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# Mathematical proof you should be generous this Christmas

A mathematical formula shows the joy of giving is the most important part of Christmas, say Stirling academics.

Who to buy presents for and how much to spend is always a complex conundrum but researchers at the University of Stirling have developed a mathematical solution.

Game theory provides tools for analysing situations in which parties, called ‘players’, consider the other person’s possible decisions, or strategies, before taking action.

Writing in The Conversation, lead researchers Professor Rachel Norman and Dr Anthony O’Hare, from the University’s Modelling and Analysis of Complex systems (MACS) research group, put the method to the test for gift giving.

Professor Rachel Norman said: “If both players buy each other a present then they both get a payoff which is the enjoyment they get from receiving a present minus the cost of the present they bought.

“If one of them buys and the other does not then one person gets enjoyment and no cost and the other gets cost and no enjoyment. Finally, if neither of them buy a present then there is no cost and no enjoyment and so the payoff is zero for each player.”

Dr Anthony O’Hare added: “The game changes completely if you include the joy of giving in your payoff. Generosity is best and the joy of giving is the most important part of Christmas.”