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Repeated Prisonners Dilemma

This section summarizes the SequentialPrisonersDilemma project, where two independently trained PPO agents repeatedly play a Prisoner's Dilemma game. The goal is to test whether learned behavior converges to persistent defection, cooperative conventions, or mixed horizon-dependent patterns.

Environment and Learning Setup​

  • Environment: envs/prisoners_dilemma_env.py
  • Agents: player_1 and player_2
  • Actions: 0 = cooperate, 1 = defect
  • Training algorithm: PPO (RLlib 2.54.0)
  • Training style: independent learning with separate policies

Payoff matrix per round:

Prisonners Dilemma payoff matrix

Episodes run with a fixed horizon n_sequential_games, so each episode is a finite repeated game.

Research Question and Hypotheses​

The core question is whether independent PPO self-play recovers backward-induction-like defection in finite-horizon repeated play.

  • H1 (game-theoretic target): behavior approaches early, persistent defection.
  • H2 (RL behavior): cooperation may survive for substantial parts of an episode, with possible end-game defection or stable cooperative pockets.

A key caveat from the repository: independent PPO is not an equilibrium solver, so convergence to a Nash-consistent outcome is not guaranteed.

Evaluation Strategy​

The project reports:

  • cooperation/defection rates,
  • mean episode return,
  • mean rounds per episode,
  • multi-seed stability,
  • unilateral defection-gain checks against fixed opponents.

It also includes two robustness workflows:

  • stability_sweep: checks variance and stability across random seeds.
  • sweep_n_sequential_pd: measures how cooperation changes as horizon length changes.

Main Reported Fixed-Horizon Result (50 rounds)​

The README reports that for n_sequential_games = 50, both agents converge to all-defect behavior in evaluation:

  • mean_episode_reward: player_1 = 50.0, player_2 = 50.0
  • cooperation_rate: player_1 = 0.0, player_2 = 0.0
  • mean_rounds_per_episode: 50.0

This matches the finite-horizon all-defect baseline where each round yields (D, D) -> (1, 1).

Sweep Results: Cooperation vs Number of Repeated Games​

The repository also reports a broader sweep across n_sequential_games = 5..100 (step 5), using 20 seeds and 95% confidence intervals.

Display 1: Mean cooperation rates across repeated games with 95% confidence bands
Display 1: Mean cooperation rates (20 seeds) across the number of repeated Prisonners Dilemma games, with 95% confidence bands.

Key observations summarized from the README:

  • Cooperation is not uniformly zero across horizons.
  • Higher-cooperation pockets appear around n=35, 50, 65, and 75.
  • Low-cooperation settings remain (n=5, 10, 15, 25).
  • Under two-sided testing with Holm correction over 40 tests, no (horizon, player) result was significant at alpha = 0.05 in the shown run.

Interpretation​

The reported pattern is non-monotonic: cooperation can reappear at specific horizons even when all-defect dominates at others. This suggests independent PPO self-play can produce horizon-dependent learned conventions rather than a single robust equilibrium profile.

Practical Takeaways​

  • Finite-horizon all-defect remains an important baseline and does emerge in some settings.
  • Multi-seed analysis is necessary because single-seed outcomes can be misleading.
  • Horizon length materially changes behavior, so it should be treated as a first-class experimental variable.
  • Defection-gain checks are useful to test whether a policy pair is resistant to unilateral deviation.

Limitations Noted by the Project​

  • Independent PPO optimizes against moving opponents and does not directly solve for Nash fixed points.
  • Cooperation estimates are seed-sensitive at many horizons.
  • Statistical correction across many tests can remove apparent single-condition significance.

Overall, the project supports a careful conclusion: in repeated social dilemmas, learned cooperation under independent PPO is possible but conditional, unstable across parts of parameter space, and strongly affected by episode horizon.

Where to Go Next​

If you want to continue from this MARL bridge toward broader cooperation questions:

  1. Selected Cooperation Theory for inherited, across-generation dynamics.
  2. Learning-Selection Interaction Theory for the full nature-nurture coupling.
  3. Cooperation (Social Behavior) for a broader behavioral framing.