Game Theory: The Game Of Life

“Are you traveling together?” the ticket agent asked.

“Yes,” you responded.

“So how’s row 15 — aisle and center or center and window?” the agent inquired.

“No, we’d like row 7, aisle and window,” you replied. The agent gave you a strange look, but decided not to question your motives and accommodated your request. 

What were your motives? You were banking on having extra room during the flight by assuming a single traveler will choose either an aisle or a window before selecting a center seat. You were participating in game theory.¹ Whether you are buying a car, selling your home, playing poker — the principles of game theory are at work. Whether two countries are negotiating a trade agreement, settling a border dispute or in the midst of an arms race — game theory strategies come into play.

The famous prisoners’ dilemma problem was first proposed by Albert Tucker in 1950. Two people are arrested, and placed in separate rooms for questioning. Each is immediately confronted with the following options:

(a) If you and your partner remain silent, there’s enough evidence to give you each 2 years in prison.

(b) If you confess and your partner doesn’t, you get off completely and your partner gets 4 years in prison.

(c) If you both confess, you both get 3 years in prison.

Can you take the chance and remain silent? That would mean either 4 or 2 years in prison. Should you confess — that gives either 3 years in prison or getting off completely. This situation is a one-time choice for each suspect to make. If you have no idea how your partner will act, your best option is to confess. But when you have an opportunity to “play” the “game” repeatedly, your actions influence your opponent’s actions.

Messages are communicated about how you will respond. For example, companies X and Y are just beginning to do business. X supplies products to Y. X fulfilled Y’s order and billed Y for their order. The terms were payable upon receipt. A month passes, and the invoice is not paid. Does X rebill Y with added interest or first call Y’s bookkeeping? X calls and learns Y supposedly never received the bill, and in fact Y wants to reorder. X says the order will be sent as soon as Y’s bill is paid. With the second order, Y again does not pay upon receipt. Now X does not give a courtesy call or grace period, but rebills Y with finance charges included. This is your typical tit for tat situation. The best game strategy here is to always first cooperate to see how your opponent acts. Then your next action is based upon whatever your opponent’s previous action was. This situation initially involves cooperation, then provocation, followed by a suitable response, which hopefully will be followed by cooperation again.

Even the game of chicken lends itself to game theory. Here drivers race toward one another. The first driver to swerve is the loser. Possible outcomes: both have an accident because neither driver swerves off and neither wins — both drivers swerve simultaneously, neither wins nor loses face (it is a tie) — one driver swerves before the other, who is the winner. To mathematize this game, number values are assigned to the possible outcomes — 0 points for a collision, 2 for a win and 1 for a swerve, and these can be arranged in a table.

Game theory pops up in all sorts of areas — in the environment with lobbyists vying for legislation for clean air and against polluters — with medical insurance companies deciding who should receive what treatment. Have you ever cut into line? Were you successful, or did someone call you on it? Or have you asked a person in front of you if you could go ahead with your one grocery item? That’s game theory at work. Game theory can sometimes bespeak cooperation, and has shown that mutual cooperation in the long term fosters the most favorable outcomes.

Choosing to contribute to public radio or television is your choice. If you decide to tune in or watch your favorite show, that’s also your choice. If you then choose not to contribute, you are banking on the other people paying for you. If on the other hand, the station goes belly up you can’t complain because you made the wrong choice in your game of life. Time and again the elements of game theory replay themselves where conflicting forces are at odds — in labor strikes, political disputes, terrorist/hostage situations, and nature. Mathematically analyzing the possible outcomes/payoffs and possible choices, action, reactions may help in the decision process. Unfortunately, in the “game of life”, it is not possible to identify and assign a number value to all factors that impact the outcomes. Even using probability, human behavior may be unpredictable; and where personalities and egos come into the picture the result may lead to chaos. In the final analysis, the game isn’t over until it’s over!

Note

 

Source: Game Theory: The Game Of Life


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