Everyone has heard of the prisoner's dilemma, but most people would hesitate if you asked them if they thought there was ever a real situation in which is was played out precisely.
I am proud to announce an annual country-wide championships for this game, in which people play with their families, friends and even their co-workers. It is called Christmas, and over the years has resulted in some novel solutions.
The initial position is where everyone must buy a christmas present for everyone they know, at some personal cost. The goal of this game is to maximise the happiness of everyone around you, plus your own happiness, plus minimise the cost to yourself. There are a number of strategies for improving your situation.
1.) Involve yourself in a large number of gift exchanges. If everyone is playing fair, you will always recieve the maximum number of gifts. Therefore the more groups in which you participate, the more presents you will get. Unfortunately this also increases the cost. However, if you don't play fair, then you can get ahead. (see pt 2)
2.) Unbalance the costs. In this model you still buy each person a gift, but you seek to buy cheap gifts, and receive expensive gifts. This works adequetly, but there is a minimum below which one cannot go and still expect to be accepted next year. However, there will always be some people who buy more expensive gifts, so if you can maintain this strategy, you will improve your situation.
3.) Don't reciprocate. This is where you aim to recieve more presents than you buy. Unfortunately, recieving a great many presents without returning the favour usually results in a feeling of hollowness, or "un-fellowship". Non-reciprocation improves the economics, but our goals relate to happiness while minimising costs. Because of the negative happiness quotient of this strategy, it is seen as a poor choice for the subtle player.
4.) The "Chris Kringle". This increasingly popular option works especially well for men, who are geared psychologically to prefer bigger presents over many presents. Women also prefer bigger presents over smaller ones, but don't connect that with the emotional value of the gift. However, in our increasingly tough competitive environment (applications of rules 1 and 2) both genders generally accept the unpleasantness of buying "crap presents" and see this strategy as an acceptable "out" from the spiral. In this model, costs and benefits are unified at the agreed upon price, meaning that no-one loses more than they win. Additionally, it is felt to increase the appreciation of the gift, although it reduces the number of interpersonal connections involved. In game theoretic terms, which are often more strongly geared towards the negative values of betrayal rather than the positive, this is known as "mutually assured destruction" - no-one may betray their neighbours.
The most difficult parts of the Prisoner's Christmas is the presence of rogue elements - broken down into two groups: Family and Unexpected Gifts.
The problem of the Family is the tendency to purchase over-the-top gifts. Whereas the pressure in friendship groups is often downward, towards the cheapest gift of quality, the pressure in families is often upwards, resulting in a rapid escalation. It is much like a house auction with closed bids. Whoever makes the lowest bid often feels like they have betrayed the process. This problem is attacked best by choosing the underdog's position or the bidder's position. When assuming the bidder's position, you need to correctly estimate the best value for your gift. You should try to spend roughly the same as a birthday-present level gift, possibly up to 20% more in some situations. It is more an art than a science. The underdog's position is however much safer, and the simplest strategy is to involve multiple gifts. The precise value of a gift is always uncertain, and the pleasure also not always comensurate with price. The purchase of around 5 gifts at values of $1.00 to $15.00 should give you a very reliable position for around $40.00 for any close family member. This is not a _bargain_ but is certainly a cheap way to obtain certainty.
The Unexpected Gift is the hardest of all elements in this game. They will happen, and there is no way to reciprocate until next year. Two non-reciprocated gifts from one person represents poor form, and three is outright rudeness. The Unexpected Gift should be rewarded with an invitation to lunch or other social reward as soon as possible. The cheapest way to deal with the Unexpected Giver is to involve them in a "Chris Kringle" circle, so that you may involve them in gift exchange without extending the number of presents which you have to purchase.
Alternative solutions to the Prisoner's Christmas are merrily invited...