Evolutionary game analysis on decision-making behaviors of participants in mega projects

Mega projects involve large investments, long timeframes, high technical complexity, and wide social and environmental impacts, making their governance highly complex. Among governance challenges, collusion among participants (owner, construction party, supervisor) to obtain additional benefits is prominent and risky. In China’s commissioned-agent construction system, the government establishes owners to manage projects, creating a principal–agent relationship. Owners entrust construction and supervision units; information asymmetry and low perceived exposure risk can induce supervisors to join collusion with owners and contractors, forming a collusion-body that threatens safety and project quality. Governance approaches span the project life cycle and include digital/AI methods, fuzzy cognitive mapping, organizational innovations integrating government–market roles, and multi-actor governance frameworks under institutional complexity. In mega projects, key actors also include the government (which should strengthen supervision and information disclosure) and the public (beneficiaries who can supervise via media, hearings, visits, and complaints). Diverse stakeholders make decisions based on cost–benefit trade-offs and limited rationality. The government may actively intervene (strict supervision, timely disclosures) or adopt formal, perfunctory intervention; the public may or may not supervise based on incentives and costs. Active government and public participation can reduce collusion. Evolutionary game theory, assuming bounded rationality and strategy updates via imitation, is suited to analyze these interactions. Prior studies examined subsets of actors (e.g., government–public; government–contractor–public; contractor–supervisor–contractor), but did not jointly model the collusion-body (owner, contractor, supervisor), government, and public. This paper fills that gap by building a tripartite evolutionary game model to study strategic stability and simulate parameter effects, offering insights for preventing collusion in mega project governance.

The paper positions its contribution within research on mega project governance and collusion. Prior work advocates life-cycle governance to address collusion, leveraging digital/AI tools and fuzzy cognitive mapping; proposes decision-making criteria, organizational procedures, and joint action mechanisms; and examines the co-function of government and market in Chinese mega projects, suggesting organizational model innovations and social governance frameworks involving enterprises, government, and society. Under institutional complexity, studies propose mechanisms to mitigate conflicts among stakeholders. In evolutionary game contexts, studies analyzed strategic interactions between local governments and the public, incorporated public supervision subsidies in tripartite models (government–contractor–public), and modeled supervision among contractors, supervisors, and contractors under digitalization. Some examined collusion involving government, owner, contractor, and supervisor under different supervision modes, optimizing probabilities of collusion and government supervision. However, existing studies lacked an integrated framework jointly modeling the owner–contractor–supervisor as a single collusion-body alongside government and public. This paper addresses that gap by constructing and analyzing a tripartite evolutionary game among the collusion-body, government, and public.

