Behavioral Experiments on Decision Horizons in Conflict Analysis Theory Education

In conflict analysis and decision-making education, decision foresight measures how far ahead -- how many moves and counter-moves -- a decision-maker can look when judging whether the current state is stable¹. A state is stable for a given decision-maker if every unilateral improvement he might attempt can be blocked by credible countermoves of the other decision-makers that leave him in a less preferred position, so that he prefers to remain at the status quo. A state is a situation formed by the strategy choices of every decision-maker. Once each participant in the conflict has settled on a strategy, a possible state comes into being.

Decision-making, as a core concept and theory in management and business education, represents the most fundamental and critical activity undertaken by managers at all levels within any type of organization². Pfeffer and Fong found that decision-making not only constitutes a key dimension in cultivating managerial competence but also serves as a vital bridge connecting theoretical instruction with practical application³. However, traditional decision-making instruction predominantly relies on abstract lectures and case analysis -- a unidirectional approach that fails to engage students, hinders comprehension of multi-agent, multi-round strategic interactions, and inadequately develops practical business decision-making skills⁴. As Carneiro noted, management is taught more effectively if instructors' skills are better leveraged to create an environment more conducive to understanding managerial activities⁵.

Behavioral experiments have recently gained prominence as an operational and intuitive pedagogical method. Through authentic scenario simulations, they provide direct experiential learning of decision-making processes, enhancing comprehension of their multi-agent nature and inherent complexity. For instance, through the use of behavioral experiments, Knemeyer and Naylor aided participants in better grasping the nuances of decision-making in today's global business environment, thereby deepening their overall comprehension⁶. By employing behavioral experiments that simulate real-world decision scenarios, Liu et al. confirmed that the key to decision-makers' tendency to make proactive safety investment decisions lies in their clear recognition of the positive correlation between safety investment and safety benefits⁷. These studies demonstrate that behavioral experiments, by simulating real-world decision scenarios and employing interactive experimental designs, transform abstract theories into tangible experiences. This approach effectively addresses the challenges inherent in traditional theoretical instruction, such as students' difficulties in understanding abstract concepts and the inability to adequately illustrate the diversity of decision-making behaviors in conflict analysis.

Conflict analysis, a branch of decision theory, is crucial for resolving complex conflicts, such as climate, trade, and environmental issues. Nonetheless, its abstract notions and absence of practical application exacerbate the challenges of theoretical instruction. Rachmad's conflict resolution theory doesn't use the term "decision-making," but its process -- identifying root causes, developing strategies, and choosing solutions -- is essentially decision-making. Furthermore, the evaluation of decision effectiveness relies on key indicators, and its application across multiple domains depends on decision-making frameworks⁸. This demonstrates a close connection between theory and decision-making in terms of practical processes, effectiveness evaluation, and application scenarios. Conflict situations involve multiple actors and a multi-round interactive game process, which implies diverse interests and preferences in decision-making, leading to behavioral complexity and diversity. Within conflict analysis theory, irrational retaliation occurs when a decision-maker does not consider the payoffs to itself of the states it may move to. In contrast, rational retaliation means that a decision-maker will only move to states it prefers⁹.

Stability is the concept used to characterize and assess the complex and varied interactive behaviors of decision-makers, making it the most critical component in conflict analysis pedagogy. The four stabilities refer to Nash stability¹⁰ (NASH), general metarationality¹¹ (GMR), symmetric metarationality¹¹ (SMR), and sequential stability¹² (SEQ). NASH stability considers a one-step decision by the focal decision-maker, GMR and SEQ stability consider two-step decisions involving both the focal decision-maker and its opponent, and SMR stability extends GMR stability by introducing a chance for the focal decision-maker to counterrespond to its opponent's response. Stability characterizes the complex interactions, decision horizons, and diverse behaviors of decision-makers in conflict games. There are many types of stability concepts, and their definitions are relatively abstract, making it difficult to explain them clearly through traditional teaching methods.

