O presente estudo teve como objetivo avaliar o desempenho ambiental, socia= l e econômico-financeiro das empresas brasileiras listadas na B3 com base na teoria dos jogos. Parte= -se do entendimento de que o desempenho sustentável resulta da integração dessas três dimensões, considerando q= ue as ações atuais de uma organização não d= evem comprometer a capacidade das gerações futuras de atender às suas pró= ;prias necessidades. Diante da relevância do tema, buscou-se analisar uma amostra de 64 companhias listadas n= a B3 entre 2010 e 2017, a partir de dados obtidos na base Thomson Reuters®.<= span style=3D'letter-spacing:-.15pt'> Para a análise, foram elaborad= os rankings de desempenho utilizando a teoria dos jogos em suas abordagens escalar e vetorial. Os resultados evidenciaram que as empresas com melhor posição nos rankings escalares não necessariamente obtiveram o mesmo destaque no ranking vetorial. As empresas Vale S.A., Telefônica Brasil S.A. e CEMIG se destacaram no desempenho sustentável agregado, entretanto, ao se exa= minar separadamente as dimensões ambiental, social e econômico- financeira, observou-se que não mantiveram o mesmo nível de desempenho em todas elas. Porta= nto, esta pesquisa avança em relação aos estudos anteriores= ao analisar, de forma conjunta, múltiplos indicadores para inferir o desempenho das empresas e identificar os diferentes níveis alcançados nos grupos de indicadores que compõem o trip&eacut= e; da sustentabilidade. Nesse sentido, o estudo demonstra, na prática, a aplica&ccedi= l;ão de uma ferramenta de avalia&cced= il;ão do desempenho sustentável que combina uma perspectiva holística e individualizada, permitindo apo= ntar em quais dimensões — ambien= tal, social ou econômico-financeira <= /span>— as organizações necessitam de maior aprimoramento. Por fim, o artigo oferece subsídios a investido= res e gestores, evidenciando a posição das empresas analisadas e destacando o potencial da ferra= menta como instrumento de comparação do desempenho organizacional em diferentes dimensões.

Palavras-chave: avaliação<= span style=3D'letter-spacing:-.25pt'> de empresas; desempenho sustentável; teoria do jogo.

<= /o:p>

<= span style=3D'font-size:9.0pt;mso-bidi-font-size:11.0pt;mso-ansi-language:PT-BR'= >Recebido em 27/02/2024. Aprovado em 10/09/2025. Avaliado pelo sistema double blind peer review. Publicado

conforme normas da APA. https://doi.org/10.22279/navu= s.v16.1880

<= /o:p>

1 INTRODUCTION

In the organizational environm= ent, companies only remain in the market if they are efficient. According to Por= ter and Kramer (2011), performance evaluation serves to quantify the efficiency= and effectiveness of an organization's actions (Neely, Adams & Kennerley, 2002). Thus, the evaluation of the results achieved by the companies is car= ried out through performance indicators (Gomes, Kneipp, Kruglianskas, Rosa & Bichueti, 2014).

The evaluation of companies us= ing performance indicators, as well as comparisons between them, has long been practiced (Bezerra & Corrar, 2006). However, according to these authors, indicator analysis is usually conducted individually,= that is, indicators are analyzed independently and according = to the organization’s needs, which does not allow for assessing the influenc= e on one another or identifying the most relevant indicator.

It is noticed that the analysi= s of the organizations’ performance affects their competitiveness in the current market. New demands and restrictions have emerged and aspects such = as sustainability, environmental protection, and social well-being are now considered as important as economic growth (Gomes et al., 2014). These aspects have gained prominence in organizational evaluation due to the emergence and growth of national and international initiatives addressing social and environmental issues (Porter & Kramer, 2011).

In terms of sustainability, there are two points of view that can be considered. On the one hand, the imposition of sustainable actions for companies is seen as an impediment to performance= at its cost, and on the other hand, it is = seen as a stimulus to innovation and a source of competitive opportunity (Porter & Van der Linde, 1995). In the research by Cecon, Hein and Kroenke (201= 8), it was found that the competitive advantage of companies increases when they voluntarily disclose their sustainable actions, as companies with greater environmental transparency exhibited higher market values.

However, research has offered contradictory results on the relationship between sustainability and the financial performance of organizations (Magon, Thomé, Ferrer & Scavarda, 2018). Research also = highlights a lack of understanding regarding sustainability, which hinders the development of tools for modeling sustainable businesses (Bell & Morse, 2005; Dossa & Kaeufer, 2014). Thus, the vision of sustainability is a continuous process,= in which the organization must adapt and renew itself (Diegues, 1992).

Related to sustainability and company valuation, the study by Kroenke, Caballero, Cecon and Hein (2018) stands out, which sought to highlight the scalar and vector games in the evaluation of social and environmental disclosure and their relationship with market value. The research by Nascimento, Kroenke and Marcos (2016) showed the effect of participation in the Corporate Sustainability Index (ISE) on the economic a= nd financial performance of companies in the transport sector. These studies attest to the importance of sustainability for entities under different approaches.

It is also worth mentioning th= at the use of quantitative information related to sustainability, as carried out in this article, is still rarely used (Stoycheva et al., 2018). This quantitat= ive analysis of sustainability facilitates inter-organizational comparability.<= span style=3D'letter-spacing:2.0pt'> As noted by Boiral and Henri (2017),= it is difficult to compare sustaina= ble performance between companie= s when analyzing sustainability reports

with = qualitative data. Not all companies follow disclos= ure standards, and in most cases, the information provided is incomplete.

