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Tiered Coalition Formation Game Stability and Simulation
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A doctoral consortium paper summarizing the author's work on stability in tiered coalition formation games (TCFGs), including a probabilistic preference framework, k-TCFG variant, socially conscious stability, and planned Pokémon simulations.
Problem
Finding stable tier lists in tiered coalition formation games where competition is intransitive, and making the stability notions and algorithms tractable under probabilistic match outcomes.
Approach
Extends Siler's deterministic TCFG preference framework to probabilistic pairwise matchups, introduces k-tiered coalition formation games with exactly k nonempty tiers, and defines socially conscious stability, which guarantees stabilizability for k-TCFGs.
Key results
- Under probabilistic preferences, Nash stability and core stability are shown equivalent to socially conscious stability for TCFGs, while the three notions are non-equivalent on k-TCFGs.
- Not all k-TCFGs with matchup preferences admit a Nash stable outcome (from prior FLAIRS 2022 work).
Surprising findings
- Not all k-TCFGs with matchup preferences admit a Nash stable outcome.
Limitations
- Pokémon simulation results are planned and not yet reported in this paper.
- Open problems on NP-completeness of Nash stability and existence of core stable outcomes remain unresolved.
- Polynomial-time singleton stable tier list under probabilistic preferences is unresolved.
Experimental setup
Datasets: Pokémon Red and Blue match simulations (planned)
Metrics: utility fairness tier size stability
Baselines: Siler 2017 deterministic TCFG framework Smogon tier list
Builds on: tiered coalition formation games core stability Nash stability
Closest papers by meaning
- Stability in Online Coalition Formation (AAAI 2024 · similarity 0.78)
- Adaptive Manipulation for Coalitions in Knockout Tournaments (AAAI 2025 · similarity 0.77)
- Individually Stable Dynamics in Coalition Formation over Graphs (AAAI 2025 · similarity 0.76)
- Learning Coalition Structures with Games (AAAI 2024 · similarity 0.75)
- Deviate or Not: Learning Coalition Structures with Multiple-bit Observations in Games (AAAI 2025 · similarity 0.75)
- Certifying Concavity and Monotonicity in Games via Sum-of-Squares Hierarchies (NeurIPS 2025 · similarity 0.74)
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