Introduction

Several industries have been affected by the growth of the "sharing economy," most notably hotels (Airbnb) and taxis (Uber, Lyft, and Sidecar) [36]. Today's socio-economic and environmental problems can be solved through the sharing economy. Even so, some are skeptical about the tangible benefits of the sharing economy for society [19]. The disruptive nature of the sharing economy has posed significant challenges for incumbent players [8]. There is a belief that this business model will threaten incumbents across the economy [36]. Existing firms, often referred to as incumbents or incumbent firms, have adapted or developed their own innovations to address disruptions caused by new market entrants, new technologies, or changes in consumer behavior [39].

A disruptive business model based on technological innovation leaves incumbent firms with two options to fend off new entrants: strengthening their existing business model or adopting the new business model exclusively [26]. Uber's impact on existing businesses remains a contentious issue. Is the disruption that the sharing economy will bring to society a genuine threat to incumbents, or is it being overestimated? [19]. Apart from this debate, several countries have suspended Uber's operations, and concerns about security and safety mechanisms for accommodation-sharing businesses have cast doubt on the growth potential of this economy [36].

Are traditional jobs threatened by the expansion of the "sharing economy"? In recent years, this debate has revolved around taxi services, where digital platforms such as Uber have intensified competition. Uber does not own any cars; rather, it matches passengers with self-employed drivers and profits from each ride by taking a cut. Few inventions have generated more controversy since their inception in 2010. In Europe, taxi drivers have protested, and courts have either banned or restricted its usage. The number of drivers partnering with Uber has surged in the U.S. [3]. In Iran's taxi industry, following Uber's business model and innovating in its position, led to a transformation in the taxi industry's business model. This coincided with the development of internet infrastructure and resulted in increased user acceptance due to enhanced security, reliability, and accessibility. Taxi drivers suddenly faced reduced profits and a saturated market that disrupted their monopoly, causing conflicts with newcomers. One of the most contentious cases has been taxi drivers' complaints against internet-based taxis. Taxi drivers have cited various reasons to oppose the launch of these technological platforms. According to industry officials and drivers, these internet-based transportation platforms have disrupted market order and harmed their business by illegitimately lowering fares. An alternative approach to the interaction between incumbents and new entrants might involve designing a conflict resolution model instead of solely focusing on price and non-price mechanisms.

The strategic behavior of a decision-maker (DM) in a conflict will influence the strategic behavior of other DMs based on their interests. To resolve conflicts and promote cooperation, it is essential to accurately identify the interests of DMs and to simulate the dynamic evolution of decision-making behaviors [24]. The use of game theory to resolve conflicts over complex environmental issues among multiple DMs allows for a more realistic simulation of stakeholders' interest-based decision-making behavior [9].

A longstanding research topic in economics literature is the evaluation of the impacts on incumbents of potential or actual competition. Studies by Chang & Sokol [5] primarily focus on the effects of entry on incumbents' business outcomes, often considering revenues or profits. Recent research has examined how emerging business models of disruptive innovation, such as Uber's impact on taxi drivers [3], 4, 7, 19 or Airbnb's impact on hotels [38, 40], affect incumbents in traditional markets. These papers predominantly discuss the impact of disruptive innovators on revenues and incumbents' price responses. However, the conflict between incumbents and new entrants has not been addressed in previous articles. Therefore, this article identifies DMs and their decision sets, determines all feasible states, illustrates possible state transitions using a graph model, ranks relative preferences, identifies equilibrium points, and provides strategic guidance for resolving transboundary conflicts. As a result, this study aims to identify strategies, guidelines, and appropriate policies to resolve this conflict.

This paper contributes to previous studies and offers several significant insights. From a managerial and policy perspective, it examines how incumbents can respond to the disruption caused by the sharing economy. Furthermore, it analyzes incumbents' strategies in response to the entry of a disruptive innovator using GMCR (Graph Model for Conflict Resolution). Notably, there have been no previous studies using GMCR in this context. The paper makes various important contributions to the existing literature. It provides managerial and policy implications on how incumbents affected by the disruption of the sharing economy should respond. Additionally, it explores the strategies of incumbents in response to the entry of a disruptive innovator using GMCR, marking one of the few studies to utilize GMCR in this area. Given that most of the industry is under government control, this research aims to determine whether government intervention is beneficial for the industry. Specifically, it investigates whether government intervention in balancing different types of taxi services is advantageous, or if the market should determine pricing and competitiveness. This research provides insights into the effectiveness of government intervention versus market-driven approaches by comparing countries that regulate prices with those that allow the market to set them.

