Computer Games as Complex Systems: Modeling Perspectives

A computer game is not a single model but a complex adaptive system integrating multiple modeling paradigms across interconnected layers.

Core Modeling Layers

1. Mathematical & Physical Models

• Rigid Body Dynamics: Newtonian physics (PhysX, Havok, Box2D, Jolt).
• Soft Body/Fluid/Cloth: FEM, SPH, PBD, XPBD solvers.
• Collision Detection: BVH, SAP, GJK/EPA, narrow-phase algorithms.
• Animation: FK/IK, blend trees, motion matching, procedural animation.
• Rendering: PBR, GI approximations, shadow mapping, temporal techniques.

2. Logical & State Models

• Finite State Machines (FSM): Character states, AI behaviors, game modes.
• Behavior Trees: Hierarchical task decomposition for complex AI.
• Utility AI: Score-based action selection.
• Planning Systems: GOAP, HTN, STRIPS for goal-oriented agents.
• Decision Trees/Random Forests: ML-driven NPC decisions.

3. Data & Information Models

• Entity Component System (ECS): Data-oriented architecture (Unity DOTS, Bevy, Flecs).
• Relational/Document Databases: Player profiles, inventory, world state (SQL, Redis, MongoDB).
• Serialization: Protocol Buffers, FlatBuffers, MessagePack, JSON for network/replay.
• Asset Pipeline: Dependency graphs, incremental builds, content addressing.

4. Gameplay & Experience Models

• Game Design Patterns: MDA framework (Mechanics, Dynamics, Aesthetics).
• Progression Systems: XP curves, loot tables, drop rates, pity systems.
• Economy Models: Sources, sinks, inflation control, market dynamics.
• Difficulty Adaptation: Dynamic difficulty adjustment (DDA), player modeling.
• Narrative Structures: Branching graphs, quest dependency DAGs, drama managers.

5. Network & Social Models (Multiplayer)

• Network Topologies: Client-server, P2P, hybrid, dedicated vs listen server.
• Synchronization: State replication, event sourcing, rollback/rollback netcode (GGPO).
• Consistency Models: Eventual, causal, strong — tradeoffs for latency.
• Matchmaking: Elo/Glicko/TrueSkill, skill-based, ping-based, premade balancing.
• Social Systems: Guilds, parties, chat, reputation, anti-toxicity.

6. Psychological & Behavioral Models

• Player Modeling: Bartle types, Big Five, motivation profiles (SDT).
• Retention/Monetization: Churn prediction, LTV modeling, bandit algorithms.
• Learning Curves: Skill acquisition models, flow channel maintenance.
• Accessibility: Cognitive load, motor capability, sensory models.

Integration Architecture

These models interact through simulation loops (fixed timestep physics, variable render), event buses, component queries, and system schedulers. Modern engines (Unreal, Unity, Godot, custom) provide frameworks to compose these layers.

Emergent Complexity

The "game" emerges from model interactions—unpredictable player strategies, meta-game evolution, social dynamics. This is why playtesting and telemetry are essential: no model fully captures the runtime experience.