Formal specification and behavioral simulation of the holiday gift exchange game
This work addresses a social game problem for researchers in game theory and behavioral simulation, but it is incremental as it builds on existing models with new decorations.
The authors tackled the strategic structure of the holiday gift exchange game by providing a formal specification and simulating 240,000 games, finding that implicit social costs reduce stealing by 27–48% and that partial information slightly increases stealing.
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.