The paper is structured into five parts. After the introduction in Section One, which outlines the contributions, research objectives, and research gap, Section Two presents the literature review, highlighting previous research. Part Three illustrates the models and research procedure. Part Four delves into data analysis, covering modeling, actors and their possible options, extraction and refinement of feasible situations, preferences and prioritization of actors, model analysis, equilibrium points, and analysis of one-sided movements of actors, along with coalition analysis. The final part, Part Five, engages in a discussion and conclusion, summarizing the research's results.

Literature Review

This research is centered around the competition between New Entrants and Incumbents. The relevant literature is discussed below to clarify our contribution. The competition between New Entrants and incumbents has captured the attention of numerous scholars. For instance, Chang and Sokol [5] evaluated the strategies of incumbent hotels in response to Airbnb's entry, examining both price and non-price responses. The authors employed a fixed-effect model to estimate variables such as hotel occupancy rate, price, investment in service quality, and hotel revenues. Results indicated that low-quality hotels engage in price competition with Airbnb, while premium hotels may opt to differentiate their products, attract end customers, and charge higher prices. Berger et al. [3] documented the effects of Uber on the employment and earnings of taxi drivers in U.S. cities. Their findings revealed that the labor supply of self-employed taxi drivers increased by nearly 50 percent on average following Uber's introduction. Kim et al. [19] provided insights into how Uber transformed the traditional taxi industry in New York. Through a time-series regression model, they examined variables such as the number of taxi trips, the average daily revenue of taxi drivers, and occupancy rates. The results demonstrated that incumbent taxi drivers proactively responded to the disruptive threat posed by Uber's entry, resulting in significant benefits for consumers who could now hail taxis from a broader area in New York.

Ren et al. [29] delved into the strategies incumbents adopt in response to a primary rival's exit. They considered variables such as product variety at each store and market structures. Their formal model and empirical study revealed that after the exit of a rival, the survivor aims to expand both its product and geographic presence by increasing store-level product variety and opening new stores. This expansion strategy involves simultaneously filling market gaps and preempting attractive locations to discourage potential new entrants. Du et al. [10] introduced a strategic mental model to analytically characterize the effects of incumbent repositioning costs and decision biases on firms' equilibrium strategies and profits. Their findings indicated that while biases are detrimental for firms individually, both the entrant and incumbent can achieve higher profits when biased, compared to when neither party is biased. Specifically, if the entrant is biased in estimating the incumbent's repositioning ability and the incumbent is aware of this bias, the entrant's performance is negatively impacted.

Islami et al. [18] examined the relationship between industry barriers that hinder new entrants entering a competitive market and the increased profitability of incumbents. Variables considered in the study included economies of scale, product differentiation of incumbents, capital requirements of non-incumbents, switching costs, access to distribution channels, cost disadvantages independent of size, government policy, and the profitability of incumbents. The findings indicated that industry barriers contribute to increased profitability for incumbents and act as obstacles for potential rivals entering the market. Whelan [37] extended the entry deterrence literature by investigating the coordination of advertising and pricing in markets with consumption externalities, utilizing a stochastic success function. The findings revealed that the fixed cost of entry that challengers must bear and the consumption externality parameter influences an incumbent's ability to deter entry through coordinated advertising.

Chang and Sokol [5] utilize the number of Airbnb listings in the Taiwanese market to examine the price and non-price responses by hotels within the framework of traditional industrial organization. Similarly, Zervas et al. [40] explore Airbnb’s staggered entries into Texas and their impact on hotel prices. Farronato and Fradkin [13] structurally estimate the parameters of a model of consumer utility and supplier costs following Airbnb’s entry into 46 cities in the United States. In their 2011 publication, Yan and Guizani discuss various theoretical methods and provide examples commonly employed in this area of research. Rahman et al. [28] propose an MEC-based sharing economy system that utilizes Blockchain and off-chain frameworks for the storage of immutable ledgers. By utilizing the AI infrastructure we propose, a future smart city can offer cyber-physical sharing economy services through the use of IoT data. The use of smart contracts enables the framework to provide intricate spatio-temporal services worldwide, eliminating the need for a central verification authority. During the Hajj in both 2019 and 2020, we envision comprehensive testing of different sharing economy scenarios on a large scale.

Zhang et al. [42] apply the existing institutional legitimacy literature to gain insights into the intricate process of forming new institutional legitimacy within the context of a disruptive sharing economy. The primary objective of their study is to develop a comprehensive framework to elucidate the myriad factors involved in shaping and influencing the process of legitimacy formation. To investigate the institutional legitimacy issues associated with Uber, a leading tech start-up in the sharing economy, we applied deep-learning techniques to news articles published between 2009 and 2016. The initial results indicate that the legitimacy of sharing economy disruption is not constant and varies depending on the time frame and geographical region. Zhou and Wan [43] conducted a study to examine the extent of the disruptive power that the mobile digital sharing economy has on the road freight logistics industry. The advent of new information technologies, including the mobile internet, mobile payment methods, and GPS, has revolutionized the way platforms operate. These technologies allow platforms to effortlessly connect freight shippers with carriers, leveraging the convenience and mobility offered by smartphones.

