Battleship Eval

---
name: battleship-eval
description: Evaluates EFCE solvers on a parametric sequential conflict-resolution game where players place ships and fire shots. It probes the solver's ability to construct incentive-compatible correlation plans that maximize social welfare through deterrence and punishment mechanisms. Use when the user wants to benchmark on Battleship, or asks about evaluating this task. Reports Social Welfare (SW).
metadata:
  skill_kind: dataset_eval
  source_arxiv: 1905.12564
  bibtex_key: farina2019correlation
  confidence: high
---

# battleship-eval

> Correlation in Extensive-Form Games: Saddle-Point Formulation and Benchmarks — Farina et al. (2019) (NeurIPS 2019, 2019)

## What this evaluates

Evaluates EFCE solvers on a parametric sequential conflict-resolution game where players place ships and fire shots. It probes the solver's ability to construct incentive-compatible correlation plans that maximize social welfare through deterrence and punishment mechanisms.

## Datasets

- **Battleship** — total ?; splits: test (-1); repo https://github.com/Sandholm-Lab/efce-subgradient

## Metrics

- `Social Welfare (SW)` **(primary)** — range: other
  - Sum of expected utilities to all players under the computed correlation plan.
- `Expected Payoff` — range: other
  - Individual expected utility for each player, calculated as the sum of values of destroyed opponent ships minus loss multiplier times value of lost ships.

## Input / output format

**Input**: Game parameters: board dimensions (H, W), set of ships S, number of shooting rounds r, and loss multiplier gamma.

**Output**: Correlation plan specifying probability distributions over ship placements and shooting actions for each player at each information set, along with punishment recommendations upon deviation.

## Scoring recipe

```python
def compute_sw(correlation_plan, game_params):
    utilities = simulate_game(correlation_plan, game_params)
    return sum(utilities)  # Social Welfare
# Check incentive compatibility: ensure no player gains by deviating from recommendations.
```

## Common pitfalls

- Assuming Nash equilibrium behavior applies directly; EFCE requires incentive compatibility checks against unilateral deviations.
- Overlooking the mediator's punishment mechanism, which is essential for enforcing cooperative outcomes like deliberate misses.

## Evidence (verbatim from paper)

> The social welfare (SW) of the game is the sum of utilities to all players. In this section we introduce the first two benchmark games for EFCE. These games are naturally parametric so that they can scale in size as desired and hence used to evaluate different EFCE solvers.

## Citation

```bibtex
@misc{farina2019correlation,
  title={Correlation in Extensive-Form Games: Saddle-Point Formulation and Benchmarks},
  author={Farina et al. (2019)},
  year={2019},
  note={NeurIPS 2019}
}
```

- arXiv: 1905.12564