In response to the aforementioned challenges, this study proposes a novel experimental teaching model for conflict analysis courses based on behavioral experiment methods. This model employs two classic game behavior experiments to dynamically simulate the strategic interaction process among conflict parties, thereby enhancing participants' profound understanding and learning outcomes regarding the stability of conflict analysis graph models, decision perspectives, and concepts such as rational and irrational retaliation^8,13. The Graph Model for Conflict Resolution (GMCR) theory originates from classical game theory and has developed into a formal and effective system for conflict analysis and resolution, grounded in Metagame Theory¹⁴ and the F-H conflict analysis method¹². GMCR can accurately predict the development of conflict situations by simulating dynamic interactions among conflict parties and provide effective conflict resolution strategies¹⁵. Compared to classical game theory, GMCR requires only relative preference information and offers a richer and more diverse characterization of decision-making behaviors. As a systematic decision analysis tool^16,17, GMCR has garnered significant attention in both theoretical research and practical applications due to its flexibility and simplicity¹⁸. It refines essential conflict elements through conflict modeling and analyzes decision-makers' behaviors via stability analysis to identify optimal conflict resolution solutions¹⁹, providing a crucial theoretical framework for addressing complex conflicts in business domains^20,21. With the acceleration of globalization and the intensification of business competition, future business leaders must not only master traditional management skills²²_, but also develop the capability to make strategic decisions in complex conflict scenarios. Teaching conflict analysis courses not only helps students build a theoretical framework for conflict cognition but also enhances conflict resolution abilities at individual, organizational, and societal levels^18,23,24; fosters critical thinking and shapes rational perspectives; and prepares talent for international conflict governance in a globalized context, facilitating the transformation of conflicts from confrontation to resolution.

The development of this experimental method is grounded in three core principles: First, behavioral experiments can create decision-making environments that closely approximate reality, thereby enhancing participants' authentic experience of conflict. Second, a multi-round game design dynamically reveals the evolution of conflict, helping participants understand the long-term consequences of their decisions. Third, an immediate feedback mechanism reinforces learning outcomes by enabling participants to reflect on and refine their decision-making strategies to achieve the most favorable results.

The experiment designed in this study consists of two interrelated components. The first part focuses on the concretization of the four fundamental solution concepts in conflict analysis theory and the expansion of decision perspectives. Through a sustainable development game between government and enterprise actors^25,26, it analyzes the evolutionary patterns of participants' decision perspectives over multiple rounds of interaction. Building on this understanding of decision perspectives, the second part deepens the investigation by emphasizing the cultivation of rational decision-making capabilities. Using a price war game between two competing firms²⁷, it helps participants grasp the consequences of both rational and irrational decision-making behaviors²⁸. This dual-part design not only encompasses the core elements of conflict analysis -- such as conflict parties, strategies and behaviors, conflict contexts, conflict outcomes, and decision perspectives -- but also aligns with the pedagogical requirement in business education to integrate theory with practice.

The applicability of this methodology is primarily reflected in three aspects. First, the modular design of the experiment allows for flexible application in business education courses. In strategic management courses, firms must formulate long-term development strategies within complex competitive environments and policy contexts. Both modules of this conflict experiment can be integrated into teaching. In the sustainable development game module, students simulate the roles of government and enterprise. The enterprise side must consider the impact of government regulatory policies on its production and investment strategies, making strategic decisions aligned with long-term sustainability -- such as choosing to "purchase new equipment" or "upgrade old equipment" in response to government regulation. This closely aligns with the core content of strategic management, where firms must adapt their strategies to changing external environments. In the price war game module, students simulate firms setting pricing strategies in market competition. Through multi-round games, they understand how different pricing strategies affect market share and profit, and learn to dynamically adjust their own strategies in response to competitors' actions. This helps students master competitive analysis and dynamic decision-making methods in strategy formulation and implementation.

Second, the interactive simulation method is particularly suitable for developing learners' practical skills²⁹. Behavioral experiments provide a platform that closely approximates real-world decision-making environments through interactive simulation, making them ideal for cultivating practical abilities. In traditional teaching methods, students often rely on theoretical learning and case analysis to understand complex decision processes, but these approaches struggle to offer dynamic, real-time interaction experiences. In contrast, behavioral experiments simulate authentic scenarios, enabling learners to personally experience various challenges and problems during the decision-making process, thereby enhancing their understanding and mastery of theoretical knowledge.

Third, the behavioral data collected during the experiment can provide empirical evidence for teaching improvement. A key advantage of behavioral experiments is their ability to collect rich behavioral data, which can serve as a basis for refining instructional methods. In traditional teaching, instructors often find it difficult to accurately assess students' learning outcomes and depth of understanding. Behavioral experiments, however, record every decision and action taken by students throughout the process, generating detailed behavioral data. These data not only help instructors monitor students' learning progress and comprehension levels but also reveal problems in students' decision-making processes. By employing this approach, this study aims to bridge the gap between theory and practice in traditional conflict analysis instruction, offering new insights and methods for developing decision-making capabilities in business education³⁰.

This research focuses on the behavioral experimental teaching method of stability theory in GMCR. Its main contributions are twofold: Firstly, it incorporates behavioral experiments into the GMCR framework by designing experiments on a sustainable-development game and a price-war game; Secondly, it analyzes the interplay of interests among decision makers (DMs) and their varying decision horizons during the conflict game and further investigates the rational and irrational sanctioning behaviors of DMs in conflicts.