In our study, we conduct empirical research to examine the impact of the emergence of mobile digital freight matching platforms in the United States on the profitability and stock performance of two specific types of incumbent road freight logistics companies: freight arrangement companies (including freight forwarders and brokers) and trucking companies (including freight carriers). Since mobile digital freight matching platforms primarily connect small and mid-sized trucking companies with shipping demand, it is anticipated that these platforms will bring direct competition to traditional freight arrangement companies and indirect competition to large trucking companies. This, in turn, may pose operational challenges for both types of established companies. Si et al. [32] explore the connection between disruptive innovation and the sharing economy. They aim to comprehensively examine the intricate mechanisms underlying a business project centered around disruptive innovation and its ability to successfully generate, distribute, and acquire value within the context of the sharing economy. The focus of their analysis is on the specific case of bike sharing in China. By utilizing an elaborate case study, they comprehensively explore the process, underlying mechanisms, and relationships among disruptive innovation, business models, bike-sharing businesses, and value creation in the sharing economy. The concept of bike sharing is a perfect fit for the theory of disruptive innovation. Its combination of affordability and exceptional convenience has resulted in swift growth and progress in China. The failures of bike-sharing companies can be attributed to their lack of improvement in products and services, as well as their inability to establish a successful business model that effectively creates, delivers, and captures value. Various factors have impeded the sustainable development of bike-sharing companies, including strategic decision-making, internal management problems, external conflicts, and uncivilized consumer behaviors. These methods include cooperative games, Nash equilibria, and allocation games, which explore the dynamics of competition versus cooperation. For a comprehensive overview of the previous research in this area, please refer to Table 1.

Table 1 summarizes these approaches
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Research Methodology

Due to the complexity and multifaceted nature of the problem, the chosen approach in this research is the method of constructing the problem. The problem structuring method is a novel approach within operations research [22] that serves to address complex problems. This method empowers actors to unveil the problem's structure, identify potential outcomes and consequences for each decision, and understand the responsibilities and implications of subsequent choices [25]. Within the realm of problem structuring methods, various tools and techniques exist, one of which is game theory. Among these methods, one of the most prominent is [11].

Game theory is a discipline that investigates human decision-making within situations of interaction or conflicts of interest with others. In essence, game theory delves into the study of conflicts and cooperation among rational players [16]. The theory revolves around examining the strategic interactions and collective decisions of multiple actors, yielding outcomes that might not have been intended by any single participant. Game theory's applications include explaining events as games, predicting game outcomes, or offering recommendations for achieving improved results [27]. In this study, game theory is employed to elucidate the problem and address the posed questions, aligning with the nature of the stakeholders' issue.

With the proliferation of conflicts in both number and diversity, various models have emerged within the realm of game theory. Depending on factors such as the number of participants, the available choices, and whether actors' preferences are quantifiable or relative, these models fall into two categories: quantitative methods (numeric preferences) and non-quantitative methods (relative preferences) [2]. Traditional game theory models such as normal or extended forms are employed for game modeling and analysis [34]. However, real-world decision-makers and their choices typically exhibit significant diversity, and preferences often tend to be qualitative and relative. As a result, for scenarios of this kind, classical models used in quantitative methods may not effectively analyze the situation. Thus, non-quantitative methods are harnessed for game modeling and analysis in such contexts [2].

In the current problem, given the significant number of actors and the extensive array of options at their disposal, coupled with the challenge of unquantifiable actor preferences, the utilization of the graph model is better suited to elucidate the problem. This model presents a comprehensive approach aimed at analyzing strategic conflicts in the real world. Each strategic conflict is viewed as a decision-making issue wherein diverse scenarios and situations encompass distinct preferences for each decision-maker [33]. To this end, the GMCR + software has been employed to model and analyze game outcomes based on the graph model. The requisite data for the problem were amassed from documents, articles, reports, and news articles from various news agencies. Using the content analysis method, the options available to each actor, potential situations, and the relative preferences of each actor were extracted. Content analysis stands as a systematic technique for dissecting text-based information in a standardized manner, enabling researchers to derive insights from textual data [35].

In the initial phase of this study, gather qualitative information by conducting stakeholder surveys, expert interviews, reviewing scholarly articles, and analyzing industry reports. To gain a thorough understanding of market dynamics, it is imperative to employ a wide variety of sources. For the development of scenarios and the analysis of GMCR + , create comprehensive scenarios based on the designated themes. The GMCR + model should be utilized to simulate a range of strategic interactions and conflicts. Analyzing the scenarios allows for the identification of both stable equilibria and semi-stable states. Take the time to understand and evaluate the findings from the GMCR + analysis. Present practical strategies for established businesses to reevaluate and refine their approaches, and assess potential intersections and opportunities for cooperation with recent arrivals.

