amount. Kunter (2015) studied the customers' motivation factors. Roy (2015) discussed the effect of internal and external reference prices on PWYW. At the same JBR has the maximum number of articles published in PWYW. Similarly, the second most frequently cited journal is the Journal of Behavioral and Experimental Economics, with two articles (Chao et al. 2015;Soulea and Madriga 2015). The Journal of Revenue and Pricing Management is also the third in Table 3.

Bibliographic coupling
For research question 2, the intellectual structure of current research was scrutinized by bibliographic coupling. Since the PWYW issue is relatively new, there could be some subfields not cited enough (Vogel and Güttel 2013). That is why bibliometric coupling analysis was conducted for mapping research fronts and smaller subfields (Zupic and Čater 2015) that are not cited enough to make a calculable link by cocitation analysis.
In order to determine the intellectual structure of the field, the most cited documents, authors, institutes, and countries in the field were determined with bibliometric Coupling analysis (See Figs. 3, 4, 5).
In Fig. 3, the most cited documents are Kim et al. (2009), Gneezy et al. (2010,and Gneezy et al. (2012). These results are consistent with the co-citation analysis shown in Table 2. However, in terms of the most cited authors, the first three names are Kim (2009), Gneezy (2010, and Gneezy (2012). These results are slightly different compared to Table 2 because, unlike co-citation, bibliographic coupling uses the number of references that two documents share (Vogel and Güttel 2013). Table 4 shows the country list of the PWYW. Accordingly, the USA (Chao et al. 2019;Santana and Morwitz 2021;Tudon 2015) and Germany (Bitsch et al. 2020;Kim et al. 2009Kim et al. , 2014b are the countries that contributed to the field most. India, Australia, England, and China are other countries that have the documents most. In terms of the institute (See Table 5), the university that has the most influence in shaping the field is Curtin University (Rabbanee et al. 2022;Roy, et al. 2021), University of  California (Jung et al. 2016), Goethe University Frankfurt (Kim et al. 2009;Natter and Kaufmann 2015), and Munich University (Riener and Traxler 2012;Schmidt et al. 2015).

Co-word analysis
In order to answer research question 3a, a co-word analysis was performed. Co-word analysis shows the network of themes that express the conceptual structure of a field and the relationships in this network (Börner et al. 2003). If words are used frequently in the document, there is a close relationship between these words and other related concepts (Zupic and Čater 2015). In order to avoid different spelling or writing of the same word or phrases, keywords were carefully examined, and different forms were corrected and rewritten as a single form. For example, it was observed that the word string "pay what you want" was written as "pay-what-you-want" or PWYW, and all of these forms were rewritten as "pay what you want".
PWYW is a pricing strategy, which can be seen in Fig. 6. Additionally, it stands out that the primary concern in this pricing strategy is to determine the factors that affect the amount of payment. For example, existing of internal-external reference prices (Gross et al. 2021;Rabbanee et al. 2022;Roy et al. 2021), information (Carter and Curry 2010;Feldhaus et al. 2019), altruism (Mak et al. 2015;Proeger and Blankenberg 2017;Sharma and Nayak 2020), fairness (Sleesman and Conlon 2017;Tripathi and Pandey 2019). Figure 6 shows the themes of these 136 articles. It can be observed that, in terms of methodology in PWYW, mainly the field experiment model is using (Kahsay and Samahita 2015;Ma et al. 2022;Park et al. 2017;Proeger and Blankenberg 2017).
As it is one of the primary methods of science mapping and visualization (Thijs et al. 2013), this study contributed to the science mapping of PWYW by bibliometric analysis. Until 2012 PWYW research remained scarce, with a minimum number of publications. Only three articles are published (see Fig. 7). However, since then, the publication number has been increasing. So, it can be assumed that the PWYW issue is an emerging field and a considerable number of areas that need to be researched.
This study analyzed co-citation, bibliographic coupling, and co-word analysis of research on PWYW and showed how the field had been shaped until now.

