Problem
The game-theoretic lens (PatternIR → equilibria, incentive compatibility) and the dynamical lens (GDSSpec/CanonicalGDS → reachability, stability) are orthogonal and can disagree. The infrastructure to perform cross-lens queries does not exist.
Type
[MATH] [CODE]
Prioritization
- Criteria: C2 (Completeness), C4 (Leverage)
- Tier: 2 — Medium Priority
- Phase: 4 — Analysis & Behavioral
- Dependencies: T1-1, T1-3
Key Disagreement Cases
- Game equilibrium does not imply dynamical stability (Nash equilibrium can be an unstable fixed point)
- Dynamical stability does not imply strategic optimality (stable attractor can be Pareto-dominated)
- Reachability does not imply incentive compatibility (reachable state may require irrational behavior)
Example Queries
query.is_nash_equilibrium_a_fixed_point(pattern_ir, canonical_gds)
query.is_stable_attractor_incentive_compatible(canonical_gds, pattern_ir)
query.is_reachable_state_individually_rational(canonical_gds, pattern_ir, state)
Steps
-
Define cross-lens agreement/disagreement formally. Compatible ExecutionContracts required. Distinguish meaningful disagreement from timestep artifacts.
-
Implement CrossLensQuery module. Consumes both PatternIR and CanonicalGDS. Initial query set: the three examples above.
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Worked case study. Axelrod tournament: game-theoretic vs. dynamical lens, where they agree, where they disagree, what the disagreement means for design.
Deliverables
Part of the GDS-Core Improvement Roadmap
Scientific Context
Evidence level: Level 4 (Cross-domain) — the unique scientific contribution no other framework offers. Analyzing the same system through a game-theoretic lens (equilibria, incentive compatibility) and a dynamical lens (reachability, stability), then asking whether the lenses agree.
A Nash equilibrium that is a dynamically unstable fixed point is a genuine finding: the equilibrium exists in theory but the system will not stay there. A stable attractor that is Pareto-dominated is another: the system converges but to a suboptimal outcome. These are the kinds of results that merit publication.
Verification Strategy
Known disagreement cases from textbook results. If the infrastructure reproduces known results, it is validated:
-
Prisoner's dilemma with population dynamics: Nash equilibrium (both defect) is dynamically stable. Tit-for-tat cooperation is Pareto-superior but dynamically unstable under invasion by defectors. is_nash_equilibrium_a_fixed_point() → True. is_stable_attractor_incentive_compatible() for the cooperative state → False (not Nash).
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Hawk-Dove with replicator dynamics: Mixed-strategy Nash equilibrium IS a stable fixed point of the replicator dynamics. is_nash_equilibrium_a_fixed_point() → True. Both lenses agree.
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Coordination game: Multiple Nash equilibria, one Pareto-dominant. The dominant equilibrium is a stable attractor; the dominated one is unstable. Queries should distinguish these.
Showcase
This is the paper. A single system (Axelrod tournament or similar) analyzed through both lenses, where the lenses disagree, and the disagreement has concrete design implications. Everything else in the roadmap is infrastructure that makes this result possible. The cross-lens case study demonstrates GDS as a diagnostic instrument for surfacing tensions between strategic and dynamical analysis.
Problem
The game-theoretic lens (PatternIR → equilibria, incentive compatibility) and the dynamical lens (GDSSpec/CanonicalGDS → reachability, stability) are orthogonal and can disagree. The infrastructure to perform cross-lens queries does not exist.
Type
[MATH] [CODE]
Prioritization
Key Disagreement Cases
Example Queries
Steps
Define cross-lens agreement/disagreement formally. Compatible ExecutionContracts required. Distinguish meaningful disagreement from timestep artifacts.
Implement
CrossLensQuerymodule. Consumes both PatternIR and CanonicalGDS. Initial query set: the three examples above.Worked case study. Axelrod tournament: game-theoretic vs. dynamical lens, where they agree, where they disagree, what the disagreement means for design.
Deliverables
CrossLensQuerymodule with initial queriesPart of the GDS-Core Improvement Roadmap
Scientific Context
Evidence level: Level 4 (Cross-domain) — the unique scientific contribution no other framework offers. Analyzing the same system through a game-theoretic lens (equilibria, incentive compatibility) and a dynamical lens (reachability, stability), then asking whether the lenses agree.
A Nash equilibrium that is a dynamically unstable fixed point is a genuine finding: the equilibrium exists in theory but the system will not stay there. A stable attractor that is Pareto-dominated is another: the system converges but to a suboptimal outcome. These are the kinds of results that merit publication.
Verification Strategy
Known disagreement cases from textbook results. If the infrastructure reproduces known results, it is validated:
Prisoner's dilemma with population dynamics: Nash equilibrium (both defect) is dynamically stable. Tit-for-tat cooperation is Pareto-superior but dynamically unstable under invasion by defectors.
is_nash_equilibrium_a_fixed_point()→ True.is_stable_attractor_incentive_compatible()for the cooperative state → False (not Nash).Hawk-Dove with replicator dynamics: Mixed-strategy Nash equilibrium IS a stable fixed point of the replicator dynamics.
is_nash_equilibrium_a_fixed_point()→ True. Both lenses agree.Coordination game: Multiple Nash equilibria, one Pareto-dominant. The dominant equilibrium is a stable attractor; the dominated one is unstable. Queries should distinguish these.
Showcase
This is the paper. A single system (Axelrod tournament or similar) analyzed through both lenses, where the lenses disagree, and the disagreement has concrete design implications. Everything else in the roadmap is infrastructure that makes this result possible. The cross-lens case study demonstrates GDS as a diagnostic instrument for surfacing tensions between strategic and dynamical analysis.