The steps involved in modeling this problem align with the graph-based approach. Adhering to the definitions and concepts elucidated within the graph model, the conflict between established and newcomer companies is framed as a game. Commencing with the delineation of the actors and their respective strategies, the process filters out infeasible combinations, eventually revealing actor preferences. The analysis subsequently delves into stable scenarios, equilibrium points, coalitions, and a multi-faceted resolution of results. Figure 2 visually outlines the modeling and analysis process for the conflict within the graph framework. GMCR's process of conflict modeling and analysis encompasses two core stages: modeling and analysis [17]. In the initial stage, through an examination of conflict history and, if necessary, consultations with experts, actors, and their forthcoming choices—encompassing an array of players' selections and strategies—are defined [23]. Post-identification of the actors and their available options, potential conflict scenarios are established.

The total number of conflict scenarios is determined using the formula 2n, where n represents the overall count of potential options across all actors. Notably, not all conceivable situations are viable. To ascertain possible situations, those that lack practical feasibility are excluded from the scenario set. An essential consideration is that while the actors' potential options may not inherently align with their interests, achieving equilibrium necessitates their inclusion. The identification of such situations can be achieved through three methods: detecting two mutually exclusive pairs, identifying the presence of at least one option, and recognizing interdependencies between the options. Once potential conflict scenarios are determined, they are prioritized using various methodologies such as option weighting, option prioritization, and direct ranking [6].

The second phase in graph models involves determining equilibrium states and analyzing the resulting outcomes. Equilibrium states signify the most probable potential resolutions of the conflict and do not inherently imply fairness or optimality for all participants. In essence, equilibrium isn't necessarily the most advantageous point for everyone; rather, it's a circumstance where an actor lacks motivation to depart from. An actor's decision to remain in or leave a situation unilaterally hinges on various factors, such as their propensity for risk-taking or risk-aversion, as well as the depth of their understanding of other participants. With this perspective, several solution concepts, which are various approaches to check the stability of each actor, have been proposed. Noteworthy among these concepts are:

Nash Stability: This concept signifies a scenario where a given actor cannot improve their situation unilaterally, assuming the strategies of other actors remain unchanged [1].

Beyond General Rationality: In this approach, an actor considers not only their own unilateral improvement options but also accounts for other actors. They decide to shift their situation only if their move wouldn't enable competitors to transition them into a worse state [14].

Beyond Symmetric Rationality: Here, it's assumed that the actor can respond after their competitors. Sustainability aligned with symmetric rationality implies that an actor doesn't gain from any unilateral improvements, as each of their moves is countered by rivals, leaving them no better off [14].

Consecutive Stability: In this context, when the situation evolves, the actor views competitors as rational entities and, beyond contemplating their unilateral improvements, also considers their own move. Sequential stability indicates a situation where an individual's unilateral enhancements are counteracted by at least one rival's unilateral improvement [15].

Constrained Movement Stability: An actor envisions h steps into the future [14].

Far-Sighted Stability: A specific state within limited movement stability wherein the parameter h approaches infinity. An actor embracing foresight stability has an extensive horizon when deciding to maintain their current situation or transition to a new one [21]. Each definition of stability characterizes a distinct type of behavioral trait. Consequently, each participant can be stable within any given scenario based on one or more solution concepts, depending on their own behavioral characteristics. Table 2 elucidates the diverse sustainability concepts along with the associated behavioral attributes for each concept. Figure 1 visually outlines the research process.

Table 2 Different concepts of sustainability and the type of behavioral characteristics (Authors made)
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Fig. 1
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Research procedure (Authors made)

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Table 2 illustrates how diverse solution concepts can analyze various actors with distinct behavioral traits, encompassing a range from cautious and conservative individuals to strategic and active participants, as well as those with forward-looking perspectives and those with shorter-term views. If a situation is deemed stable for all decision-makers according to one or more stability definitions, it is termed an equilibrium point within the game, offering a plausible solution to the conflict. Given that different solution concepts reflect a variety of conceivable behavioral attributes for decision-makers, the more a situation is identified as a point of balance across multiple solution concepts, the higher the likelihood it will be embraced by decision-makers. Consequently, this increased recognition enhances the potential for its practical realization within the real world.

Data Analysis

In this section, according to the steps mentioned in Fig. 2, we will model and analyze the actors' conflict.