The value of this study lies in being the first to systematically apply the behavioral experiment method to the teaching process of the GMCR methodology. This study innovatively introduces an interactive behavioral experiment-based teaching pedagogy, overcoming the limitations of conventional conflict analysis instruction -- such as overreliance on lecture-based delivery, difficulty in grasping abstract concepts, and lack of practical engagement. This method enhances students' understanding and ability to apply complex theoretical concepts, thereby improving overall teaching and learning effectiveness. Furthermore, it establishes an effective bridge between theoretical instruction and practical application. Not only does it transform abstract conflict analysis theories into intuitive and accessible knowledge, but it also enables students to directly apply the learned theories to real-world conflict resolution through practical case studies and scenario simulations^10,11,12.

Experimental design:
The experiment consists of two parts. The first experiment simulates the strategic interaction process between government and enterprise in sustainable development to help students understand the four fundamental stability concepts in conflict analysis theory and the differences of the decision-making foresights and their evolutionary patterns. The second experiment aims to strengthen participants' awareness of rational and irrational decision-making behaviors in conflict analysis by simulating the complex strategic interaction process of price wars between enterprises, helping students recognize the significance of both rational and irrational sanctioning behaviors in conflictual interactions. It is important to note that rational and irrational countermoves only emerge in decision-making processes involving two or more steps. In one-step decisions, such as NASH stability, the focal decision-maker does not consider any response from the opponent; therefore, the concepts of rational or irrational retaliation do not apply. In SEQ stability, the focal decision-maker assumes that its opponent's countermoves are rational. In contrast, in GMR stability, the focal decision-maker assumes that its opponent's countermoves are irrational. SMR stability extends GMR stability by introducing a chance for the focal decision-maker to counter respond to its opponent's response (see Table 1).

Table 1: Solution concepts describing human behavior under conflict. Stability and its scope.

The experimental task requires participants to engage in multiple rounds of gameplay under two specific decision scenarios -- sustainable development games and enterprise price war games -- until the expected experimental outcomes are reached. Data, including participants' strategy choices, preference tendencies, decision perspectives, and game outcomes, are recorded for each round.A total of 40 participants were involved, primarily consisting of undergraduate and graduate students who were about to study conflict theory. All participants are confirmed to have no prior knowledge of conflict analysis and have not participated in similar experiments before. Background information for both experimental scenarios is provided to participants at the beginning of the experiment. Participants are given unlimited time to complete the tasks.

Experiment 1: Sustainable development game experiment between government and enterprises
A total of 20 participants took part in this experiment (all participants were unrelated to the experimenters and to each other), forming ten pairs, with two participants in each pair. In each pair, one participant assumed the role of the government, and the other the role of an enterprise. In this sustainable development game, the government is responsible for promoting local economic development while also safeguarding environmental protection. The enterprise aims to maximize its economic benefits but must ensure its production activities comply with local environmental regulations. Accordingly, the government has two strategic options: "Strict Regulation" or "Lenient Regulation." The enterprise has three strategic options: "Purchase New Equipment," "Upgrade Old Equipment," or "Delay" (i.e., make no changes to existing equipment).The experimental scenario is set in a virtual city where economic development is relatively stable, but environmental protection pressures exist.

In each round of the game, both participants must simultaneously and independently choose one strategy -- collusion or communication is not allowed. After each round, participants record their chosen strategies on a response sheet. The experimenter then asks each participant three questions: Did you consider your own payoff? Did you consider which strategy the other party might choose? Based on that, did you consider what strategy you would choose in response to the other party's current move? Participants' answers to these questions are recorded on a shared form for the pair. After each round, there is a 30-second reflection period before the next round begins. Based on the payoff matrix (see Table 2), the resulting state from the combination of both players' choices is determined, and the corresponding payoff values for each player are displayed on a whiteboard. According to the matrix, the six possible states (s₁-s₆) arise from the combinations of strategies (see Table 2). Theoretically, the expected outcome of the experiment is state s₅ -- where the government chooses "Strict Regulation" and the enterprise chooses "Upgrade Old Equipment" -- which corresponds to the NASH equilibrium. The numerical values above each state in the matrix represent the respective payoffs for the two players under that strategy combination.

The hypothesis of this experiment is that as the number of game rounds increases, participants' decision horizons may change and potentially extend further into the future. Participants are required to complete three steps. First, they must understand their assigned role and the payoff matrix. Second, in each round of the game, they make their strategic choice. Third, when a participant determines that their strategy will no longer change, the experiment concludes for that pair. Since different pairs may complete the game in varying numbers of rounds, the longest number of rounds across all pairs is used as the standard for data analysis. After each pair completes the experiment, the instructor delivers a focused debriefing based on the recorded data-particularly the evolution of strategy choices and decision horizons across multiple rounds. This session emphasizes the four fundamental stability concepts (NASH, GMR, SMR, and SEQ) in the GMCR and explains the concept of decision horizons in conflict analysis theory. The goal of this simulated decision-making experience is for students to gain a thorough understanding of the differences between decision horizons and how they evolve, thereby improving their comprehension of interactive decision-making processes in conflict situations.

