Monday, September 1, 2025

Wealth Accumulation: Prisoner's Dilemma Model

Wealth Accumulation: Prisoner's Dilemma Model

From Pure & Perfect Models to Imperfect Real-World Constraints

Conceptual Framework

Wealth accumulation can be modeled as a prisoner's dilemma game where individuals choose strategies to maximize their wealth:

Pure & Perfect Model

Individuals freely choose how to earn, save, and invest without constraints. This represents an ideal free market with no externalities or government intervention.

dWi/dt = riWi

Imperfect Model

Constraints exist: government (taxes, regulations), nature (resource scarcity), and individual limitations. These forces distort choices and outcomes.

dWi/dt = (1-τ)riWi - λiWi + random shocks

Prisoner's Dilemma Analogy

Players choose between cooperation (fair competition) and defection (exploitative practices). Defection offers individual short-term gains but leads to societal suboptimal outcomes when everyone defects.

Wealth Simulation Controls

20%
8%
5%
3/10 years
$100

Simulation Results (After 20 Years)

Player 1 Final Wealth: $0

Player 2 Final Wealth: $0

Wealth Inequality (Gini Coefficient): 0.00

Wealth Accumulation Over Time

Conclusion: Can One Side Control 100%?

Pure Model Scenario

In the pure model without constraints, if one player consistently defects while the other cooperates, the defector can capture nearly all wealth over time. The equations show wealth ratio approaching 1 for the defector.

Imperfect Model Reality

In the real world with constraints, 100% control is unlikely due to:

  • Government interventions (progressive taxation, antitrust laws)
  • Diminishing returns on capital
  • Economic shocks and resource limitations
  • Social and political resistance to extreme inequality

The Balancing Equation

While complete wealth control is theoretically possible in pure models, real-world systems tend toward balance through various feedback mechanisms. The "equation must balance" in the long run through economic forces, policy interventions, and social dynamics.

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