Model building: The study models the owner, construction party, and supervisor as a potential collusion-body that may choose to collude with some probability. The three players are: collusion-body (owner–contractor–supervisor), government, and public. Each chooses between two strategies: collusion-body {collude, not to collude}; government {active intervention, formal intervention}; public {participate in supervision, not participate}. Players are boundedly rational and update strategies via evolutionary dynamics to maximize expected payoffs given costs, benefits, and others’ behaviors. Parameters: Costs and benefits for each actor include: collusion-body costs when colluding C11 and not colluding C12; normal benefits R11; additional collusion benefits R12; loss upon exposure L1 (credit/social influence), fine P1, and compensation to public R31. Government’s active intervention cost C21 and benefit R2 (reputation/superior rewards), and formal intervention cost C22; if collusion occurs, government suffers losses L22; under general/formal intervention, further losses of reputation/public trust L21, superior penalty P2, and compensation to public R33. Public incurs supervision cost C3 and may receive government reward R32. Collusion harms the public (loss L3). Typically, C21 > C22, P1 > R33, and R31 + R33 > C3. Assumptions: (1) Tripartite dynamic game with bounded rationality; strategies evolve toward ESS. (2) Each actor selects one of two strategies as above to maximize expected payoff. (3) Strategy probabilities: collusion-body chooses collude with probability x (not collude 1−x), government active intervention with probability y (formal 1−y), and public participate with probability z (not 1−z), with 0 ≤ x, y, z ≤ 1. (4) All costs, benefits, fines, losses, and compensations are positive and quantifiable. Payoffs and replicator dynamics: From the payoff matrix (eight strategy combinations), expected payoffs Uij are derived and used to form replicator dynamics. For the collusion-body: F(x) = x(1−x)[ z(y−1)(L1+P1+R31) − y(L1+P1+R31) − C11 + C12 + R12 ]. For the government: F(y) = y(1−y)[ xz(L21−P1+P2+R33) + x(P1+R33) − zR32 + C22 − C21 + R2 ]. For the public: F(z) = z(1−z)[ −xy(R31+R33) + yR32 + x(R31+R33) − C3 ]. These three coupled ODEs define the evolutionary dynamics in (x, y, z). Strategic stability analyses: Setting F(x)=0 yields x*=0, x*=1, and a critical z* = [ y(L1+P1+R31) + C11 − C12 − R12 ] / [ (y−1)(L1+P1+R31) ]. Proposition 1: z* increases with (C12−C11) and with R12 (higher non-collusion vs. collusion cost gap or higher collusion benefit raises the public’s supervision participation probability). Setting F(y)=0 yields y*=0, y*=1, and z* = [ yR32 + C22 − C21 − R2 ] / [ 2(L21−P1+P2+R33) + P1 − R33 ]. Proposition 2: z* increases with (C22−C21) (i.e., larger cost gap discourages active intervention and increases collusion) and decreases with R2 (higher active-intervention rewards reduce collusion). Setting F(z)=0 yields z*=0, z*=1, and a critical y* = [ x(R31+R33) − C3 ] / [ x(R31+R33) − R32 ]. Proposition 3: y* decreases with R32 and with C3 (with other conditions fixed), indicating government active intervention probability declines as public rewards or public costs change as specified by the model’s expression. Local stability is analyzed via the Jacobian matrix evaluated at eight pure-strategy equilibria E1–E8, with eigenvalues interpreted in terms of cost–benefit parameters. Asymptotic stability requires all three eigenvalues negative. System-level ESS: Among the eight pure-strategy equilibria, three are unstable (E1(0,0,0), E2(0,0,1), E5(1,0,0)). Five may be ESS under parameter conditions: E3(0,1,0): (not collude, active intervention, not participate) when C12−C11+R12 ≤ L1+P1+R31, C21−C22 ≤ R2, and R32 ≤ C3. E4(0,1,1): (not collude, active intervention, participate) when C12−C11+R12 ≤ L1+P1+R31, C21−C22 < R2−R32, and C3 < R32 (ideal state). E6(1,0,1): (collude, formal intervention, participate) when C12−C11+R12 ≤ L1+P1+R31, C21−C22 > L21+P2+R2−R32. E7(1,1,0): (collude, active intervention, not participate) when C12−C11+R12 ≤ L1+P1+R31, C21−C22 < P1+R2−R33, and R32 < C3. E8(1,1,1): (collude, active intervention, participate) when C12−C11+R12 ≤ L1+P1+R31, C21−C22 < L21+P2+R2−R32, and C3 ≥ R32. Simulation analysis: With initial probabilities x=y=z=0.5 and parameter settings elicited via expert input, the study simulates evolutionary paths and threshold effects. Sensitivity analyses vary: (i) C12−C11 (cost gap), (ii) R12 (collusion benefit), (iii) C21−C22 (active vs. formal intervention cost gap), (iv) R2 (government’s additional benefits), (v) C3 (public supervision cost), and (vi) R32 (public reward). Key simulated patterns: thresholds in C12−C11 and R12 drive transitions from E3 to E7; larger C21−C22 reduces government active intervention and can destabilize the system beyond certain ranges; higher R2 stabilizes towards E3; higher C3 reduces public participation, shifting from E4 to E3; R32 has non-monotonic effects with stability when low but possible oscillations as it increases, with threshold-dependent participation (some effects not fully reflected in simulation due to parameterization). Evolutionary diagrams illustrate convergence to the five ESS under respective parameter scenarios.