Based on the foregoing, the re= search question that directs this investigation emerges: What is the sustainability ranking of Brazilian companies listed in B3? In order to answer this questi= on, the objective of this research is to evaluate the environmental, social and economic-financial performance of Brazilian companies based on game theory.= In this way, the sustainable performance of companies listed on B3 will be assessed in the period from 2010 to 2017.

Based on previous studies, game theory can be applied in this evaluation, as, according<= span style=3D'letter-spacing:-.55pt'> to Fiani (2009), it analyzes decisio= n making among agents who interact in competitive situations, including their ability to influence one<= span style=3D'letter-spacing:-.05pt'> another. Contextualizing this statement for the present study, it can be said that in the analysis of companies' performance, eac= h indicator has the potential to affect the classification of organizations.

This research is justified by = the number of studies on this topic, which present controversial results, indicating a gap and enabling new discussions and investigations. Additiona= lly, economic and financial performance is indispensable for organizations and is expected to boost social and environmental performance. According to Nossa, Rodrigues and Nossa (2017), there are many articles that analyze the relationship between sustainability indicators and economic-financial indicators with controversial results, indicating that t= he theme deserves deeper analysis. Moreover, the focus on quantitative indicat= ors should be highlighted, as Stoycheva et al. (2018), note that most research = on sustainability relies on qualitative indicators.

In this perspective, it is exp= ected to contribute theoretically to research on the list of environmental, social and economic-financial indicators, further encouraging the discussion on sustainability in companies. On practical issues, this article seeks to contribute to both investors and business managers, highlighting the positi= ons of the analyzed companies and demonstrating the potential of this tool to compare their performance with other organizations across multiple<= span style=3D'letter-spacing:-.3pt'> dimensions.

= 2 LITERATURE REVIEW

This topic presents the theore= tical discussion of the themes that support this research. In this way, the performance analysis of companies is approached and then, this analysis wil= l be funneled towards sustainable performance.

2.1 Performance analysis of companies

Companies differ from each oth= er in several ways: history, organization, location, people, products, size, and these differences interfere with their performance (Brito & Vasconcelos, 2005). The performance analysis of organizations has the function of helping the compa= ny to verify its situation in relation to the other organizations belonging to= the market (sector) in which it is inserted (Callado, Callado & Almeida, 20= 08; Cruz, 2017). According to the study by Boff, Procianoy and Hoppen (2006), w= ith the performance analysis, the analysts have the possibility to predict the performance of the

organizations, that is, based on the information disclosed by companies, analysts can project how these organizations= are likely to perform in the future.

The analysis of companies' performance is not a recent practice and it is usually done through the data contained in the financial statements, which represent the current situatio= n of the company, being a source of innumerable information to the managers, whi= ch helps in more efficient analyses in the decision-making process(Bortoluzzi, Ensslin & Ensslin, 2011).

However, it can be said that the evaluation of the companies' performance comp= iles the financial statements into indicators (Camargos & Barbosa, 2005). Therefore, the analysis process of these indicators is beneficial for organizations, as it provides managers with the necessary information to assess the results of adopted strategies and evaluate management performance it= self (Ittner & Larker, 1998). Th= us, performance indicators are fundamental for measuring organizational perform= ance (Callado, Callado & Almeida, 2008).

Regarding sustainable development, its= concept is parallel and compatible with economic development and environmental protection (Chen= , Yu & Hu, 2018). According to the IAEA (2005), sustainable development is an economic policy that aims to guide society toward the proper implementation of measures that ensure environmental protection and benefit investors and consumers. Furthermore, the analysis of sustainable performance in organizations= is still considered a challenge, due to the vague concept of sustainability indicators (Li & Mathiyazhagan, 2018; Jiang, Liu, Liu, Li, Cong, Zhang & Shi, 2018). Another difficulty lies in the absence of a universal standa= rd for analyzing the Triple Bottom Line (TBL) or for each of its components. This is because the TBL is a dynamic con= cept that can be adapted according to the country, sector, and company, with no clear guidelines on how to implement the measures required to achieve sustainability objectives (Aris,

Marzuki, Othman,<= span style=3D'letter-spacing:-.25pt'> Rahman & Ismail, 2018).

Based on this, the performance analysis of companies, in addition to considering economic- financial and profitability aspects, must also consider environmental and social aspects, including resulting in sustainability analyses, as reported by Gomes et al. (2014). These sustainable aspects will be further discussed below.

2.2 Sustainable Performance

The term sustainability and sustainable performance arose from the concern about the impacts of producti= on and human actions on the environment, as expressed in the report of the World Commission on Environment and Development (WCED, 1987). This report defines sustainable development as development that meets the needs of the present = without compromising the ability of future generations to meet their own needs (Brundtland, 1987).

However, the number of compani= es adopting sustainability strategies, initiatives, and the disclosures of environmental and social activities has increased, causing changes in busin= ess models (Xie, Nozawa, Yagi, Fujii & Managi, 2019). Thus, sustainable development se= eks to meet the economic progress of organizations wh= ile also addressing socio-cultural interests and protecting the environment = (Aris et al., 2018).

Among the various definitions = of sustainable development found in the literature, the one that was most widespread was the definition by Elkington and Burke (1989), which states thatsustainable development involves the simultaneous search for economic p= rosperity, environmental quality and social equity. This definition became known as the Triple Bottom Line (TBL), or the Sustainability Tripod, and arg= ues that sustainable development must consider these three dimensions: environmental, s= ocial and economic-financial.

Thus, according to Brundtland (1987), environmental sustainability is the maintenance of the quality of air, land, water and living beings. The social dimension of sustainability, on the other hand, is related to issues of social equit= y and the improvement of the quality of life of society in general, encompassing employees, the community, consumers and suppliers (CALLADO, 2010). Finally, sustainability related to finance, refers to the growth of book value of balanced equity, with the growth of its assets and revenues and liabilities (Gómez-Bezares, Przychodzen & Przychodzen, 2017).

