# Nash Equilibrium Uniqueness on Linear quadratic network games Single activity, β=0

Source: [Nash Equilibrium Uniqueness on Linear quadratic network games Single activity, β=0](<https://www.sota2.com/research/sota/nash-equilibrium-uniqueness-on-linear-quadratic-network-games-single-activity-0>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-06-05T07:14:27.422Z

Evaluation of algorithms or theoretical results concerning the uniqueness of Nash Equilibria in linear quadratic network games, specifically for the single activity case where β=0. Metrics focus on verifying sufficient mathematical conditions for uniqueness.

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

| Scope | Recorded value |
| --- | --- |
| Task | Nash Equilibrium Uniqueness |
| Dataset (including any stated split) | Linear quadratic network games Single activity, β=0 |
| Metric | Sufficient Condition (Complements, δ \> 0) |
| Unit | SCALAR |
| Direction | Higher is better |
| Results loaded | 2 of 2 |
| Coverage | All results currently returned for this benchmark |

Evaluation settings may differ between results. The original papers and recorded configurations are needed to establish comparability. A shared metric name alone does not establish an identical protocol.

## Metrics

- [Sufficient Condition (Complements, δ \> 0)](<https://www.sota2.com/research/sota/nash-equilibrium-uniqueness-on-linear-quadratic-network-games-single-activity-0.md?metric=Sufficient%20Condition%20(Complements%2C%20%CE%B4%20%3E%200)>): Higher is better; unit: SCALAR.

- [Sufficient Condition (Substitutes, δ \< 0)](<https://www.sota2.com/research/sota/nash-equilibrium-uniqueness-on-linear-quadratic-network-games-single-activity-0.md?metric=Sufficient%20Condition%20(Substitutes%2C%20%CE%B4%20%3C%200)>): Higher is better; unit: SCALAR.

## Recorded results

| Method | Sufficient Condition (Complements, δ \> 0) | Result date | Report paper |
| --- | --- | --- | --- |
| Ballester et al. | 2 | Not recorded | 68fa38211e209131ce8b7c72 |

### Ballester et al.

Sufficient Condition (Complements, δ \> 0): 2. Result ID: 6a227737fbc373592c1ff5f6.

[Reporting paper](<https://www.sota2.com/research/paper/68fa38211e209131ce8b7c72.md>)

Recorded evaluation configuration: {"μ":"0","βi":"β","G":"G^T","Xi":"R^2\_≥0","Activity Mode":"Single activity (β = 0)"}. This record does not assert independent reproduction.

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