Co-evolutionary Equilibrium Compression in Competitive Systems

Quantitative Approach to Game Balancing using Nash Equilibirum concentration and Variance compression to ensure strategic entropy and fix soft dominance problem

Quantifying Game Balance

Systemic Boringness

Using Shannon Entropy to quantify strategic entropy within a system, and inferring "boringness" as inverse function of the variety in strategic entropy.

Variance Compression

Gouldian Insight

0.400 Batter Problem

Co-evolutionary Model Explanation

Implications

Inevitability of Hard Dominance Metric Inflation

In any closed relational system with co-evolutionary dynamics, if system variety is present, variance compression of co-evolutionary strategy necessarily occurs over time.

Proof outline:
1. Co-evolutionary systems have reciprocal fitness functions
2. Optimal strategies converge due to mutual best responses
3. Physical constraints create right-wall bounds
4. Selection pressure eliminates sub-optimal variants (left-tail pruning)
5. Therefore: Var(t+1) ≤ Var(t) with strict inequality when system is active

Necessity of Externalities if Strategy Variance is the Goal

Soft Dominance Focus over Hard Dominance