The environmental dimension<= span style=3D'letter-spacing:-.6pt'> aims to keep ecosystems alive and diverse. The social dimension suggests that organizations should encourage education, culture, leisure and social justice to the community, while the economic-financial dimension emphasizes that companies must remain profitable and generate income value (Vellani & Ribeiro, 2009). Thus, Elkington and Burke (1989) argue that companies may not be able to keep their customers, employees, or other Trip= le Bottom Line stakeholders indefinitely, however, the greater the loyalty, mu= tual respect and benefits, the higher the likelihood that the organization will = be sustainable.

Regarding sustainability, the = study by Kroenke, Caballero, Cecon and Hein (2018) highlights the relevance of companies operating in sectors with high environmental impact. These involve information about their employees, the community in general, the environmen= t in which they operate, the use of natural resources and the way in which they protect the environment. Based on this, the authors recommend that organizations with a high environmental impact seek to enhance their market value, noting that greater disclosure is associated with higher market valuation.

According to another research r= elated to sustainability, the findings indicate that sustainable practices maintai= ned over a long period, result in an increase in economic and financial gains f= or companies (Nascimento, Kroenke & Marcos, 2016). In the research by Ceco= n, Hein and Kroenke (2018), the association between enviro= nmental disclosure and the market value of Brazilian companies is an= alyzed. The results showed that the company's position improves with the disclosure of the Annual or Sustainability Reports with greater quality of information. Thus, the importance of timely disclosure is highlighted, covering a greater number of subcategories, = in order to improve their assessment and, consequently, competitiveness in the market (Cecon, Hein & Kroenke, 2018).

The various definitions of sustainable development, the definition of methods and metrics to assess the sustainable performance of organizations are also considered a challenge for institutions (Hay & Noonan, 2005). In this sense, several studies have = been dedicated to evaluating the existing indicators and to developing new quantitative indicators that are more easily measurable (Costanza, Daly, Fioramonti, Giovannini, Kubiszewski, Mortensen, ...& Wilkinson, 2016; Engebretsen, Heggen & Ottersen, 2017; Nossa, Rodrigues & Nossa, 201= 7).

3 METHODOLOGY

This research aims to evaluate= the environmental, social and economic-financial performance of Brazilian companies base= d on game theory. This analysis had as population the companies<= span style=3D'letter-spacing:-.05pt'> listed in B3, in the period from 2010 to 2017. Since not all companies provided the necessary information fo= r the research, the sample was reduced to those companies that presented= the necessary information for the analysis.

Starting from the defined population, organizations that did not disclose information on environmenta= l, social and economic-financial indicators were excluded. In a second step, financial organizations were excluded, as they have peculiar accounting cha= racteristics, and those companies that presented negative equity were also excluded, in o= rder not to bias the results of the economic- financial indicators. Thus, the research sample included 64 companies listed in B3, as shown in Table 1.

Table 1

Research Sample

Description	Companies
Population	490
(-) Did not present information in the environmental and social indicators	407
(-) Financial	13
(-) Negative PL	6
(=3D) Sample	64

Source: Research Data.

Even starting from a comprehen= sive population, that is, all companies listed on the Brazilian stock exchange, Brazil Bolsa Balcão (B3), the sample of this study was quite reduced= , as most companies were excluded from the analysis because they did not present data regarding the focus of this research (environmental and social). When analyzing the sector of the analyzed sample, it is noticed that most of the companies belong to the manufacturing sector (32.8%), serv= ices and public utility (21.8%) and retail trade (9.37%), as can be seen in Tabl= e 2, shown below.

Table 2

Description of the Sectors of the Companies in the Sample

Sector<= /b>	Companies	% Sample
Agriculture, forestry, fishing and<= span style=3D'letter-spacing:-.3pt'> hunting	1	1,56%
Construction	5	7,81%
Educati= onal Services	2	3,12%
Health<= span style=3D'letter-spacing:-.2pt'> and social assistance	2	3,12%
Information	2	3,12%
Manufacturing	21	32,81%
Mining,= quarrying and oil and gas extraction	2	3,12%
Profess= ional, scientific and technical= services	1	1,56%
Real estate and rent and leasing	4	6,25%
Retail<= span style=3D'letter-spacing:-.25pt'> trade	6	9,37%
Transpo= rtation and Warehousing	3	4,68
Utilities	14	21,87
Wholesa= le Trade	1	1,56%
Total	64	100%

Sour= ce: Research Data.

In this study, environmental, social and economic-financial indicators were<= span style=3D'letter-spacing:-.6pt'> examined to analyze the sustainab= le performance of the sampled organizations. These indicators were obtained fr= om the Thomson Reuters® database, and Table 3 presents a summary of what each of the environmental and social indicator represents.

&= nbsp;

Table 3

Environmental and social variables

Variables	Description
Environmental<= /span>
Resource Use	They reflect the ability of an organization to reduce the use of materials, energy or wa= ter, by finding efficient solutions.
Emissions	Measures the company's commitment and= effectiveness in reducing environmental emissions in production and operational processes.
Innovation	The organization's ability to reduce costs and environmental charges for its customers, creating opp= ortunities through new technolo= gies, environmental processes and eco-designed products.
Social<= /b>
Workforce	The company's effectiveness for job satisfaction, providing a hea= lthy and safe workplace, with diversity and equal development opportunities for its employees.
Human rights	The organization's ability to respect fundamental = human rights conventions.
Community	The company's commitment to be a good citizen, which protects= public health and respects bu= siness ethics.
Product Responsibility	The company's ability to produce quality products and services with the safety, integrity and privacy of i= ts customers.