Experiment 2: Price war game between two enterprises
A total of 20 participants took part in this experiment, forming ten pairs, with two participants in each pair. Each participant assumed the role of either Company A or Company B. As market competition intensifies, price wars have become a common competitive tactic. However, frequent price wars may not only erode corporate profitability but also undermine the healthy development of the industry. In this experiment, both Company A and Company B have three strategic options: "High Price," "Keep Price Unchanged," or "Low Price." The experimental scenario involves two beverage companies, A and B, whose products have similar features, pricing strategies, and target markets, resulting in a competitive relationship between them. In each round of the game, both participants must simultaneously and independently choose one strategy -- collusion or communication is not allowed.

After each round, participants record their chosen strategies on a response sheet. The experimenter then asks each participant one question: "Following your choice, do you consider all possible responses the other party might take, or only the rational responses (i.e., responses where the opponent acts in their own interest)?" In this context: When a participant considers their opponent's potential irrational responses, they exhibit the GMR stability in their decision-making process. If a participant only considers the opponent's rational actions and assumes they will always respond in their own best interest, this reflects a decision-making pattern characterized by SEQ stability. After the question is posed, the participants' responses are recorded on a shared form for the pair. Each round is followed by a 30 s reflection period before the next round begins. Based on the payoff matrix (see Table 3), the resulting state from the combination of both players' choices is determined, and the corresponding payoff values for each player are displayed on a whiteboard. According to the matrix, the nine possible states (s₁-s₉) arise from the strategy combinations (see Table 3). The NASH equilibrium solution of the experiment, calculated using the GMCR software, is state s₁ -- where both Company A and Company B choose "High Price." The numerical values above each state represent the respective payoffs for the two companies under that strategy combination.

The hypothesis of this experiment is that during the process, participants will assume that their opponent's countermoves may be either rational or irrational. That is, under a two-step decision horizon, participants' decision-making behaviors will exhibit both GMR and SEQ stabilities. Participants are required to complete three steps: First, they must understand their assigned role and the payoff matrix. Second, in each round of the game, they make their strategic choice. Third, when a participant determines that their strategy will no longer change, the experiment ends for that pair. Since different pairs may conclude the game after different numbers of rounds, the longest number of rounds across all pairs is used as the standard for data analysis. After each pair has completed the experiment, a debriefing session is held based on students' strategy choices, manifestations of rational and irrational behavior, and overall game results. This session provides an in-depth explanation of the concepts of rational and irrational decision-making in conflict analysis theory, ensuring that students gain a deep understanding of the differences and evolutionary patterns associated with two-step decision horizons.

This study includes two experiments and recruited a total of 40 participants (mean age: 22.975 ± 1.625 years). All participants were undergraduate and graduate students from Jiangsu University of Science and Technology. After completing the preparatory procedures, participants engaged in the experimental tasks. Prior to the start of each experiment, both participants were required to test their Bluetooth headphones individually to ensure clear audio transmission and prevent interruptions or audio dropouts during the session. The procedure for both experiments was identical, as illustrated in Figure 1.

Table 2: The payoff matrix of the government and the enterprise.

Table 3: The payoff matrix of Company A and Company B.

Figure 1: Experiment procedure flowchart. Please click here to view a larger version of this figure.

This study was conducted in accordance with the principles of the Declaration of Helsinki and was approved by the Institutional Review Board of Jiangsu University of Science and Technology. We obtained the informed consent of the participants to use and release their data.This behavioral experiment was no risks are present throughout the entire process.

