Generic catastrophic poverty when selfish investors exploit a degradable common resource.

Area of Science:

• Economics
• Game Theory
• Resource Management

Background:

• The tragedy of the commons describes resource degradation from overexploitation by self-interested individuals.
• In unregulated scenarios, investors balance costs and returns to optimize individual investments.

Purpose of the Study:

• To analyze the emergent properties of investment in common pool resources without regulation.
• To rigorously prove the scaling of payoffs with the number of investors (N).
• To identify conditions leading to "catastrophic poverty" and the emergence of oligarchs.

Main Methods:

• Mathematical modeling of agent-based investment in a common pool resource.
• Derivation of Nash equilibrium conditions for investment optimization.
• Rigorous proof of payoff scaling as a function of N.

Main Results:

• Typical payoffs scale as (1/N)^2, not the expected 1/N, leading to "catastrophic poverty."
• This poverty arises from a fine-tuned balance between investment costs and resource returns.
• A finite number of "oligarchs" may emerge with non-decreasing payoffs as N increases.

Conclusions:

• Unregulated common pool resource exploitation results in significantly lower payoffs than anticipated.
• The structure of cost functions critically influences the Nash equilibrium, potentially causing market entry barriers or forced exits.