SGT Cheating Dilemma Simulator

Nash vs Societrics Equilibrium: How system stability redefines rationality

Scenario Presets

Primary Controls

Percentage of students who cheat per cohort

Simulation length (academic years)

Threshold Ratio (Θ)

STABLE: System healthy

Trust Level

NaN%

Education Quality

NaN%

Equilibrium Predictions

NASHClassical Game Theory

Maximizes individual utility, ignores system cost

Predicted Strategy:

Cheat (always +5 short-term)

βœ— Does not account for threshold crossing or payoff reclassification

SGT Οƒβ‚‘Societrics Equilibrium

Requires moral, strategic, and structural conditions

Predicted Strategy:

Either (System stable)

βœ“ Excludes strategies that breach SOC limit (|Ξ”C| ≀ SOC)

Dynamic Payoff Matrix

System Holds (High Standards)System Fails (Low Standards)
Student: Honest
Student: +10
System: +5
Constructive Win
Student: +5
System: -5
Frustration Zone
Student: Cheat
Student: +5 β†’ -15 (T=5)
System: -20
Delayed Crash (Sieve)
Student: (reclassified)
System: -50
Crisis Risk

SIP Trap Active: When Θ > 1, payoffs are reclassified. Current effective cheat payoff:

System Evolution Over Time

Key Insights:

  • β€’ Nash Equilibrium: Always predicts "Cheat" as rational (immediate +5 payoff)
  • β€’ Societrics Equilibrium (Οƒβ‚‘): Excludes "Cheat" once Θ > 1 due to system collapse
  • β€’ The System Sieve: Time (T) exposes incompetence; short-term gains become long-term losses
  • β€’ SIP Trap: When trust falls, all signals invertβ€”even genuine reforms are seen as manipulation
  • β€’ Policy Implication: Protect SOC capacity through enforcement, or the entire credential system collapses