Add complete 2x2 normal-form game datasets (Parquet, zstd)

README.md

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+---
+license: cc-by-4.0
+pretty_name: Nash Equilibria of 2x2 Normal-Form Games
+tags:
+  - game-theory
+  - nash-equilibrium
+  - normal-form-games
+  - combinatorics
+  - synthetic
+size_categories:
+  - 100M<n<1B
+configs:
+  - config_name: default
+    data_files:
+      - split: payoffs_0_10
+        path: matrices_2x2_0_to_10.parquet
+      - split: payoffs_0_5
+        path: matrices_2x2_0_to_5.parquet
+      - split: payoffs_0_3
+        path: matrices_2x2_0_to_3.parquet
+      - split: payoffs_0_2
+        path: matrices_2x2_0_to_2.parquet
+---
+
+# Nash Equilibria of 2×2 Normal-Form Games
+
+An **exhaustive enumeration** of every two-player 2×2 normal-form (bimatrix) game with
+non-negative integer payoffs in a fixed range, each annotated with its pure- and
+mixed-strategy Nash equilibria and a set of game-theoretic classifications.
+
+Because the payoff space is enumerated completely, the largest split contains **all
+`11^8 = 214,358,881`** games with payoffs in `0..10` — not a sample.
+
+## Splits
+
+Each split is the complete enumeration for a payoff range. Payoffs `0..k` is a strict
+subset of payoffs `0..10` (identical rows), so the smaller splits are convenience
+subsets of `payoffs_0_10`.
+
+| split | payoff range | games (rows) |
+|---|---|--:|
+| `payoffs_0_10` | 0–10 | 214,358,881 |
+| `payoffs_0_5`  | 0–5  | 1,679,616 |
+| `payoffs_0_3`  | 0–3  | 65,536 |
+| `payoffs_0_2`  | 0–2  | 6,561 |
+
+```python
+from datasets import load_dataset
+ds = load_dataset("AlexDunstan/nash-equilibria-matrices", split="payoffs_0_10")
+```
+
+## Game encoding
+
+A 2×2 game has two players (p1, p2) choosing a row / column. Each of the 4 cells holds a
+payoff pair. The 8 payoff columns are named `r{row}c{col}_p{player}` (row-major, 0-indexed):
+
+|  | col 0 | col 1 |
+|---|---|---|
+| **row 0** | `r0c0_p1`, `r0c0_p2` | `r0c1_p1`, `r0c1_p2` |
+| **row 1** | `r1c0_p1`, `r1c0_p2` | `r1c1_p1`, `r1c1_p2` |
+
+## Columns (32)
+
+**Payoffs (8)** — `r0c0_p1 … r1c1_p2`: `int8`, the integer payoff to each player in each cell.
+
+**Equilibria**
+- `num_equilibria` (`int8`): number of pure-strategy Nash equilibria.
+- `equilibrium_positions` (`string`): list of `(row, col)` pure-NE cells, e.g. `"[(0, 0), (1, 1)]"`.
+- `category` (`string`): `Solved` if ≥1 pure NE, else `Unsolved`.
+
+**Structural flags** (`bool`)
+- `p1_has_dominant`, `p2_has_dominant`, `both_dominant`: dominant-strategy existence.
+- `is_zero_sum`, `is_symmetric`: structural properties of the payoff matrix.
+- `has_pareto_dom_ne`, `all_ne_pareto_eff`: Pareto properties of the equilibria.
+
+**Welfare**
+- `max_welfare` (`int16`): maximum total payoff (`p1+p2`) over all cells.
+- `ne_welfare` (`string`): total welfare at each NE, e.g. `"[0, 2]"`.
+- `welfare_loss` (`int16`): efficiency gap between `max_welfare` and the equilibria.
+
+**Mixed-strategy equilibrium** (populated for 2×2 games with no pure NE; `null`/empty otherwise)
+- `mixed_exists` (`bool`).
+- `mixed_p`, `mixed_q` (`double`): equilibrium mixing probabilities.
+- `mixed_payoff_p1`, `mixed_payoff_p2` (`double`): expected payoffs under the mixed NE.
+
+**Payoff asymmetry at equilibria**
+- `ne_p1_payoffs`, `ne_p2_payoffs`, `ne_payoff_diffs` (`string`): per-NE payoff lists and differences.
+- `ne_has_equal_payoffs` (`bool`).
+- `ne_mean_abs_diff` (`double`): mean absolute payoff difference across the equilibria.
+
+**Classification**
+- `game_type` (`string`): a categorical label. Distribution over `payoffs_0_10`:
+
+| game_type | rows |
+|---|--:|
+| Harmony | 56,150,160 |
+| Dominant (P1 only) | 51,967,234 |
+| Dominant (P2 only) | 51,967,234 |
+| Other | 18,295,200 |
+| No Equilibrium | 18,283,848 |
+| Deadlock | 11,809,512 |
+| Prisoner's Dilemma | 5,814,336 |
+| Zero-Sum | 65,307 |
+| Coordination | 6,050 |
+
+> **List columns are stored as strings** (Python `repr` of a list), for exact
+> round-trip fidelity. Parse them with `ast.literal_eval`:
+> ```python
+> import ast
+> positions = ast.literal_eval(row["equilibrium_positions"])
+> ```
+
+## Provenance
+
+Games were generated by exhaustive Cartesian enumeration of the payoff space, then
+enriched with equilibrium detection and classification computed deterministically from
+the payoff matrix (no sampling, no randomness). Payoffs are compact integer types and
+repetitive categorical/list columns are dictionary-encoded, so the full 214M-row split is
+~172 MB of Parquet.
+
+## License
+
+CC-BY-4.0 — free to use with attribution.

matrices_2x2_0_to_10.parquet

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