Melioration Learning in Two-Person Games

Abstract

Melioration learning is an empirically well-grounded model of reinforcement learning. By means of computer simulations, this paper derives predictions for several repeatedly played two-person games from this model. The results indicate a likely convergence to a pure Nash equilibrium of the game. If no pure equilibrium exists, the relative frequencies of choice may approach the predictions of the mixed Nash equilibrium. Yet in some games, no stable state is reached.

Fig 1. The situation of sequential decision-making.

Fig 2. A prisoner’s dilemma and simulation results.

Fig 3. The game “guess 23 of the average” and simulation results.

Fig 4. A game with three optimal Nash equilibria.

Fig 5. A coordination game and simulation results.

Fig 6. Relationship between the rewards of (B,B) and frequencies.

Fig 7. Relationship between non-equilibrium rewards and frequencies.

Fig 8. A “battle of the sexes” and a game of chicken.

Fig 9. A dispersion game and simulation results.

Fig 10. The game “matching pennies” and simulation results.

Fig 11. The game “rock-paper-scissors” and simulation results.

Fig 12. An example of the inspection game and simulation results.

Fig 13. The inspection game with low or high punishment.

Fig 14. Shapley’s game and simulation results.