When a strategic interaction happens more than once, players can use history to inform future decisions. A one-shot Nash equilibrium might recommend "always defect," but in a repeated game, cooperation can emerge — and be sustained — through the right policy.

## What is a Repeated Game?

A repeated game is the same normal-form game played over multiple rounds. After each round, both players observe what happened. This history opens up strategies that aren't possible in a single encounter:

- **Reward cooperation** by continuing to cooperate when the other player does
- **Punish defection** by switching to a harsher strategy after a betrayal
- **Adapt over time** by tracking what the other player tends to do

## What is a Policy?

A policy is a rule that determines what a player should do in the next round based on the history of past rounds. Instead of computing your strategy from scratch each time, you assign a policy and let it manage the decision-making.

Mieza provides a library of well-studied policies:

| Policy | Strategy | Best For |
|---|---|---|
| **Tit-for-Tat** | Copy what the opponent did last round | Building mutual cooperation |
| **Grim Trigger** | Cooperate until the opponent defects, then punish forever | Maximum deterrence |
| **Pavlov** | Repeat your action if you "won," switch if you "lost" | Recovering from mistakes |
| **Best Response** | Play the best action against the opponent's historical frequencies | Exploiting predictable opponents |
| **Nash Equilibrium** | Play the computed Nash equilibrium every round | Guaranteed safety |
| **Always** | Play the same fixed action every round | Simple baseline strategies |
| **Random** | Choose uniformly at random | Unpredictable baseline |

## How Policies Work on Mieza

The workflow for repeated games is:

1. **Create a game** — define the players, actions, and payoffs
2. **Assign policies** — bind each player to a policy (e.g., Player 1 uses Tit-for-Tat, Player 2 uses Best Response)
3. **Record plays** — after each round, record what actually happened
4. **Query next action** — ask the platform "what should I do next?" and it evaluates the policy against the full history

The key insight is that the platform holds the state. You don't need to track history yourself — just record plays as they happen and query the policy when you need a decision.

## Outsourcing Strategy

This design is particularly powerful for AI agents. An agent can:

- Assign a policy to itself at the start of an interaction
- Record each round's outcome as it plays out
- Query the next action with a single reference ID — no need to hold strategy state in the context window

The platform reconstructs the full history and evaluates the policy automatically. This makes strategic reasoning composable: the agent focuses on understanding the situation, and the platform handles the game theory.

## See also
- [What is the Normal-Form Solver?](/docs/what-is-the-normal-form-solver) — solving one-shot games
- [Solving Your First Game](/docs/solving-your-first-game) — hands-on tutorial including policies
- [What is an Equilibrium?](/docs/what-is-an-equilibrium) — the foundational concept