1. Experiment 1: Sustainable development game experiment between government and enterprises

1. Preparation
   1. Select a set of opaque colored card papers with the same texture in red and blue. Prepare two blue cards and three red cards; cut them into cards of the same size, 15 cm × 10 cm. Mark the two blue cards, representing the government, with the strategies "Strict Regulation" and "Lenient Regulation" respectively. Mark the three red cards, representing the enterprise, with the strategies "Purchase New Equipment," "Upgrade Old Equipment," and "Delay," respectively.
   2. Print the Government Individual Recording Form (Supplemental File 1 - Supplemental Table S1), the Corporate Individual Record Form (Supplemental File 1 - Supplemental Table S2), and the Government and Corporate Two-Person Record Form (Supplemental File 1 - Supplemental Table S3). Ensure that each participant has one copy of the individual record form, and the experimenter has the government and corporate two-person record form.
   3. Obtain written informed consent from the participants.
   4. Display the payoff matrix on the whiteboard in advance to ensure that participants can clearly see it throughout the experiment.
   5. Arrange for the participants to sit side by side with a 2 m gap between each participant to ensure that participants cannot see each other's strategy choices, thereby preventing them from changing their strategies multiple times.
   6. Place the Bluetooth headphones, cards, and 0.5 mm black gel pens on the table.
2. Experimental process
   1. Introduce the entire experimental procedure to the participants comprehensively.
   2. Explain the payoff matrix to the participants.
   3. Have each participant randomly explain one state in the payoff matrix to ensure they fully understand it.
   4. Conduct a pilot experiment before the formal experiment to ensure the formal experiment can proceed smoothly.
      1. Conduct a pilot experiment. Address the issue of participants' insufficient understanding of the experimental procedure. Ensure that the participants fully understand the experimental procedure before beginning the experimental task.
   5. Give the instruction: "Both parties make their decision choices."
   6. Upon hearing the instruction, have the participants simultaneously display their chosen strategies directly in front of themselves. The experimenter records the choices of both parties on the Government and Corporate Two-Person Record Form.
      NOTE: Make strategy choices simultaneously and only once, and do not collude.
   7. Have the participants record their chosen card strategies on the Government Individual Record Form (Supplemental File 1 - Supplemental Table S1) and the Corporate Individual Record Form (Supplemental File 1 - Supplemental Table S2), respectively, ensuring the accuracy of the records.
   8. Implement individual interviews using a standardized protocol. Ensure the other participant wears noise-canceling Bluetooth headphones and listens to music at 65-70 dB to prevent eavesdropping. After confirming no audio leakage, strictly follow the preset script by asking three prepared questions with 5 s intervals to ensure independent thinking. Simultaneously complete the information recording on the Government and Corporate Two-Person Record Form (Supplemental File 1 - Supplemental Table S3).
   9. Write both parties' choices and the corresponding payoffs on the whiteboard. This marks the end of one round of the experiment.
   10. Allow the participants 30 s for independent thinking.
       NOTE: Participants remained in a classroom maintained at room temperature throughout the experiment.
   11. Begin the next round of the experiment.
   12. Repeat steps 1.2.5 to 1.2.11 until both parties' choices no longer change.
   13. Explain to the participants the theoretical content related to rational and irrational behavior in Experiment 2 based on the experimental results. Ensure that the participants have a deep understanding of rational and irrational behavior.
   14. End the experiment.

2. Experiment 2: Price war game between two enterprises

1. Preparation
   1. Select a set of opaque colored card papers with the same texture in red and blue, with three blue cards and three red cards. Cut them into cards of the same size, 15 cm × 10 cm. The blue cards represent Company A, with the three cards marked with Company A's strategies: High Price, Maintain Price, and Low Price. The red cards represent Company B, with the three cards marked with Company B's strategies: High Price, Maintain Price, and Low Price.
   2. Print the Company A Individual Record Form (Supplemental File 1 - Supplemental Table S4), the Company B Individual Record Form (Supplemental File 1 - Supplemental Table S5), and the Company A and B Two-Person Record Form (Supplemental File 1 - Supplemental Table S6). Ensure that each participant has one copy of the individual record form, and the experimenter has the Company A and B Two-Person Record Form.
   3. Obtain written informed consent from the participants.
   4. Display the payoff matrix on the whiteboard in advance to ensure that participants can clearly see it throughout the experiment.
   5. Arrange for the participants to sit side by side with a 2 m gap between each participant to ensure that participants cannot see each other's strategy choices, thereby preventing them from changing their strategies multiple times.
   6. Place the Bluetooth headphones, cards, and 0.5 mm black gel pens on the table.
2. Experimental process
   1. Introduce the entire experimental procedure to the participants comprehensively.
   2. Explain the payoff matrix to the participants.
   3. Have each participant randomly explain one state in the payoff matrix to ensure they fully understand it.
   4. Conduct a pilot experiment before the formal experiment to ensure the formal experiment can proceed smoothly.
      1. Conduct a pilot experiment. Address the issue of participants' insufficient understanding of the experimental procedure. Ensure that all the participants fully understand the experimental procedure before beginning the experimental task.
   5. Give the instruction: "Both parties make their decision choices."
   6. Upon hearing the instruction, have the participants simultaneously display their chosen strategies directly in front of themselves. The experimenter records the choices of both parties on the Company A Individual Record Form (Supplemental File 1 - Supplemental Table S4) and the Company B Individual Record Form (Supplemental File 1 - Supplemental Table S5).
      NOTE: Make strategy choice simultaneously and only once, and do not collude.
   7. Have the participants record their chosen card strategies on the Company A Individual Record Form and the Company B Individual Record Form, respectively, ensuring the accuracy of the records.
   8. Conduct individual interviews using a standardized protocol. Ensure the other participant wears noise-canceling Bluetooth headphones and listens to music at 65-70 dB to prevent eavesdropping. After confirming no audio leakage, proceed with the interview by strictly following the preset script and asking the prepared questions. Simultaneously, complete the information recording on the Company A and B Two-Person Record Form (Supplemental File 1 - Supplemental Table S6).
   9. Write both parties' choices and the corresponding payoffs on the whiteboard. This marks the end of one round of the experiment.
   10. Allow the participants 30 seconds for independent thinking.
       NOTE: Participants remained in a classroom maintained at room temperature throughout the experiment.
   11. Begin the next round of the experiment.
   12. Repeat steps 2.2.5 to 2.2.11 until both parties' choices no longer change.
   13. Explain to the participants the theoretical content related to rational and irrational behavior in Experiment 2 based on the experimental results. Ensure that the participants have a deep understanding of rational and irrational behavior.
   14. End the experiment.