Source: Adapted from Thomson Reuters®.

&= nbsp;

Table 4 provides a summary of the economic and financial indicators used in this analysis.

These indicators were obtained from the Thomson Reuters® database.

Table 4

Economic and financial variabless

Variable	*Próxy*	Authors=
Return on Total Assets (ROA)	ROA =3D EBIT / total assets	Tan and Peng (2003); Daniel and Astruc = (2004); Laffranchini and Braun (2014).
Returno n Equity (ROE)	ROE =3D net profit / net worth	Tan and Peng (2003); Daniel and Astruc = (2004); Laffranchini and Braun (2014).
General Liquidity (LG)	LG =3D (current asset= s + non- current assets) / (current liabilities + non-current liabilities)	Bezerra and Corrar (2006); Schuhmann (2008); McLean (1997); Morel, Santos, Franci= sco and Paranaiba (2019).
General Indebtedness (EG)	EG =3D (current liabi= lities + non- current liabilities) / (current assets + non-current assets)	Bezerra and Corrar (2006); Gapenski and Pink (2007); Silva, Rodrigues, Sousa, Nascimento <= /span>and <= /span>Vieira (2019).

Source: Research Data.

𝑗 = 𝑗

<= ![endif]>1 = 722; &= nbsp; for indicators whose interpretation is “the smaller the better”.

After data normalization, the rankings were elaborated. The first ranking was based on

environmental= indicators, the second ranking considered social information, the third ranking considered economic-financial information and the fourth ranking analyzed the set of these indicators (environmental, social and economic-financial) in order to verify sustainable performance orga= nizations.

These rankings were<= span style=3D'letter-spacing:-.55pt'> developed using game theory models, solved through linear programming prob= lems. According to Gomes, Silva and Parré (2017), this technique models the strategic behavior between two or more players (agents, which in this study= are companies) and determines the strategy adopted that ensures the best result= of the game, among the behavior and actions of opponents.

For the environmental ranking,= a scalar game was applied, in which the first three restrictions refer to the three environmental variables (resource use, emissions and innovation). The fourth constraint ensures that the sum of strategies equals 100%, and the f= inal constraint enforces non- negativity.

𝑀𝑎𝑥 𝑍 =3D 𝑣₁

𝑆𝑎 = ; 𝑎1,1 𝑒1 + 𝑎2,1 𝑒2 +...+ 𝑎64,1 𝑒64 ≥ 𝑣1

𝑎1,2 𝑒1 + 𝑎2,2 𝑒2 +...+ 𝑎64,2 𝑒64 ≥ 𝑣1

𝑎1,3 𝑒1 + 𝑎2,3 𝑒2 +...+ 𝑎64,3 𝑒64 ≥ 𝑣1

𝑒1 + 𝑒2 + … + 𝑒64 =3D = 1

𝑒1 + 𝑒2 + 𝑒3 + … + 𝑒64 ≥ 0

For the social ranking, a scal= ar game was also applied, where the first four restrictions refer to the four social variables (workforce, human rights, community and product responsibility). The fifth restriction refers to the sum of strategies that must add 100% and the last constraint represents non- negativity.

𝑀𝑎𝑥 𝑍 =3D 𝑣₂

𝑆𝑎 &= nbsp; 𝑎1,1 𝑒1 + 𝑎2,1= 𝑒2 +...+ 𝑎64,1 𝑒64 ≥ 𝑣2

𝑎1,2 𝑒1 + 𝑎2,2= 𝑒2 +...+ 𝑎64,2 𝑒64 ≥ 𝑣2

𝑎1,3 𝑒1 + 𝑎2,3= 𝑒2 +...+ 𝑎64,3 𝑒64 ≥ 𝑣2

𝑎1,4 𝑒1 + 𝑎2,4= 𝑒2 +...+ 𝑎64,4 𝑒64 ≥ 𝑣2

𝑒1 + 𝑒2 + … + 𝑒64 =3D = 1

𝑒1 + 𝑒2 + 𝑒3 + … + 𝑒64 ≥ 0

&nbs= p;

Similarly, for the economic-financial ranking, a scalar game was applied, where the first four restrictions refer to the four economic-financial variables (ROA, ROE, LG a= nd EG). The fifth constraint refers to the sum of strategies which must add up= to 100% and the last constraint represents non- negativity.

𝑀𝑎= 9909; 𝑍 =3D 𝑣₃

𝑆𝑎 &= nbsp; 𝑎1,1 𝑒1 + 𝑎2,1= 𝑒2 +...+ 𝑎64,1 𝑒64 ≥ 𝑣3

𝑎1,2 𝑒1 + 𝑎2,2= 𝑒2 +...+ 𝑎64,2 𝑒64 ≥ 𝑣3

𝑎1,3 𝑒1 + 𝑎2,3= 𝑒2 +...+ 𝑎64,3 𝑒64 ≥ 𝑣3

𝑎1,4 𝑒1 + 𝑎2,4= 𝑒2 +...+ 𝑎64,4 𝑒64 ≥ 𝑣3

𝑒1 + 𝑒2 + … + 𝑒64 =3D = 1

𝑒1 + 𝑒2 + 𝑒3 + … + 𝑒64 ≥ 0

For the sustainable ranking, encompassing the three dimensions analyzed, environmental, social and economic-financial indicators, a vector game was applied. In this linear programming problem, the three dimensions are analyzed in a single model, enabling the analysis in general. Thus, the first three restrictions refer = to environmental variables, the next four restrictions refer to social variabl= es and, subsequently, the four restrictions refer to economic and financial variables. The 12th constraint refers to the sum of strategies that must ad= d up to 100% and the last constraint (13th) represents non-negativity.

