EGT on Arbitrary Graph Topologies — k=3 Cooperation Boundary

Undergraduate research simulation for MATH 499C, CSUN, Fall 2026. Advisor: Dr. Bernardo Abrego.

Research Question

Ohtsuki et al. (2006) proved that for two-strategy evolutionary games on regular graphs, cooperation evolves if and only if b/c > k (benefit-to-cost ratio exceeds average degree). This project asks: does that result generalize to k=3 strategies, and if so, does crossing number cr(G) — rather than average degree alone — govern the cooperation boundary?

Approach

1. Replicate the Ohtsuki k=2 result as a validated baseline
2. Extend to a generalized k=3 payoff matrix on arbitrary graph topologies
3. Sweep across graph families (grid, cycle, star, random, scale-free, complete graph)
4. Test whether crossing number predicts the k=3 cooperation boundary

Status

Early stage — simulation architecture in progress.

Dependencies

• Python 3
• NumPy
• NetworkX
• Matplotlib