Formal specification and behavioral simulation of the holiday gift exchange game
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918430601379840 |
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| author | Quigley, Daniel |
| author_facet | Quigley, Daniel |
| contents | The holiday gift exchange game is a familiar social institution with nontrivial strategic structure. We provide a formal treatment of the game's mechanics, defining the state space, action sets, and the recursive structure of stealing chains; we prove termination and derive an algorithm for counting distinct game trajectories, which grow far faster than the space of possible final allocations. Beyond the base mechanics, we introduce a decorated model incorporating partial information, social costs, and adaptive strategies grounded in discrete choice theory and the frustration-aggression literature. A full factorial simulation of 240,000 games yields three findings of note: implicit social costs are the dominant regulator of aggression, reducing stealing by 27--48\% and outweighing both uncertainty and strategic sophistication; partial information, contrary to expectation, slightly increases stealing through asymmetric uncertainty; correlated valuations amplify every behavioral effect, so that consensus about gift quality, rather than the features themselves, is what intensifies competition. The first-player advantage is robust across all conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05219 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Formal specification and behavioral simulation of the holiday gift exchange game Quigley, Daniel Computer Science and Game Theory Combinatorics History and Overview 05A15 (Primary) 91A06, 91A60 (Secondary) G.2.1; I.6.8; I.6.5 The holiday gift exchange game is a familiar social institution with nontrivial strategic structure. We provide a formal treatment of the game's mechanics, defining the state space, action sets, and the recursive structure of stealing chains; we prove termination and derive an algorithm for counting distinct game trajectories, which grow far faster than the space of possible final allocations. Beyond the base mechanics, we introduce a decorated model incorporating partial information, social costs, and adaptive strategies grounded in discrete choice theory and the frustration-aggression literature. A full factorial simulation of 240,000 games yields three findings of note: implicit social costs are the dominant regulator of aggression, reducing stealing by 27--48\% and outweighing both uncertainty and strategic sophistication; partial information, contrary to expectation, slightly increases stealing through asymmetric uncertainty; correlated valuations amplify every behavioral effect, so that consensus about gift quality, rather than the features themselves, is what intensifies competition. The first-player advantage is robust across all conditions. |
| title | Formal specification and behavioral simulation of the holiday gift exchange game |
| topic | Computer Science and Game Theory Combinatorics History and Overview 05A15 (Primary) 91A06, 91A60 (Secondary) G.2.1; I.6.8; I.6.5 |
| url | https://arxiv.org/abs/2604.05219 |