There are many flavors of games in Game Theory which are interesting from Machine Learning perspectives, especially from multi-agent Reinforcement Learning applications. Here is the summary of multiple game types are if MinMax algorithm works and what type of strategy one needs to employ.

Game ID | #Players | Outcome | Deterministic? | Information | #Round | Strategy |

1 | 2 | Zero-sum | Deterministic | Perfect Information | Single | MinMax works, Pure strategy |

2 | 2 | Zero-sum | Stochastic | Perfect | Single | MinMax works, Pure strategy |

3 | 2 | Zero-sum | Stochastic | Hidden | Single | MinMax does NOT work, Mixed Strategy |

4 | 2 | Non-zero sum | Stochastic | Hidden | outcome is same for every round | Solve for Nash Equilibrium, Pure or mixed |

5 | 2 | zero-sum | Stochastic | Hidden | defined by gamma | With finite states, it is a Markov Decision Process. Solve Minimax-Q algorithm |

6 | 2 or more | Non-zero sum | Stochastic | Not-hidden | Defined by gamma | Active Research! |

## Comments on Strategy

**Game ID#4: **If strongly dominant strategy is present, then pure strategy might work or else might need a mixed strategy

**Game ID#5: ** For small number of rounds (gamma~=0), betrayal might provide more reward, but for infinite number of rounds (gamm~=1), cooperation yields more reward

**Interesting Facts from the Theory **

- Tit-for-Tat is not subgame perfect when considering a longer future time horizon! It means it can give itself more rewards overall if it does not choose to retribute against the other player! So forgiveness is a better virtue! This forgiving strategy is called Pavlov state machine!