Best-AI Selection Game

• Best-AI Selection Games are formal frameworks that evaluate AI agents using performance metrics designed to stress skill depth and adaptability.
• They combine evolutionary algorithms, multi-armed bandit methods, and sequential decision models to isolate high-performing strategies.
• These games integrate human-AI collaboration and subjective measures like trust and interpretability to ensure fair and effective agent selection.

A Best-AI Selection Game is any formal or experimental framework where the objective is to identify, select, or evolve the best-performing artificial intelligence agent(s) among a pool or population of candidates according to criteria designed to expose meaningful differences in skill, adaptability, or reliability. Research in this area spans algorithmic selection paradigms (evolution, bandit allocation, sequential decision-making), experimental economics (beauty contest games, partner selection), general game playing evaluation frameworks, and collaborative human-AI teaming. This domain synthesizes combinatorial, statistical, and behavioral methodologies to rigorously isolate and promote high-performance AI strategies and game mechanics capable of distinguishing nuanced differences in agent competence.

1. Foundational Principles and Evaluation Criteria

Best-AI Selection Games are constructed to ensure that agent evaluation reflects meaningful distinctions in capability. This is accomplished by specifying performance metrics designed to maximize "skill-depth"—the degree to which the best agent is reliably better than others—and by exposing agents to environments that challenge exploration, adaptability, and generalization. For instance, in evolutionary design settings, such as the N-Tuple Bandit Evolutionary Algorithm (NTBEA) (Kunanusont et al., 2017), "game quality" is measured by the minimum skill gap that a game instance produces between agents of different skill levels:

$\text{Fitness} = \min(T_3 - T_2, T_2 - T_1)$

where $T_k$ is the normalized win gap for an agent at skill level $k$. Similar selection games use bandit-based allocation, where agents ("arms") are sampled based on regret bounds, maximizing the expected improvement over time (Stephenson et al., 1 Jul 2025).

In human-AI collaborative or competitive settings, subjective measures such as trust, interpretability, and teamwork supplement objective scores (Siu et al., 2021, Jiang et al., 17 Jul 2025). Best-AI Selection Games thus integrate diverse, context-specific evaluation metrics in order to capture both raw effectiveness and emergent qualities of agent interaction.

2. Algorithmic Selection Paradigms

2.1 Evolutionary and Model-Based Optimization

Evolutionary algorithms, especially NTBEA (Kunanusont et al., 2017, Lucas et al., 2019), have been shown highly effective in tuning agent parameters and game rules in noisy, high-dimensional spaces typical of general game AI frameworks (e.g., GVGAI, Ludii). NTBEA models the fitness landscape using summary statistics over n-tuples of parameters, with selection driven by Upper Confidence Bound (UCB) criteria:

$$a^* = \underset{a \in A(s)}{\arg\max}\left\{ Q(s,a) + C\sqrt{\frac{\ln N(s)}{N(s,a)}} \right\}$$

where $Q(s,a)$ is the mean fitness estimate, $N(s)$ and $N(s,a)$ are evaluation counts, and $C$ balances exploration/exploitation.

Other evolutionary selection games (Random Mutation Hill Climber, SMAC) compare parameter configurations directly, emphasizing rapid convergence in noisy environments and explicit control over exploration strategies (Lucas et al., 2019).

2.2 Multi-Armed Bandit and Regret Minimization

In multi-task selection environments, identifying the best agent for each sub-task is formalized as a multi-bandit best arm identification problem (Stephenson et al., 1 Jul 2025). Algorithms like Optimistic-WS use Wilson score intervals for reward uncertainty and select the next agent evaluation based on potential regret reduction. For bandit $m$ and agent (arm) $k$,

$$\text{Wilson}(\hat{p}, n, \alpha) = \left( w^-, w^+ \right)$$

and potential for regret improvement is:

$$\Delta_{mk} = \begin{cases} \hat{\mu}_m^* - w^-_{mk} & \text{if } k \text{ is best} \ w^+_{mk} - \hat{\mu}_m^* & \text{otherwise} \end{cases}$$

Here, agents are sampled adaptively to most quickly reduce the expected simple regret under limited evaluation budgets.

3. Sequential Decision Models: Secretary Problem Generalizations

Best-AI selection frequently leverages sequential choice models generalized from the classical secretary problem. Both uniform and weighted versions have been thoroughly analyzed.

3.1 Pattern-Avoidance and Positional Strategies

Pattern-avoidance restricts candidate orderings to those avoiding certain rank patterns. The "bar-raising" (231-avoidance) model yields a win probability of $C_{N-1}/C_N$ (Catalan numbers), converging to 25% as $N\to\infty$ regardless of observation threshold (Fowlkes et al., 2018). In "disappointment-free" (321-avoidance) settings, late selection maximizes success (asymptotically ≈48%) (Fowlkes et al., 2018). Table:

Model	Rule	Asymp. Success
231-avoid (bar-raise)	Any positional strategy	25%
321-avoid (no dips)	Reject N–3 then pick	48.4%

Weighted secretary games with Ewens or Mallows statistics further generalize selection strategies to account for candidate quality trends (Jones, 2019). For Ewens (left-to-right maxima weighting), the optimal cutoff is

$k \approx N / e^{1/\theta}$

with constant $1/e$ win probability.