Fig. 2
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Impossible situations in GMCR + software (Authors made)

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Modelling

The process of conflict modeling and analysis in GMCR encompasses two primary stages of modeling and analysis [31]. In the initial stage, historical conflict review and, when necessary, consultations with experts and actors, including discussions about their forthcoming options—comprising an array of players' selections and strategies [30]—inform the process. Post-identification of the actors and their potential options, potential conflict scenarios are pinpointed. The total count of conflict scenarios arises from the formula 2n, where n signifies the overall number of possible options within the entire participant set. It's important to note that not all conceivable situations are feasible. To identify viable situations, those that lack real-world feasibility are culled from the set of scenarios. An essential consideration is that while the feasible options for the actors may not inherently align with their interests, achieving equilibrium remains crucial. These situations can be identified using three methods: identification of two mutually exclusive pairs, recognition of the presence of at least one option, and acknowledgment of interdependencies among the options. After determining feasible conflict scenarios, these situations are prioritized using distinct methodologies such as option weighting, option prioritization, and direct ranking. Within this section, adhering to the aforementioned steps, we proceed to model the conflict between established and newcomer companies.

The GMCR + uses theme analysis ideas innovatively. This combination enables a quantitative examination of qualitative insights, identifying stable equilibria and semi-stable states among plausible possibilities. The report provides a detailed analysis of potential consequences and considers multiple scenarios. The in-depth scenario analysis offers a comprehensive understanding of the competitive environment through a broad spectrum of strategic interactions and possible equilibria. Strategic alignment and conflict resolution offer several avenues for established businesses to adjust their tactics and coexist with new competitors. Market entry research focuses on defensive actions by established corporations.

Parameters

Groups and Individuals Involved: These are the decision-makers who have conflict strategies and preferences.

Options for Decision-Makers: These are the available choices, which are interchangeable. Decision-makers may reject options. Conflict scenarios or configurations are determined by the choices of the decision-makers. Each scenario represents a conflict situation.

Achievable Situations: These are represented by constraints and option interactions. Desirability determines the ranking of situations for each decision-maker, and preferences can be represented by rankings or utility values.

Feasibility of Transition: This is determined by the constraints dictating the course of conflicts. The possibilities and strategic interactions of decision-makers establish these rules.

Stability Evaluation

We must evaluate the stability of each scenario to identify which ones are likely to last. Well-recognized stability concepts include Nash stability, generic meta-rationality, symmetric meta-rationality, and sequential stability.

Equilibria

Equilibria refer to stable states determined by selected ideas and pertain to the settlement of conflicts. Decision-makers establish alliances to accomplish objectives, examining the influence of coalitions on the dynamics and outcomes of conflicts. The strength of preferences enhances the analysis. Analyzing the progression of conflicts requires studying the modifications that occur over time and the strategic adjustments made by decision-makers.

Actors and Possible Options of Each of Them

In the initial phase, following the methodology outlined in the methodology section, the actors and their corresponding options were identified. While selecting actors and delineating their potential options, it is important to recognize that not all stakeholders play a role in the conflict; those unable to take action are excluded as conflict actors. Conversely, the options available to each actor encompass practical actions that the respective player can implement in reality. These options do not encompass the entirety of an actor's interests. In essence, an actor might be interested in undertaking a specific action but may lack the practical means to execute it. Consequently, this action isn't considered as an option for that actor. The actors were classified into three distinct categories: newcomers, taxi drivers, and the government. This classification is grounded in the distinctive attributes of each actor. Within this study, new entrants are represented by companies, and owing to their analogous upcoming choices, they are grouped under the newcomers category. A mature company, conversely, refers to an established entity currently operational in the industry. In this study, Taxirani serves as a representative example of a mature company. The government, as an entity, bears the responsibility of exercising sovereignty within the realm of policy formulation.

Extraction and Refinement of Feasible Situations

As indicated in Table 3, a total of 8 options are available to the actors. Considering that each option may or may not be included in the strategy of the corresponding actor, theoretically, 28 or 256 combinations emerge for all conceivable game scenarios. However, it's important to note that not all of these combinations are feasible. Their occurrence in reality is limited, meaning that their realization in actual circumstances is implausible. Factors such as preferences and priorities of the actors contribute to this, making the realization of certain scenarios unlikely. Thus, before proceeding to subsequent stages, it is essential to identify and eliminate impossible scenarios.

Table 3 Actors and options before them (Authors made)
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These impossible situations are influenced by constraints and limitations that need to be applied to the game. These include:

Existence of at Least One Option: This stipulation mandates that each player must select at least one of their possible actions. For example, newcomers must choose from the options presented in Table 3.

Two-by-Two Incompatible Options: By implementing this condition, combinations in which certain options cannot coexist are removed from the potential combinations.