Experiment 1: Sustainable development game experiment between government and enterprises
The representative results of this experiment mainly include data on changes in decision-making horizons and game equilibrium results. This study included ten experimental groups, each with varying numbers of rounds. To standardize the statistical analysis of the experimental results, the longest number of rounds (22 rounds) from the experimental groups was used as the statistical benchmark. For experimental groups that ended before the 22nd round, the data processing for the subsequent rounds was as follows: Since each experimental group had confirmed that their results would no longer change at the end of the experiment, we extended the results of these groups from their actual ending round to the 22nd round using the final results. In this way, all experimental groups had the same number of rounds for statistical purposes, facilitating unified analysis and comparison.

Taking 22 rounds as the statistical benchmark: In the initial stage (Rounds 1-5), the proportion of participants with a one-step decision horizon accounted for 62%, those with a two-step horizon for 28%, and those with a three-step horizon for 10%. In the later stage (Rounds 16-22), the proportion of one-step horizons dropped to 8%, two-step horizons rose to 42%, and three-step horizons increased to 50%.

The majority (80%) of the participants experienced fluctuations in their decision horizons within the first 8 rounds. After Round 12, 90% of the participants had stable decision horizons, among which 60% had a three-step horizon, 30% had a two-step horizon, and 10% had a one-step horizon. All 10 groups stabilized at the s5 state, with an average convergence round of 14.2 (the fastest convergence took 8 rounds and the slowest took 20 rounds).

Changes in decision-making horizons
One-step decision-making occurs when a participant considers only their own immediate action in the game, without taking into account the opponent's possible retaliation. Two-step decision-making involves the participant considering their own action and then further anticipating the opponent's potential countermove. Three-step decision-making extends the two-step process by introducing the participant's consideration of whether they have an opportunity to counterrespond and escape the opponent's retaliatory sanction.

Figure 2 shows that the decision-making horizons of all participants are mostly two or three steps, with only a few being one step. Furthermore, as the number of game rounds increases, the majority of participants' horizons shift toward the long term. It validates the role of the feedback mechanism. In the initial stage of the experiment, participants had a limited understanding of role objectives, the payoff matrix, and the logic of the opponent's strategies. Most of them made decisions based on a "one-step horizon" (only considering their own payoffs), leading to random strategy choices. However, after each round, the payoff feedback displayed on the whiteboard (e.g., enterprises that chose "Delay" experienced a decline in payoffs when the government switched to "Strict Regulation") and the 30 s thinking time enabled participants to gradually shift from "passively accepting results" to "proactively summarizing rules". They began to predict the opponent's strategies (two-step horizon) and plan subsequent responses (three-step horizon), ultimately achieving the expansion of decision-making horizons.

Figure 2: Histogram of changes in participants' decision horizons. Please click here to view a larger version of this figure.

Figure 3 shows that the decision horizons of most participants initially exhibit a jumping phenomenon and then tend to stabilize. As shown in Figure 3, there exists a certain degree of synchronization between the decision horizons of the two participants in the game. This indicates that a decision-maker's decision horizon is influenced by that of its opponent. For example, when the government considers the enterprise's strategic choices, the enterprise likewise considers the government's potential strategic choices, demonstrating how their decision horizons mutually influence each other.

Figure 3: Distribution of individual changes in decision-making horizons. Please click here to view a larger version of this figure.