3.2 Strategy-Indifferent Games

In strategy-indifferent selection games (Jones et al., 2021), every stopping rule is equally effective, and win probability is the reciprocal of the expected number of left-to-right maxima:

$P_\text{win} = 1/(E_{lrmax}(J') + 1)$

Ideal for constructing selection mechanisms resistant to strategic manipulation by candidates.

4. Human-AI Competitive and Collaborative Selection

Best-AI Selection Games increasingly involve both direct AI-human competition and human-in-the-loop agent selection. In penny-matching (Tian et al., 2019) and iterated RPS (Wang et al., 2020) games, model adaptation—based on cognitive hierarchy theory, Bayesian learning, and Markov chains—enables AI algorithms to outperform human players by exploiting predictive weaknesses and short-term behavioral patterns.

Selection games in collaborative tasks (e.g., Hanabi teaming (Siu et al., 2021), partner selection (Jiang et al., 17 Jul 2025)) reveal that, although objective performance is critical, subjective measures—trust, interpretability, teamwork—become decisive. Humans often prefer rule-based, legible agents over highly-optimized, opaque learning agents, even when the latter achieve similar or superior objective results.

Beauty contest experiments (Alekseenko et al., 5 Feb 2025) demonstrate that most LLM-based agents adapt strategies more rapidly and iteratively than humans, converging toward Nash equilibrium with "over-sophisticated" behavior—highlighting both strengths and limits of AI as proxies for boundedly rational agents.

5. Selection Game Applications in Game Design and Content Curation

Applications of Best-AI Selection principles include automatic tuning of game parameters for difficulty and player distinction (Kunanusont et al., 2017, Lucas et al., 2019), agent selection in general game playing competitions (Stephenson et al., 1 Jul 2025), quest content curation (Yu et al., 30 Sep 2024), and evolving cooperative strategies in collaborative games (Salta et al., 2020).

Curated AI Directors for quest selection (PaSSAGE, CMAB) in FarmQuest (Yu et al., 30 Sep 2024) illustrate selection game impact on user experience and efficiency: curated directors present fewer quests yet maintain similar completion and acceptance rates, improving player enjoyment (Mann–Whitney U, p=0.032, 0.047 for efficiency, p=0.016 for enjoyment).

In Geometry Friends (Salta et al., 2020), multi-agent selection game frameworks reward both solo and coordinated task-solving, with layered planning, motion-control architectures, and scoring formulas enforcing efficiency and robustness:

$$\text{score}_i = V_\text{completed} \times \frac{(T_\text{max} - t)}{T_\text{max} + V_\text{collect} \times N_\text{collect}}$$

6. Implications, Limitations, and Design Considerations

Best-AI Selection Game research elucidates how choices in evaluation methodology, agent pooling, and rule design shape the effectiveness and fairness of AI selection processes. Several implications and limitations are recurrent:

• No single strategy or evaluation metric is optimal across all domains; careful design choices are required for noisy, multi-task, or collaborative environments.
• Opaque learning agents may excel objectively but face rejection if their behavior is untrustworthy or inscrutable to human teammates.
• Fine-grained modeling of selection dynamics—including strategic manipulation and misattribution—highlights the importance of transparency and feedback mechanisms, especially when humans and AI compete for roles in partner selection (Jiang et al., 17 Jul 2025).
• Adaptive, cost-aware evaluation mechanisms (e.g., Optimistic-WS (Stephenson et al., 1 Jul 2025)) enable robust agent selection under computational constraints but may require further refinement for correlated tasks or variable evaluation costs.
• Pattern-avoidance and strategy-indifference frameworks provide mechanisms to anchor fairness and prevent gaming of selection policies, but may incur lower success rates in some regimes (Fowlkes et al., 2018, Jones et al., 2021).

7. Future Directions

Research continues to explore improved regret minimization algorithms, better integration of subjective human metrics, dynamic content curation, and cross-task agent evaluation. Cost-awareness, leveraging inter-task correlation, and greater interpretability in AI agent design stand as essential future objectives to further advance the quality, trustworthiness, and fairness of AI selection systems.

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Best-AI Selection Games form a rigorous foundation for both practical and theoretical advances in agent evaluation, game content optimization, and the paper of strategic choice under uncertainty and competition. They integrate selection algorithms from combinatorics, statistics, and behavioral science to confront the emerging challenges of distinguishing and promoting artificial agents capable of robust, interpretable, and adaptive decision-making across diverse domains.