&= nbsp;

𝑀𝑎𝑥 𝑍 =3D 𝑣1 + 𝑣2 + 𝑣= 3

𝑆𝑎 &= nbsp; 𝑎1,1 𝑒1 + 𝑎2,1= 𝑒2 +...+ 𝑎64,1 𝑒64 ≥ 𝑣1

𝑎1,2 𝑒1 + 𝑎2,2= 𝑒2 +...+ 𝑎64,2 𝑒64 ≥ 𝑣1

𝑎1,3 𝑒1 + 𝑎2,3= 𝑒2 +...+ 𝑎64,3 𝑒64 ≥ 𝑣1

𝑎1,1 𝑒1 + 𝑎2,1= 𝑒2 +...+ 𝑎64,1 𝑒64 ≥ 𝑣2

𝑎1,2 𝑒1 + 𝑎2,2= 𝑒2 +...+ 𝑎64,2 𝑒64 ≥ 𝑣2

𝑎1,3 𝑒1 + 𝑎2,3= 𝑒2 +...+ 𝑎64,3 𝑒64 ≥ 𝑣2

𝑎1,4 𝑒1 + 𝑎2,4= 𝑒2 +...+ 𝑎64,4 𝑒64 ≥ 𝑣2

𝑎1,1 𝑒1 + 𝑎2,1= 𝑒2 +...+ 𝑎64,1 𝑒64 ≥ 𝑣3

𝑎1,2 𝑒1 + 𝑎2,2= 𝑒2 +...+ 𝑎64,2 𝑒64 ≥ 𝑣3

𝑎1,3 𝑒1 + 𝑎2,3= 𝑒2 +...+ 𝑎64,3 𝑒64 ≥ 𝑣3

𝑎1,4 𝑒1 + 𝑎2,4= 𝑒2 +...+ 𝑎64,4 𝑒64 ≥ 𝑣3

considered. <= /span>Specifically, when the application resulted in pure strategy, the best company was removed from the mod= el, whereas when a mixed strategy was obtained, all companies were retained in = the analysis.

= 4 RESULTS AND DISCUSSION

The analysis and discussion of the results begin with the presentation of the developed rankings. At first, the rankings were developed to individually anal= yze the environmental, social and economic- financial aspects. Subse= quently, these three dimensions were analyzed in general in a single model to form the ranki= ng of sustainability, since according to Elkington and Burke (1989), sustainabili= ty encompasses environmental, social and economic-financial issues.

Table 5 presents the results of applying the scalar model to the environmental indicators, showing the ten = best positioned companies for 2017, as described in the methodology.

Table 5

Ranking of the environmental performance of companies in 2017

Companies	Position	Value	Z	Strategy
EDP Energias do Brasil SA<= /p>	1ª	𝑥40 =3D 0,480	0,829	Mixed
Companhia Energética de Minas Gerais CEMIG	2ª	𝑥₆ =3D 0,382	0,829	Mixed
Tim Participações SA	3ª	𝑥29 =3D 0,138	0,829	Mixed
Lojas Renner SA	4ª	𝑥₄ =3D 0,501	0,806	Mixed
Ecorodovias Infraestrutura e Logística<= /p> SA	5ª	𝑥61 =3D 0,499	0,806	Mixed
Engie Brasil Energia SA=	6ª	𝑥15 =3D 0,543	0,798	Mixed
Klabin SA	7ª	𝑥34 =3D 0,391	0,798	Mixed
Companhia Siderúrgica Nacional	8ª	𝑥₂ =3D 0,066	0,798	Mixed
Centrais Elét= ricas Brasileiras SA	9ª	𝑥25 =3D 0,597	0,791	Mixed
Ultrapar Participações SA	10ª	= 𝑥31 =3D 0,403	0,791	Mixed

Source: Research Data.

&= nbsp;

Table 5 presents only the firs= t ten companies classified in relation to their environmental performance in 2017= due to the number of companies analyzed, highlighting the companies with the be= st performances. It should be noted that until the tenth position, the applicatio= n of the model resulted in mixed strategies, so that in each round more than one company was indicated, most of which were withdrawn from 3 companies per ga= me. For this game 32 rounds were applied.

The first round resulted in the classification of the companies EDP Energias do Brasil SA, CEMIG and TIM as the best companies in relation to environmental performance in 2017. Subsequently,

after their removal from the game, subsequent roun= ds ranked Rener and Ecorodovias in the following positions. The game continued until the the last company, Fibria Celulose SA, was classified.

The same model was applied to = the other years analyzed and to the other groups of indicators verified so that= an environmental ranking, a social ranking, an economic-financial ranking and a sustainability ranking for each year were obtained, totaling 32 rankings.

Table 6

Ranking of Environmental Performance

Companies	2010	2011	2012	2013	2014	2015	2016	2017	Run Points	RG
Vale AS	1°	1°	1°	3°	1°	4°	9°	15°	477	1°
CEMIG	7°	7°	11°	1°	4°	3°	1°	2°	476	2°
Ecorodovias SA	4°	2°	3°	4°	6°	15°	14°	5°	459	3°
Tim Participações SA	2°	4°	6°	10°	10°	8°	12°	3°	457	4°
CCR as	3°	3°	2°	8°	7°	7°	3°	37°	442	5°
Natura <= /span>Cosméticos SA	6°	18°	8°	5°	13°	13°	5°	11°	433	6°
Even Constr. e Incorp.SA	9°	9°	7°	13°	9°	9°	10°	23°	423	7°
Cia Brasileira de Distrib.	31°	31°	5°	7°	16°	2°	8°	13°	399	8°
Engie Brasil Energia as	33°	24°	35°	9°	2°	1°	6°	6°	396	9°
Cia Paranaense de Energia	13°	20°	18°	6°	8°	23°	11°	21°	392	10°

Source: Research Data.