Dependency Between Options: This condition introduces conditional relationships where the occurrence or absence of one option depends on the occurrence or absence of other options.

Upon the application of the constraints listed in Table 4, infeasible combinations are removed, thereby reducing the count of potential situations to 21, as depicted in Table 5. Each entry in this table signifies a specific situation. Within each situation, an actor's decision to choose an option is denoted by "Y" (Yes), while the absence of a choice is indicated by "N" (No). Figure 2 provides a visualization of the impossible scenarios within the GMCR + software.

Table 4 Untenable situations in the conflict between mature companies and new entrants (Authors made)
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Table 5 Possible situations in the conflict between mature and newcomer companies (Authors made)
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Lastly, following the application of the constraints outlined in Table 5, unviable combinations were eliminated, resulting in a reduction of the potential situations to 21, as outlined in Table 6. Significantly, this table encapsulates distinct situations. Within each situation, an actor's decision to opt for a specific choice is denoted by "Y" (Yes), while the absence of a choice is marked by "N" (No).

Table 6 Policy preferences of newcomers (Authors made)
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Moving forward in the modeling process, the next step involves determining the potential transitions that each actor can make between various states, with a focus on defining irreversible movements. The nature of reversibility in a movement hinges on the answer to the fundamental question: if an actor transitions from an ideal state A to an ideal state B, is it feasible for them to revert back to state A subsequently? For a visual representation of the actors' reversibility within each option, please refer to Fig. 3.

Fig. 3
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Reversibility of actors in each option (Authors made)

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Preferences and Prioritization of Actors

The final stage of modeling involves determining feasible priorities and preferences for each actor. In the realm of game theory, multiple methods exist for establishing actors' preferences, encompassing direct ranking, strategy prioritization, and strategy weighting. For this purpose, the option prioritization approach was employed. Data gleaned from document analysis, individual interviews, and group discussions with various stakeholders in the subject were subjected to content analysis. Subsequently, based on this analysis, the political preferences of each participant were deduced, as delineated in Table 6. Preferences attributed to each actor can be classified as unconditional, conditional, or a combination of both. Unconditional preferences are indicated through connecting terms like "opposite (*)," "conjunction (&)," or "disjunction (or)," whereas conditional preferences are linked through the usage of "if." The policy preferences of the actors, categorized by available options, are illustrated in Tables 6, 7, and 8.

Table 7 Taxi policy preferences (Authors made)
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Table 8 Government policy preferences (Authors made)
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Upon inputting these preferences into the software, the prioritization of prevailing scenarios for all actors across various situations is established in accordance with Table 9.

Table 9 Government policy preferences (Authors made)
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Model Analysis

Following the ranking and determination of priorities, and in anticipation of predicting the ultimate outcomes of the game, the model is subjected to analysis. This analysis encompasses stability assessment, examination of unilateral movements by actors, and coalition analysis, and concludes with formulating policy recommendations.

Equilibrium Points

To achieve a state of equilibrium in the conflict, it's necessary to first determine stable states for each actor. A stable state refers to a condition where an actor has no incentive to deviate or leave [20]. If all actors find themselves in stable states, this collectively constitutes an equilibrium state. The attainment of equilibrium states in the conflict involves different approaches, contingent upon actors' attitudes and perspectives. As revealed by the outcomes in Table 10, out of the 21 possible states, there exist 3 equilibrium states and one semi-stable state among the actors' various states. This analysis is elaborated as follows:

Table 10 Equilibrium states of conflict between mature and new entrants (Authors made)
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Situation 14: According to the Nash, GMR, SMR, SEQ, and SIM logics, detailed features of which are outlined in Table 3, this represents the equilibrium state of the game. Here, the government amends the legislation for public transportation development while refraining from intervening in setting fare rates for new entrants and taxi companies. Taxi companies, recognizing the existing scenario, choose not to oppose it and instead cooperate with newcomers in aspects related to traffic planning and the initiation of services such as ride requests, cargo transport, parcel delivery, and student transportation. Newcomers, to secure a taxi fleet, contribute 30% of the commission per trip as city fees to the municipality. This state primarily benefits taxi drivers and new companies.

Situation 20: Similarly, based on Nash, GMR, SMR, SEQ, and SIM logics, this is another equilibrium state in the game. It closely resembles situation 14, with the distinction that taxi companies strive to equalize fare rates while newcomers remain indifferent to innovative technological advancements. This configuration holds substantial priority for taxi drivers and new companies, albeit it may not hold a commensurate priority for the government.

Situation 21: Aligned with Nash, GMR, SMR, SEQ, and SIM logics, this also marks an equilibrium state in the game. Analogous to situation 20, the difference lies in newcomers actively innovating and developing technological services to enhance passenger and driver safety. Alongside being stable, this situation is recognized as a coalition equilibrium, resulting in an elevated priority for taxi companies. Consequently, this holds high significance for taxi drivers and new companies, while again potentially falling lower on the priority scale for the government.

