Formal specification and behavioral simulation of the holiday gift exchange game

TL;DR

This paper formally models the holiday gift exchange game, analyzing its mechanics and simulating behaviors to understand social costs, information effects, and strategic advantages.

Contribution

It introduces a formal framework for the game, incorporates social and informational factors, and provides extensive simulation results revealing key behavioral insights.

Findings

Implicit social costs significantly reduce stealing behavior.

Partial information slightly increases stealing due to asymmetric uncertainty.

Consensus about gift quality amplifies competitive behaviors.

Abstract

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.