Based on Table 6, it is possib= le to analyze the classification of companies in relation to their environmental<= span style=3D'letter-spacing:-.25pt'> performance annually, as well as a general ranking of the environmental = performance of these companies in the analyzed period. Vale SA was the highest-ranked company in the general ranking. This= was due to the fact that it had a good classification in the years 2010, 2011, = 2012 and 2014. However, its ranking declined from 2015, reaching fifteenth place in 2017, which may serve as a signal for the company to improve its management practices.

CCR SA is also notable, as it = ranked 37th in 2017; however, due to its strong performance in 2010, 2011, 2012, and 2016, it was ranked fifth overall for the period. Engie Brasil Energia SA exhibited a similar pattern, ranking 35th in 2012, but achieving first place in 2015, which secured its ninth position in the overall environment= al ranking.

Thus, even with these companies showing a prominent position in the period, the decline in performance may indicate to managers the need to adapt strategies and policies. Following analyzing of environmental performance, the same procedures were applied to evaluate social, economic-financial and s= ustainable performance. Table 7 presents the ranking of the social performance of the companies analyzed annually and the general ranking (RG) for the period based on accumulated points.

Table 7

Ranking of Social Performance

Companies	2010	2011	2012	2013	2014	2015	2016	2017	Run Points	RG
Eletropaulo SA	1°	1°	1°	4°	1°	1°	1°	1°	501	1°
Vale SA	9°	3°	2°	1°	2°	2°	3°	8°	482	2°
Petróleo Brasil SA<= /p> Petrobras	2°	2°	9°	2°	4°	8°	4°	10°	471	3°
EDP Energias do Brasil SA	11°	6°	6°	3°	3°	3°	6°	4°	470	4°

Fibria Celulose SA=	6°	14°	10°	7°	9°	7°	19°	2°	438	5°
CPFL Energia SA=	3°	19°	28°	6°	5°	13°	14°	7°	417	6°
Duratex SA	7°	17°	16°	21°	7°	17°	10°	6°	411	7°
Gafisa SA	8°	11°	12°	16°	10°	19°	12°	14°	410	8°
MRV SA=	5°	43°	34°	5°	6°	4°	2°	3°	410	9°
Cosan SA	14°	9°	8°	26°	8°	5°	18°	23°	401	10°

Source: Research Data.

&= nbsp;

When analyzing the position of companies in relation to social performance, it can be seen that they have behaved differently f= rom what happened in their environmental indicators. The ranking of social performance is led by Eletropaulo SA, which occupied the first position in most years and only in 2013 was in the fourth position.= The other companies in the top ten for social performance are not the same as t= hose ranked in the top ten for environmental performance.

However, Vale SA, for example, dropped from the first position in the environmental ranking to the second position in the social ranking= . When analyzing 2017 specifically, its social performance was better rate= d higher than its environmental performance, ranking eighth in social indicators compared to fift= eenth in environmental indicators. Thus, although Vale achieved stronger overall environmental performance, its<= span style=3D'letter-spacing:-.1pt'> social performance in the final year was better classified. It is al= so interesting to note that MRV SA occupied 43rd position in 2011 and 34th position in 2012, but even so, in the general social ranking it was in ninth place.

Next, the ranking of the econo= mic and financial performance of the companies in the sample was developed, the result of which is shown in Table 8 following the same procedures previousl= y explained.

&= nbsp;

Table 8

Ranking of Economic-Financial Performance

Companies	2010	2011	2012	2013	2014	2015	2016	2017	Run Points	RG
M = Dias Branco SA<= /p>	6°	3°	4°	1°	3°	6°	4°	1°	484	1°
Odontoprev SA	4°	2°	6°	6°	4°	3°	3°	2°	482	2°
Cia Hering	15°	1°	3°	2°	1°	1°	8°	4°	477	3°
Petro Rio SA<= /p>	1°	19°	1°	3°	22°	4°	1°	11°	450	4°
CTEEP	9°	9°	10°	5°	10°	10°	2°	10°	447	5°
Estacio Participacoes SA	8°	20°	15°	4°	7°	12°	11°	7°	428	6°
Kroton Educacional SA	5°	39°	11°	8°	6°	8°	6°	6°	423	7°
Ambev SA	17°	6°	38°	9°	5°	7°	7°	3°	420	8°
Raia Drogasil SA	10°	7°	5°	7°	12°	17°	13°	23°	418	9°
Telefonica Brasil SA	14°	8°	8°	10°	19°	13°	14°	9°	417	10°

Source: Research Data.

Analyzing the results of this model, it is evidentthat the companies ranked in the top ten positions in relation to economic and financial performance are not the same listed among the ten best classified in relation to environme= ntal performance or in relation to social performance. The company M Dias Branco= SA stood out in the first position in the general economic-financial ranking, followed by Odontoprev SA. Cia Hering, despite achieving first place in 201= 1, 2014, and 2015, ranked third overall due to fluctuations in other years.

Through these partial analyzes (environmental, social and economic-financial), it appears that companies h= ave different performance in relation to each group of indicators. These results can be analyzed by managers in order to adapt strategies in order to mainta= in or improve the performance of companie= s.

Based on this observation, and in order to assess the sustainable performance of the companies analysed, the vector model and the ranking of sustainable performance prese= nted in Table 9 were elaborated.