State 19: This state is semi-stable, achieving equilibrium solely based on GMR and SEQ logics. Here, the government revises the public transportation development legislation without intervening in fare determination for new entrants and taxi companies. Taxi companies do not raise objections to the existing setup and collaborate with newcomers in aspects pertaining to traffic planning and the inception of services. Within this state, new entrants exhibit indifference towards attracting a taxi fleet. Notably, this situation provides greater benefits to taxi drivers than newcomers and the government.

The outcomes derived from analyzing the stability of potential actor states using the Nash, GMR, SMR, SEQ, and SIM logic calculations demonstrate that in all four equilibrium scenarios, taxi drivers do not oppose the current situation. Instead, they prefer collaborating with newcomers on traffic planning and service initiation for various purposes. Meanwhile, the government refrains from intervening in the fare-setting process for both newcomers and established taxi companies.

Analysis of One-Sided Movements of Actors

Through the assessment of the stability of each actor within the scope of the potential conflict situations, it becomes possible to discern unilateral changes and improvements that actors can achieve. This delineates the capacity of each player to shift the game's outcome from one state to another through individual actions, unilaterally and without relying on the actions of other players. These transformative actions are depicted in both a tree format (Fig. 4) and a graph format (Fig. 5).

Fig. 4
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Tree diagram of actors' unilateral movements and improvements (Authors made)

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Fig. 5
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A graph of the actors' unilateral movements and improvements (Authors made)

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The illustrated outcomes of individual movements and enhancements (depicted in Fig. 6) showcase bold lines to signify unilateral improvements and lighter lines to denote unilateral movements. The various colors correspond to distinct actions of different actors. For instance, referring to the above figure, managers can transition from state 14 to state 15 through either a unilateral move or a unilateral enhancement from state 8 to state 14. Notably, it is evident that state 20 offers no advantage when compared to the other states.

Fig. 6
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The graph of the unilateral improvements of the actors (Authors made)

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Coalition Analysis

Another analysis that can be conducted based on the obtained results is coalition analysis, which seeks to ascertain whether the establishment of a coalition among actors could potentially lead to a new equilibrium state with greater priority. If such a coalition fails to produce an equilibrium state that holds higher priority for the actors involved, the existing stable equilibrium retains its status. Figure 6 depicts the graphical representation of unilateral improvements undertaken by the actors.

The results of the coalition analysis indicate the absence of a coalition between the actors in situations 14 and 20. Considering that a coalition between actors fails to yield an equilibrium state of greater priority for them, the existing stable equilibrium remains unchanged. As evident from the analysis, the number of improvement moves is fewer in situation 21 compared to the others. Therefore, it can be inferred that situation 21, aside from its stability, is also recognized as a coalition equilibrium. From this perspective, it holds a higher priority for taxi companies, albeit without a high priority for the government.

The academic literature has paid little attention to the distinguishing characteristics of established corporations and emerging competitors. This tool is invaluable for gaining a deeper understanding of the implementation of tactics in diverse contexts. This approach facilitates a comprehensive analysis of strategic decisions, offering a novel perspective compared to traditional methodologies. The approach I utilize integrates multiple disciplines to provide a comprehensive perspective on strategy. Through this integration, it unveils crucial insights that transcend particular theoretical frameworks.

Discussion

Fresh arrivals often offer innovative solutions and novel concepts, attracting customers in search of state-of-the-art products. Mature organizations are frequently compelled to innovate or enhance their value propositions due to the disruptive impact of these innovations, leading to heightened competition and a disruption of the status quo. Increased market fragmentation is a common outcome when new competitors enter the market. If consumers begin to prefer the offerings of new competitors, established enterprises may experience a decrease in both market share and profitability. Established organizations often employ diverse strategies to mitigate the risks presented by new market participants. Potential strategies could involve capitalizing on economies of scale, enhancing product attributes, optimizing customer loyalty initiatives, and implementing price adjustments. Additionally, certain corporations may endeavor to erect barriers to entry by employing legal tactics, safeguarding their intellectual property, or forging strategic alliances. According to the report, established businesses should consider seeking avenues for collaboration with recent entrants, rather than solely focusing on defensive measures. Generally, the introduction of new competitors is advantageous for consumers, as it can lead to joint ventures, acquisitions, or partnerships. Typically, competition results in improved pricing, services, and products. The readiness of customers to embrace new rivals demonstrates the necessity for established enterprises to maintain flexibility and adapt to the evolving demands of their clientele. As consumers actively search for optimal value and innovation, established enterprises prioritize the preservation of their market standing. With the rise of new competitors, this rivalry has the potential to escalate into fierce competition for both market share and customer loyalty. The themes present in this work provide a nuanced outlook on the intricacies of the market and the tensions that arise between established enterprises and emerging contenders.

