Formal specification and behavioral simulation of the holiday gift exchange game

Researcher Daniel Quigley has published a formal game theory paper titled 'Formal specification and behavioral simulation of the holiday gift exchange game' on arXiv. The work provides a rigorous mathematical treatment of the popular social game, defining its state space, action sets, and the recursive structure of stealing chains. Beyond the base mechanics, Quigley introduces a decorated model that incorporates real-world complexities like partial information, social costs, and adaptive strategies grounded in discrete choice theory and frustration-aggression literature.

To test the model, Quigley ran a massive full factorial simulation of 240,000 distinct games. The simulation yielded several counterintuitive findings. First, implicit social costs were the dominant regulator of aggressive 'stealing' behavior, reducing it by 27–48% and outweighing both uncertainty and strategic sophistication. Second, partial information slightly increased stealing through asymmetric uncertainty, contrary to expectations. Finally, the research found that correlated valuations—consensus about which gifts are good—amplified all behavioral effects, meaning competition intensifies not from the gifts' features but from shared opinions about them. The robust first-player advantage held across all simulated conditions.