Table 9

Sustainability Performance Ranking

Companies	2010	2011	2012	2013	2014	2015	2016	2017	Run Points	RG
Vale AS	2°	2°	1°	3°	1°	1°	4°	6°	492	1°
Telefônica Brasil SA<= /p>	39°	6°	5°	2°	4°	4°	6°	4°	442	2°
CEMIG	5°	5°	14°	10°	6°	14°	7°	17°	434	3°
Duratex SA	12°	21°	11°	4°	7°	6°	10°	12°	429	4°
Tim Participações SA	11°	15°	6°	8°	12°	10°	28°	5°	417	5°
Gafisa SA	9°	14°	2°	6°	5°	13°	22°	25°	416	6°
Multiplan SA	13°	28°	34°	1°	2°	2°	81°	9°	415	7°
EDP Energias do Brasil SA<= /p>	14°	35°	20°	21°	11°	18°	1°	2°	390	8°
Engie Brasil Energia SA	31°	12°	22°	7°	27°	8°	3°	19°	383	9°
CCR SA	4°	4°	10°	20°	24°	16°	12°	42°	380	10°

Source: Research Data.

Most of the companies ranked in the top ten for sustainable performance al= ready had prominent positions in the previous rankings, except Multiplan SA, which was not among the 10 best classified in any of the individual rankings (environmental, so= cial or economic-financial). The first ranked company in the sustainable perform= ance ranking is Vale SA, which had already been classified as the best company in relation to environmental performance and as the second best company in relation to social performance. Vale SA ranked first in relation to sustainable performance in 2012, 2014 and 2015, and second in the years 2010 and 2011, which ensured i= ts classification as the best company in relation to sustainable performance.<= /span>

The other two companies that s= tood out in the sustainable ranking were Telefônica Brasil SA and CEMIG. The second best position was for Telefônica Brasil SA, having previously appeared only in the economic-financial ranking in tenth position. The third ranked in relation to sustainable performance was the company CEMIG, = which had presented the second position in the environmental ranking, no standing= out in the other groups.

These results show the importance of evaluating organizations as a whole, holistically and in a general context, considering the economic prosperity, environmental quality= and social progress of companies (Liern & Pérez-Gladish, 2018). This= is because, as verified, the segmented analysis of organizational sustainabili= ty, that is, the individual analysis of environmental or social aspects can only lead to partial conclusions related to an organization.

This need for a holistic analy= sis of sustainability has already been reported in the bibliographic review made by Gbededo, Liyanage and Garza-Reyes (2018), when they evidenced the scarcity = of research that analyzes susta= inability with a holistic approach, integrating environmental, social and

economic-financial aspects. Most most studies focu= s on segmented analyses, examining only a single aspect of sustainability, which makes it difficult to understand the overallsituation of organizations in v= iew of the preservation of sustainability.

These results also highlight t= he importance of analyzing organizational sustainability as a multidimensional aspect, that is, that addresses environmental, social and economic-financial issues (Elkington & Burke, 1989). This is because the individual analys= es of environmental or social aspects may= not show the totality of the reality of organizations, as evidenced in the results of this investigation.

This holistic analy= sis of sustainability has also been addressed by Costanza et al. (2016), when discussing= that the dimensions of sustainability (environmental, social and economic-financ= ial) are not aspects with independent objectives in organizations, that is, these dimensions are interconnected, aiming to develop the organization as a whol= e.

= 5 CONCLUSIONS

To achieve the objective of th= is study, which sought to evaluate the environmental, social and economic-financial performance of Brazilian companies based on game theory, performance rankings were obtained for each group of indicators using scalar games. In addition, a general r= anking was developed using the vector model for sustainability analysis. Thus, four rankings were prepared: a ranking of environmental performance, a ranking of social performance, a ranking of economic and financial performance and a ranking of sustainable performance.

This study covered a longitudi= nal analysis of the sustainable information of the analyzed companies, since the period from 2010 to 2017 was analyzed. Thus, it was possible to verify that= the classification of companies varied according to the years and according to = the group of indicators analyzed. Thus, the results showed that, according to sustainable performance, the best ranked companies are Vale SA, Telefônica Brasil SA and CEMIG. However, these companies do not hold = the same classification when environmental, social, and economic-financial indicators were analyzed individually.=

It is also noteworthy that, despite<= span style=3D'letter-spacing:-.15pt'> some companies achieving prominent posi= tions in the overall ranking, Vale SA experience= d a decline in performance in recent years. This decline is a cause for concern= and highlights the need for a detailed analysis of its indicators as well as strategies and policies adopted and implemented. T= herefore, this research sought to contribute to the previous studies showing the importance of analyzing several indicators simultaneousl= y to assess a company’s performance and to point to the different degrees of performance in relation to the groups of indicators that form the tripod of sustainability.

This study has some methodolog= ical limitations that should be considered. The analysis was restricted to the period from 2010 to 2017 and to the sample of specific companies on the B3 stock exchange that had data available in the Thomson Reuters® database, which may limit the generalizability = of the results to other contexts and periods. Furthermore, the choice of game theory as a classification method may not fully capture the complexity of t= he interactions among sustainability indicators, and different results could potentially be obtained using other statistical or multicriteria methodologies.

For future research, it is recommended to explore new methodologies for classifying and analyzing organizational performance. Att= ention should also be given to the indicators and positions of the companies evaluated in this s= tudy that showed a decline in performance over the period, such as Vale SA, and = to the factors that may have caused this drop.

