@carlosgracial.bsky.social

This work took more time & effort than expected, but it is finally out for good! 🎉

Big thanks to my collaborators Carlos Gracia Lázaro & @ymoreno.bsky.social — always a real pleasure to work together.

See the full article at: doi.org/10.1016/j.ch...

While our model is still a simplified representation of real behavior, it provides an insightful extension to evolutionary game theory by explicitly incorporating competition into the dynamics.

Take a look at the phase diagram:

· Resource depletion: acts as a temporal filter (memory). Too little → exploitation dominates. Too much → past investment loses value. Between these poles lies a narrow window where cooperation & competition coexist.

· Nonlinearities: a phase transition leads from full cooperation to coexistence with fighters at a critical resource investment. Fighters grow with investment but only up to a point—too much is too risky, and their population shrinks again.
...

And the results are cool and rich!
• Up to 5 macroscopic phases, incl. coexistence of cooperation + competition
• Fighters extend cooperation survival beyond classical PD thresholds
...

We also introduce a resource depletion parameter. This prevents runaway growth and lets us explore more realistic settings with finite resources.

The setup:
• Agents live on a lattice
• Strategies: Cooperation (C), Defection (D), Fighting (F)
• C & D follow standard weak PD rules
• Fighters operate under the Tullock's contest function. Invest resources → winner takes both, loser loses stake.

…effectively bridging (Evolutionary) Game Theory and Contest Theory, and adding a third way between standard cooperative and exploitative stances. We call this the CDF model (Cooperate–Defect–Fight).