The GMCR + (Graph Model for Conflict Resolution) decision support model proves to be highly beneficial in examining and illustrating possible strategic scenarios and outcomes. The investigation revealed a total of twenty-one situations, out of which three equilibria and one semi-stable condition were discovered. These findings suggest that by being open to change and potential partnerships with newcomers, established businesses can attain stable and mutually advantageous results. It is advisable for established businesses to contemplate adjusting their tactics in order to leverage potential synergies and counter new rivals. This could encompass examining joint ventures, allocating resources towards innovation, and adopting more versatile company models. Furthermore, mature organizations should engage in active interaction with new competitors rather than merely reacting to market fluctuations. This could involve joint development of innovative products and technology, making financial investments in other companies, or forging strategic alliances. It is imperative for well-established businesses to prioritize understanding and fulfilling shifting customer demands. To ensure continued relevance and competitiveness, they should strive to better align their offerings with consumer preferences. Applying theme analysis in this context is new. The integration of theme analysis in GMCR + is particularly creative, as it enables the quantitative examination of qualitative understanding, identifying stable equilibria and semi-stable states among plausible possibilities.

The report thoroughly analyzes 21 scenarios and their consequences, covering a wide range of strategic interactions and equilibria. Among these scenarios, three stable equilibria and one semi-stable state were identified. Strategic alignment and conflict resolution offer various options for established businesses to adapt to new competitors. Traditional studies on market entry barriers often focus on defensive strategies employed by established companies. In contrast, this study explores collaboration and synergies between established businesses and recent arrivals. Collaborative methods are encouraged as an alternative to defensive posturing, fostering innovation and growth. This research offers a broader perspective than traditional analyses of market entry barriers. It considers the wider effects of new competitors on market dynamics, customer preferences, and the strategic responses of established businesses. This comprehensive approach enhances the understanding of the industry. The study covers multiple aspects and includes all key industry players, providing well-rounded conclusions and suggestions.

Conclusion

This research delved into the analysis of the competitive behavior between mature and new companies, highlighting the pivotal role of government in legislative matters. Given the nature of the problem faced by stakeholders, game theory was employed to elucidate the issue and address the raised inquiries. Owing to the challenge of quantifying certain upcoming options and actor preferences in the real world, the graph model was utilized as a problem-solving approach. Data crucial to this endeavor was sourced from documents, articles, reports, and news agencies. By employing thematic analysis on actors' upcoming options, feasible situations, and relative preferences, the results of the games were analyzed through the use of GMCR + software.

Results stemming from the analysis of stability for feasible states among actors, grounded in Nash, GMR, SMR, SEQ, and SIM logic calculations, reveal that out of 21 feasible states, 3 equilibrium states (14, 20, 21) and one semi-stable state (19) exist among the different states of the actors. The semi-stable state 19 only exists based on GMR and SEQ logics. Situations 14, 20, and 21 exhibit stability across all logics. In these situations, no actor can improve their position through unilateral actions given fixed strategies by other players (Nash equilibrium). The actors do not gain from any individual behavior (SEQ equilibrium). Actors won't be placed in worse conditions by competitors if they decide to change their situation (GMR equilibrium). Additionally, none of the actors are confined by competitors' strategies (SIM equilibrium). Furthermore, foreseeable behaviors of the actors against competitors are stable (SEQ & SIM balance), which remain stable over the long term (SMR balance).

In all four equilibrium scenarios, taxi drivers show no resistance to the current situation and exhibit a preference for collaboration with newcomers and startups involved in car requests, cargo transportation, parcel delivery, and student services. Meanwhile, the government amends public transportation development laws but refrains from interfering in determining route fares for newcomers and taxi companies. Situation 21, apart from being stable, is recognized as a coalition equilibrium, thereby affording a higher priority to traditional taxi companies over internet-based ones.

Based on the findings derived from the stability analysis of actors' possible situations using Nash, GMR, SMR, SEQ, and SIM logic calculations, taxi drivers are recommended to adopt a cooperative stance with newcomers within the framework of traffic and air pollution plans. Collaborating with other startups for car requests, cargo transportation, parcel delivery, and student services, in exchange for commissions, is also advised. Additionally, matching fare rates with internet companies can help augment demand. This research aimed to conceptually elucidate the interaction between mature and newcomer companies in the intra-city transportation sector using the graph model. Future research could enhance these findings through qualitative investigations, while further development of the model in industries where mature companies face challenges can offer valuable comparative insights.