- Existence of critical probabilities: For each actor, there are critical values of others’ strategy probabilities determining switches between strategies. For the collusion-body, a critical public participation probability z* governs the shift between collude vs. not collude; for the government, a critical collusion probability x* (embedded in the conditions) affects active vs. formal intervention; for the public, a critical government active-intervention probability y* affects participate vs. not. - Cost–benefit drivers: Increasing the cost gap (C12−C11) or the collusion benefit R12 raises the public’s participation probability (Proposition 1). Increasing active–formal intervention cost gap (C22−C21, i.e., higher relative cost of active intervention) increases collusion, while increasing government rewards R2 for active intervention reduces collusion (Proposition 2). The public’s participation is shaped by its supervision cost C3 and reward R32, with the model’s critical y* decreasing as specified; lower C3 and/or appropriately set R32 increase public participation (Proposition 3 and simulations). - Five possible ESS combinations under parameter conditions: E3 (not collude, active intervention, not participate); E4 (not collude, active intervention, participate) – ideal; E6 (collude, formal intervention, participate); E7 (collude, active intervention, not participate); E8 (collude, active intervention, participate). Three equilibria (E1, E2, E5) are unstable. - Policy-relevant thresholds from simulations: There are thresholds in C12−C11 and R12 where the system shifts from E3 to E7; government’s active intervention decreases as (C21−C22) rises, with stability only when (C21−C22) is below specific values (e.g., ≤9–10 in the simulated setup). Higher R2 (≥ about 8–9 in simulations) promotes convergence to E3. Increasing C3 shifts the system from E4 to E3; keeping C3 below about 1–3 (simulation range) supports public participation. R32 affects both government and public strategies; high R32 can induce oscillations and reduce government’s active intervention, with effective ranges (e.g., ≤4) stabilizing at E3 in simulations. - Managerial insight: Active government intervention, complemented by calibrated public participation incentives, can steer the system to the ideal ESS (E4). Adjusting fines, exposure losses, compensation, and cost/benefit parameters for the collusion-body can transform collusive ESS (E6, E7, E8) into non-collusive ESS (E3 or E4).

The findings address the core question of how the collusion-body, government, and public strategically interact in mega projects and under what conditions collusion can be deterred. The model shows that strategy choices are interdependent and governed by cost–benefit thresholds. Active government intervention raises deterrence against collusion, while public participation provides additional monitoring pressure. However, government and public strategies can substitute or complement each other depending on costs and incentives. The analyses reveal critical probabilities at which actors switch strategies, clarifying when interventions are most impactful. The five ESS illustrate that even under active government involvement, collusion can persist unless the collusion-body’s payoff structure is altered (e.g., higher exposure losses/fines or reduced collusion gains). Simulations demonstrate practical parameter ranges that tip the system toward desired equilibria. Managerially, the study suggests: (i) maintain high-pressure governance with timely, active intervention; (ii) calibrate public rewards and reduce participation costs to foster effective supervision; (iii) increase expected costs of collusion (losses L1, fines P1, compensation R31) and/or reduce collusion benefits R12; and (iv) avoid large gaps between active and formal intervention costs (C21−C22) that discourage active oversight. Together, these measures align incentives to reach the ideal ESS (E4: not collude, active intervention, participate).

This paper integrates the owner, construction party, and supervisor into a collusion-body and constructs a tripartite evolutionary game with the government and public to analyze decision-making behaviors in mega projects. It derives replicator dynamics, characterizes critical probabilities and conditions for ESS, and identifies five possible stable strategy combinations. Simulations validate theoretical results and reveal threshold ranges for key parameters. Main contributions include: (1) a unified evolutionary game framework capturing interactions among collusion-body, government, and public; (2) analytical conditions for multiple ESS and transition mechanisms; and (3) actionable insights on how adjusting costs, fines, rewards, and supervision incentives can deter collusion. The study recommends that governments lead with active intervention and enable public supervision through appropriate incentives and reduced participation costs, while increasing expected penalties and exposure losses for collusion. Future work could extend the model to heterogeneous publics, dynamic information revelation, multi-stage project phases, or networked projects, and empirically calibrate parameters with real project data to refine policy design.

The paper does not report a dedicated limitations section, but two constraints are evident: (1) Model scope and assumptions: the collusion-body is aggregated (owner–contractor–supervisor), and only two strategies per actor are considered under quantifiable, positive parameters; richer behaviors (e.g., partial collusion, mixed regulation modes) are not modeled. (2) Simulation parameterization: some theoretically predicted effects (e.g., threshold-driven increases in public participation with higher R32) were not fully reflected in simulations due to specific parameter settings, indicating sensitivity to calibration. Additionally, empirical validation with real-world data is not presented.