Game equilibrium results
An equilibrium is a state that is stable for every decision-maker under the specified stability concept. In Figure 4, the final results (the outcomes of the last round of the game) of each group of participants all tend towards state s5.s5 represents the state where the government chooses "Strict Regulation" and the enterprise chooses "Upgrade Old Equipment", while s1 represents the state where both Company A and Company B choose "High Price".From the perspective of the game process, in the initial rounds, the strategic choices of participants were relatively dispersed, with some groups reaching non-equilibrium states such as s3 (government chooses "Lenient Regulation" and enterprise chooses "Delay") or s1 (government chooses "Lenient Regulation" and enterprise chooses "Purchase New Equipment"). This indicates that in the early stages of the game, participants' understanding of the payoff structure was not yet deep, their decision horizons were shorter, and they tended to pursue short-term benefits. However, as the number of game rounds increased, participants gradually realized that under the government's "Strict Regulation," continuing to adopt the "Delay" strategy would entail higher compliance risks and lower long-term benefits for the enterprise. Consequently, they progressively adjusted their strategies toward the more sustainable option of "Upgrade Old Equipment."

Figure 4: Distribution of government-enterprise game equilibrium results. The figure shows how the game outcomes between the government and enterprises change as the number of experimental rounds increases. Please click here to view a larger version of this figure.

Experiment 2：Representative results of the price war game experiment
The representative results of this experiment include the changes of participants' assumptions about their opponents' rational and irrational countermoves within a two-step decision-making horizon and game equilibrium results. In this experiment, a total of 10 experimental groups were completed, with varying numbers of rounds in each group. The longest experimental group conducted 18 rounds, while the shortest group only conducted six rounds. To standardize the statistical analysis of the experimental results, the number of rounds of the longest experimental group (18 rounds) was used as the statistical benchmark. For experimental groups that ended before the 18th round, the data processing for the subsequent rounds was as follows: Since each experimental group confirmed that their results would not change at the end of the experiment, we used their final results to extend their status results to the 18th round. In this way, all experimental groups had the same number of rounds for statistical purposes, facilitating unified analysis and comparison.

Taking 18 rounds as the statistical benchmark: In the initial stage (Rounds 1-6), the proportion of rational countermoves was 35%, and that of irrational countermoves was 65%. In the later stage (Rounds 13-18), the proportion of rational countermoves increased to 85%, while that of irrational countermoves decreased to 15%.

The proportion of participants with SEQ stability (rational) rose from 25% to 80%, and the proportion of those with GMR stability (irrational) dropped from 75% to 20%. Eight groups stabilized at the s1 state, with an average convergence round of 11.5, and the remaining two groups stabilized at the s5 state.

Changes in the assumptions of rational and irrational countermoves by the opponent
Figure 5 shows that participants' judgments over their opponent's rational or irrational countermoves will change. The experimental results indicate that, under a two-step decision-making horizon, the countermoves of opponents can be either rational or irrational. Moreover, as the number of experimental rounds increases, the frequency of rational countermoves increases, indicating that participants become more rational in making their decision choices.

Figure 5: Distribution of changes in rational and irrational countermoves. The figure shows the changes in participants' assumptions about the opponent's countermoves. Please click here to view a larger version of this figure.

Figure 6 shows the changes in strategy stability under a two-step decision-making horizon in terms of the proportion of participants.

Figure 6: Distribution of changes in GMR/SEQ stability. The figure shows the changes in decision-making behavior patterns under a two-step decision-making horizon in terms of the proportion of participants. Abbreviations: GMR = general metarationality; SEQ = sequential stability. Please click here to view a larger version of this figure.

Game equilibrium results
Figure 7 shows that in the price war game experiment, the final results of most groups are consistent with the theoretically calculated NASH equilibrium, that is, they stabilize in state s1. s1 represents the state where both Company A and Company B choose "High Price". In the early stages of the game, some participants exhibited strong competitive tendencies, opting for the "Low Price" strategy to capture market share, which led the system into low-payoff states such as s9 (both companies choose "Low Price"). However, as the number of game rounds increased, participants gradually recognized the detrimental effects of a vicious price war on both parties' interests and began exploring cooperative possibilities through strategies such as "Keep Price Unchanged" or "High Price". Particularly through multiple rounds of interaction, by observing their opponent's responses and changes in payoffs, participants progressively adjusted their own strategies, eventually converging toward the mutually beneficial state s1.

Figure 7: Distribution of price war game equilibrium results. The figure shows how the game outcomes between Company A and Company B change as the number of experimental rounds increases. Please click here to view a larger version of this figure.

Supplemental File 1. Participant record forms for behavioral experiments. This file contains the blank record sheets used by participants during both behavioral experiments. Supplemental Table S1, Supplemental Table S2, and Supplemental Table S3 correspond to the Sustainable Development Game between the government and enterprises, including the Government Individual Record Form (Supplemental Table S1), the Enterprise Individual Record Form (Supplemental Table S2), and the Government-Enterprise Two-Person Record Form (Supplemental Table S3). Supplemental Table S4, Supplemental Table S5, and Supplemental Table S6 correspond to the Price War Game between Company A and Company B, including the Company A Individual Record Form (Supplemental Table S4), the Company B Individual Record Form (Supplemental Table S5), and the Company A-B Two-Person Record Form (Supplemental Table S6). These tables provide standardized templates for documenting strategy choices, decision horizons, and responses across multiple rounds of gameplay. Please click here to download this File.

