Final answer:
The equilibrium division of the fee between Santa Claus and the Snow Maiden in the sequential bargaining game would take into account the risk of the director's arrival. As the probability of interruption approaches zero, the split is likely to be more equitable. Empirical evidence suggests that actual divisions often deviate from purely rational predictions due to considerations of fairness.
Step-by-step explanation:
The scenario described by the student involves Santa Claus and the Snow Maiden engaging in a sequential bargaining game for dividing a fee for a New Year's party. This model can be analyzed using principles of game theory, particularly the theory of bargaining and negotiations under the threat or risk of receiving less value if an agreement is not reached. What is being described resembles the ultimatum game, where one player offers a split of resources and the other player can either accept or reject. The sequential nature, combined with the risk of interruption by the director, complicates the decisions.
In equilibrium, rational players would consider the probability α of the director arriving and weigh their offers against the expected outcomes of continued negotiation versus immediate settlement. As α approaches 0, implying almost no chance of the director's interruption, the division of the fee would likely be closer to an even split since both players would be less concerned about the deadline and more willing to negotiate for a fair distribution.
When players are rational and self-interested, we might expect Santa Claus to offer a division which, although it may seem unfair, still provides the Snow Maiden with more than what she would expect if the director arrives. However, if we consider experimental data that shows players are not entirely self-interested and often reject highly uneven offers, the equilibrium split might be more generous than the purely rational prediction.