Conclusion
This study provides a potential basis for future researchers interested in this field whose papers have contributed to shaping the field of PWYW. And with this aspect, it tried to answer the research question 3b. The first thing that stands out in PWYW studies is that the field has not been adequately evaluated regarding marketing theories. For example, Gneezy et al. (2012) discussed the issue from the perspective of social norm theory. Accordingly, if unselfish behaviors are essential in the markets, how does this situation work in actually? And they found, at least in part, that people want to maintain their sense of being good and fair. However, if the subject is considered with the Social Dilemmas Theory (SDT) (Dawes 1980), it is possible to obtain different results. Future researchers may consider the issue from the view of SDT because, according to SDT, individuals gain a higher income when she/ he makes a choice individually compared to a collaborative social choice.
In his study investigating the effects of the presence of IRP (Internal Reference Price) on the willingness to pay, Roy (2015) emphasized that this might be a result of adaptation level theory (Helson 1964) and assimilation-contrast theory (Sherif and Houland 1964). In his study, he concluded that the presence of IRP reduces the willingness to pay. However, this situation can also be evaluated with Construal Level Theory (CLT) and different results can be obtained. Because, according to CLT (Trope and Liberman 2010), when people try to make decisions about the future or try to understand the thoughts of others, they do so by remembering their past experiences, making predictions about the future, or calculating the reactions of others.
Various methodologies can be used in a literature review of a field. Future studies may focus on other models (like systematic literature reviews or meta-analyses). In particular, the meta-analysis approach will help determine the quantitative structures (Maseeh et al. 2021) of the studies in the field. Because determining which antecedents and mediators (if any) are influential on payment amount are used in the studies and how the relationship between these variables is examined will make an essential contribution to shaping the field (Jaramillo et al. 2005).
In terms of testing variables, both quantitative and qualitative methods can be used. The analysis results show that the variables in PWYW were generally tested by the field experiment method. Although field experiment is a very valid and effective method to test this kind of relationship, the fact that many different variables can be examined in the field requires diversification of the methodology. For example, the effects of the part-time or full-time employment status of customers on the amount of payment can be tested by field experiments and survey methods. This may be in the form of verification/falsification of the structures applied field experiment by survey, or sometimes verification/falsification of the variables applied survey by field experiment. In his study, Roy (2015) investigated the effect of "satisfaction" on the amount of payment with the survey method. Future researchers could test these or similar effects in a laboratory setting or by observing real customers in the field.
Given that PWYW is a pricing strategy, researchers can focus on more interdisciplinary factors. The effects of different antecedents on the payment amount can be researched in different sectors. For example, the effects of psychological factors (hope, trust, etc.), sociological factors (shopping trends in the region, education level of customers, etc.), or economic conditions of consumers (work-income status, etc.) can be investigated.
As a pricing strategy, PWYW seems profitable. However, it can be argued that even though people can pay more when they are informed about the impact of their payment, it is still less profitable than posted prices (Schmidt et al. 2015). Since the competitive advantage of the PWYW pricing strategy can be mentioned as there is a risk of elimination from the market for sellers using posted price (Gneezy et al. 2010), the best pricing strategy may be using the PWYW and posted price together. For example, to attract customers' attention, the PWYW pricing system can apply to some basic products, and posted pricing mechanism can apply to higher-cost products.
In PWYW studies, mainly two research styles come forward. Some studies have investigated the effects of an existing situation on the amount of payment (gender, age, education). For example, Santana and Morwitz (2021) studied the effect of gender on the payment amount. The result of their study shows the current situation. However, some studies aim to increase the amount of payment by manipulations applied to the antecedents. For example, Hoffman et al. (2020) discussed the "closeness effect" in their study. They observed that buyers pay more when they are close to other buyers during payment.
Managers can focus on identifying the main situation because it is vital to create strategies according to this. However, the intervention to the independent variable is also critical because it will allow the managers to intervene in possible problems in the work process. For example, a manager can determine the product group he wants to sell by examining the existing structure. After the structure is created, it can examine the variables that will increase the payment amount and determine its strategies according to this structure.
This bibliometric analysis has a few limitations. First, although the data has been meticulously studied, all the data  obtained for the study includes articles published in English. However, other articles may be published in other languages and contribute to the field. Secondly, keywords, titles, and abstracts are used for the searching criteria, but some publications did not use the word "Pay-What-You-Want" in these parts, but it may still be related to the field. Hence, some articles were missed. Finally, the data was obtained from the WoS database in this study. Although WoS is one of the most comprehensive databases in the world in terms of publications, analyses including other databases (like Scopus or Dimensions) can use in order to obtain more de facto results.
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