This protocol can be readily implemented in both classroom and research settings, providing a readily applicable experimental teaching tool for conflict analysis and decision-making courses in business schools and management institutes.

Critical steps in the protocol:
To ensure the reliability of the results, the following steps need to be considered: First, participants who are familiar with the decision-making theories in the experiment are excluded, as these participants may complete the experiment based on their knowledge, which may lead to behavioral biases and result in unrepresentative data³¹. Second, to ensure that both parties think independently when answering questions, the other party should wear headphones when one party is being questioned to prevent participants from making inappropriate decision choices in the subsequent experiment due to hearing the other's thoughts.

Modifications and troubleshooting:
Firstly, the experiment can provide a more immersive experimental context. By utilizing VR technology to create an immersive experimental environment, decision-makers can feel as if they are in a real decision-making scenario. For instance, in a sustainable development game experiment, a resource-limited ecosystem can be simulated through VR technology. Decision-makers can observe dynamic changes in resources as well as environmental destruction and recovery, allowing them to more realistically assess the risks and payoffs of their decisions. Second, during the experimental process, decision-makers' payoffs are only displayed in numerical form on the whiteboard, which may result in a lack of sensitivity to changes in their own payoffs. Therefore, actual rewards and punishments, such as monetary rewards or point deductions, can be introduced in the experiment to enhance decision-makers' perception of payoffs and risks. Consequently, the introduction of tangible rewards and punishments, such as financial incentives or point deductions, may be implemented in the experiment to improve decision-makers' awareness of payoffs and risks.

Limitations of the method:
The experiment has the following limitations in terms of design and application. First, the scope of the theory is limited, as it only applies to decision-making theories for analyzing conflicts with simple preferences. This means that it cannot cover more complex and diversified preferences and motivations. Therefore, future research should focus on expanding the scope of the theory to make it applicable to more complex situations. Second, the number of decision-makers is limited, with the experiment only involving two participants. This somewhat restricts the applicability and scalability of the study to multi-person decision-making situations. Future experiments may expand to include multiple participants in decision-making. Third, there is a lack of a neuroscience perspective, which means that decision-makers' psychological and behavioral mechanisms cannot be explained in terms of neurophysiology. Modern neuroscience research has shown that the decision-making process is influenced by brain neural activity, and self-awareness of goals and planning to achieve goals can drive decision-makers³². For example, Cristofaro et al. found through systematic analysis that functions such as emotional regulation, risk assessment, and value judgment are closely related to the activity of specific brain regions³³. Future research will focus on combining with neuroscience to gather more comprehensive data.

Significance with respect to existing methods:
The significance of this study is mainly reflected in two aspects. First,this study pioneers the use of behavioral experiments to systematically investigate conflict game interactions, overcoming the simplified rationality assumptions and neglected complexities of traditional game theory experiments. As Botelho et al. have shown in their research, in dynamic experiments, details such as group size can significantly affect experimental outcomes³⁴. This method overcomes the limitations of traditional theoretical research by combining theoretical analysis with real behavioral data, verifying the four basic stability theories in real behavioral decision-making, and providing a new empirical basis for conflict analysis theory. Second, this method overcomes the limitations of traditional teaching by replacing abstract concepts with concrete experimental contexts and behavioral data, thereby enhancing the understanding of stability types and decision-making horizons.

Future applications:
In the field of conflict resolution education, this study effectively promotes the transformation of conflict analysis stability theory from abstract concepts to concrete teaching by revealing the diverse characteristics of decision-makers' behaviors in real conflict situations through behavioral experiments. By combining the dynamic data from multiple rounds of game experiments (including changes in strategy choices and state point evolution), it is possible to clearly reconstruct the entire evolution process of conflicts from the initial state to the equilibrium. This helps students comprehend conflict analysis theory and conflict evolution mechanisms and provides empirical support for conflict analysis behavioral experiment teaching. Furthermore, it cultivates students' dynamic analytical thinking in dealing with complex conflicts and their practical ability to analyze real conflict problems. The behavioral experimental model of this study provides a reusable paradigm reference for the practical teaching of other decision-making theory courses, addressing the limitations of traditional decision-making theory teaching that focuses only on theoretical derivation. Meanwhile, by exploring and analyzing the diversity of decision-makers' behaviors in experiments, it can help students gain a thorough understanding of the application scenarios of decision-making theories, such as team decision-making³⁵ and cross-cultural decision-making³⁶.