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Requirements & Scope

This document outlines the research questions, modelling scope, and limitations of the NHRA Game Theory toolkit.

Research Questions

The simulation toolkit is designed to explore:

  1. Funding mechanism effects: How do different NHRA funding mechanisms (block vs activity-based, Commonwealth/State cost-sharing) affect hospital system pressure?

  2. Strategic incentives: What equilibrium behaviours emerge from the current institutional structure?

  3. Policy interventions: Which policy levers (pooled funding, governance integration, transparency) most effectively reduce system pressure?

  4. Interface coordination: How do aged care, NDIS, and discharge coordination interfaces affect flow?

Modelling Scope

In Scope

  • Stage game equilibria: Nine two-player games representing key strategic decision points
  • System dynamics: Annual evolution of pressure, efficiency gap, and flow metrics
  • Sensitivity analysis: Sobol global sensitivity analysis for parameter importance
  • Policy comparison: Scenario modelling for intervention evaluation

Out of Scope

  • Patient-level microsimulation: The model operates at system level, not individual patients
  • Spatial heterogeneity: No geographic variation (state/regional differences)
  • Dynamic games: Games are static (one-shot); no repeated game dynamics
  • Private sector: Focus is public hospital funding; private not modelled

Key Assumptions

Assumption Justification
Two-player games Simplifies multi-stakeholder dynamics to bilateral negotiations
Annual time step Aligns with NHRA funding cycle; sufficient for policy analysis
Nash equilibrium Standard solution concept; represents strategic stability
Parameter independence First-order sensitivity analysis; interactions via Sobol indices

Limitations

Model Limitations

This is a stylised mechanism model for policy reasoning, not a forecast. It should be used to understand strategic incentives and compare policy directions, not to predict specific outcomes.

Key limitations

  1. Simplified payoffs: Payoff functions are parameterised approximations, not empirically estimated
  2. Equilibrium selection: When multiple equilibria exist, selection rules are heuristic
  3. Exogenous shocks: The model does not include pandemic-like exogenous disruptions
  4. Behavioural factors: Assumes rational utility-maximising agents; bounded rationality not modelled

Data Sources

All parameters must be grounded in publicly accessible sources. See:

  • Context and Handover for the evidence system
  • context/04_parameter_registry.csv for the full parameter registry

Roadmap

Completed

  • Core game theory engine with 9 stage games
  • Nash equilibrium solver (pure + mixed)
  • Monte Carlo simulation with confidence intervals
  • Sobol sensitivity analysis integration
  • Streamlit dashboard
  • MkDocs documentation site

Planned

  • Repeated game extensions (trigger strategies)
  • Bayesian calibration against empirical data
  • Geographic disaggregation (state-level)
  • Interactive policy scenario builder