REFERENCE

Aris, N. A., Marzuki, M. M., Othman, R., Rahman, S. A., & Ismail, N. H. (2018). Designing indicators for cooperative sustainability: The Malaysian perspective. Social Responsibility Journal. https://doi.org/10.1108/SRJ-01-2017-0015

Bell, S., & Morse, S. (2005). Holism and understanding sustainability. Systemic Practice and Action Research, 18(4), 409-426.

https://doi.org/10.1007/s11213-005-7171-9

Bezerra, F. A., & Corrar, L. J. (2006). Utiliz= ação da análise fatorial na identificaç&a= tilde;o dos principais indicadores para avaliação do desempenho financeiro: uma aplicação nas empresas de seguros. Revista Contabilidade & Finanças, 17(42), 50-62. https://doi.org/10.1590/S1519- 70772006000300005

Boff, L. H., Procianoy, J. L., & Hoppen, N. (2006). O uso de informa&cce= dil;ões por analistas de investimento na avaliação de empresas: à procura de padrões.= Revista de Administração= <= /i>

Con= temporânea, 10<= /span>(4), 169-192. https://doi.org/10.1590/S1415-65552006000400009

Boiral, O., & Henri, J. F. (2017). Is sustainability performance comparable? A<= span style=3D'letter-spacing:-.15pt'> study of GRI reports of min= ing organizations. Business & Socie= ty, 56(2), 283-317. https://doi.org/10.1177/000765031= 5576134

Bortoluzzi, S. C., Ensslin, S. R., &am= p; Ensslin, L. (2011). Avaliação de desempenho multicrité= rio como apoio à gestão de empresas: aplicação em uma empresa de serviços. Gestão & Produ&cc= edil;ão, 18(3), 633-650. https://doi.org/10.1590/S0104-530X2011000300014<= /p>
Brito, L. A. L., & Vasconcelos, F. C. D. (2005). Desempenho das empresas brasileiras: efeitos ano, r= amo de negócios e firma individual. Revista de Administração Contemporânea, 9(SPE1), 65-

85. https://doi.org/10.1590/S1415-65552005000500004

Callado, A. A. C., Callado, A. L. C., & Almeida, M. A. (2008). O uso de indicadores de desempenho<= span style=3D'letter-spacing:-.15pt'> no âmbito das empresas do Por= to Digital. In 8º Congresso USP Controladoria e Contabilidade.

Callado, A. L. C. (2010). Modelo de mensuração de sustentabilidade empresarial: uma aplica&cce= dil;ão em vinícolas localizadas na = Serra Gaúcha. 216f. Tese (Doutorado em Agronegócios) UFRGS – Universidade Federal do Rio Grande do Sul. Porto Alegre.<= /p>
Camargos, M. A. de, & Barbosa, F. = V. (2005). Análise do desempenho econômico-financeiro e da criação de sinergias em processos de fusões e aquisições do mercado brasileiro ocorridos entr= e 1995 e 1999. REGE Revista de Gestã= ;o, 12(2), 99-115.

Cecon, B., Hein, N., & Kroenke, A. (2018). Associação do Disclosure Ambiental com o Valor de Mercado de Empresas Brasileiras. Revista de Negócios, 23(2), = 24-37. https://doi.org/10.7867/1980-4431= .2018v23n2p24-37

Chen, C. S., Yu, C. C., & Hu, J. S. (2018). Constructing performance measurement indicators to suggested corporate environmental = responsibility framework. Technological Forecasting and Social Cha= nge, 135, 33-43. https://doi.org/10.1016/j.techfore.2017.05.033

Costanza, R., Daly, L., Fioramonti, L., Giovannini,= E., Kubiszewski, I., Mortensen, L. F., ... & Wilkinson,

R. (20= 16). Modelling and measuring<= span style=3D'letter-spacing:-.15pt'> sustainable wellbeing in connection with the UN Sustainable Development Goals. Ecological Econo= mics, 130, 350-355. https://doi.org/10.1016/j.ecoleco= n.2016.07.009

Janine Patrícia Jost de Miranda

Jéssica Ta&iacut= e;s Petri

Adriana Kroenke

Ronaldo Leão de Miranda

Nelson Hein

ABSTRACT

RESUMO

1 INTRODUCTION

= 2 LITERATURE REVIEW

2.1 Performance analysis of companies

2.2 Sustainable Performance

3 METHODOLOGY

Table 1

Table 2

Table 3

Table 4

𝑀𝑎𝑥 𝑍 =3D 𝑣₁

𝑀𝑎𝑥 𝑍 =3D 𝑣₂

𝑀𝑎= 9909; 𝑍 =3D 𝑣₃

𝑀𝑎𝑥 𝑍 =3D 𝑣1 + 𝑣2 + 𝑣= 3

= 4 RESULTS AND DISCUSSION

Table 5

Table 6

Table 7

Table 8

Table 9

= 5 CONCLUSIONS

REFERENCE

Janine Patrícia Jost de Miranda

Jéssica Ta&iacut= e;s Petri

Adriana Kroenke

Ronaldo Leão de Miranda

Nelson Hein

ABSTRACT

RESUMO

1 INTRODUCTION

= 2 LITERATURE REVIEW

2.1 Performance analysis of companies

2.2 Sustainable Performance

3 METHODOLOGY

Table 1

Table 2

Table 3

Table 4

𝑀𝑎𝑥 𝑍 =3D 𝑣1

𝑀𝑎𝑥 𝑍 =3D 𝑣2

𝑀𝑎 = 9909; 𝑍 =3D 𝑣3

𝑀𝑎𝑥 𝑍 =3D 𝑣1 + 𝑣2 + 𝑣= 3

= 4 RESULTS AND DISCUSSION

Table 5

Table 6

Table 7

Table 8

Table 9

= 5 CONCLUSIONS

REFERENCE

𝑀𝑎𝑥 𝑍 =3D 𝑣₁

𝑀𝑎𝑥 𝑍 =3D 𝑣₂

𝑀𝑎= 9909; 𝑍 =3D 𝑣₃