Gift Giving and Game Theory
This article applies game theory to the practice of exchanging gifts with others for holidays and special events. Gift giving can be complicated- givers must consider how much enjoyment the ‘receiver’ will get from any given item while also considering the cost of the item. Additionally, they must anticipate the gift that they will in turn receive from the other person: the present one is giving would ideally be of comparable value to that they receive.
The article represents the gift giving process in a payoff matrix, using enjoyment (‘E’) and cost (‘C’) to compute payoff. If we assume that E>C, as the article explains, the best option intuitively seems to be for both players to cooperate and buy each other gifts. However, the Nash equilibrium for the matrix shows is actually (0,0) – neither player exchanges gifts. This holds true even for situations in which zero or negative enjoyment is derived from a gift. However, this relies on being able to compare monetary costs and feelings of enjoyment on the same scale. If a gift cost nothing, or created an ‘infinite’ amount of enjoyment, the equilibrium no longer holds.
The article also explores the addition of a ‘joy of giving’ term to the equations in the matrix, which would cause the payoff of giving someone a present to change. Another possible inclusion could be feelings of guilt if you receive a gift but don’t give one in turn. Further, not receiving any gifts could cause both players to feel sad, which would push the zeros in the Nash equilibrium value to negatives. All these additions result in very different matrix.
Furthermore, gift giving is a recurring occurrence- if considered in the long term, the iterated prisoner’s dilemma becomes a more appropriate model. This model includes a memory component- people remember what gifts you gave them in previous years and make future decisions based on this knowledge. In such instances, depending on the strategy each player employs, it could be more beneficial to purchase gifts (considering the original payoff matrix without guilt, sadness, etc. introduced.
Thus the concepts of Game theory and payoff matrices can be used to model the ultimate pros/cons of purchasing gifts for others, although the utility of the model could be compromised as more emotional considerations are included in calculations.
Article: https://theconversation.com/how-to-apply-game-theory-to-buying-your-christmas-presents-52233