Sydney Howland
Math 49S
December 2, 2011
Game Theory of Negotiations
Negotiating is a part of every day life. Negotiating the restaurant to eat at, the
price you will pay for a new car, or what would be the best curfew on Friday night,
are all common situations that involve making concessions. Some people enjoy
negotiating and find that it comes in handy for business and sales. Others try to
avoid negotiating at all costs, and would rather let others take the lead when making
decisions. There are several aspects of negotiations that we can apply to game
theory in order to come up with a strategy and mathematically analyze the results of
certain choices. Game theory is an important aspect of negotiating because it is a
practical way to maximize one’s continual success.
When you think of a negotiation you usually picture two people having a
conversation. This situation results in one winner and one loser. An example of a
two person game situation would be if two people-say your mom and your dadwhen one owes the other money. Your dad bought your mom an ice cream cone last
weekend at Dairy Queen and therefore your mom is in debt to him, and they have to
agree on how much. Each has two options of what strategy they can choose, but the
outcome of their negotiation is dependent on what their opposition does. Obviously
your dad would want to have the maximum amount of money while your mom
would hope to pay the minimum amount of money.
This situation is a real life application of the minimax theorem. This theorem
states that you should pick the strategy where the maximum advantage of your
opponent is minimized. This theorem is very useful and simple to understand, but it
does not take into account real life complications. In some negotiations that involve
two people, both opponents do not always have perfect information. A car salesman
might be offering to sell a car for one price, but the buyer does not know exactly
what the car is supposed to be sold for and how low the absolute minimum cost
would be. One such way to put yourself at an advantage for situations like these is to
research your options and make sure you have all of the information possible. In
this scenario, looking up common car prices online or comparing the prices between
dealerships could make you a more knowledgeable and prepared negotiator.
A successful strategy to winning negotiations is trying to reduce variables
available. In an extreme scenario, when a robber puts a gun to your head and asks
for all our your money your variables quickly diminish. You can either hand over the
cash in your wallet or get shot and die. While this is an extreme, it is an example of
how certain pressures or stresses can limit the amount of strategies you have at
your disposal.
In a larger negotiation scenario one strategy that is worth considering is that
of unpredictability. If a company always sells its products for the same price, and
then suddenly raises its price twofold, its consumers are going to have little interest
in remaining loyal and purchasing their product. On the other hand, if a retail
company like J-Crew is constantly coming out with new products and hosting sales
on old products, their prices are always going to be varying giving them more room
to negotiate with their customers. There is a disadvantage in predictability because
this leaves room for one’s opponent to state the obvious historical patterns. If you
always forget to take out money from the ATM before going to dinner, your
opponent is going to say no when you propose a restaurant that does not take credit
cards. You lose your creditability to negotiate because your past actions have
already spoken for themselves.
Negotiation situations are referred to a zero sum games in the game theory
world. They are titled zero sum games because the benefits and loses of all
participants always add up to zero. One such participant can only gain at another’s
expense. In the real world, this is not always completely true because there are
many other factors to consider and usually several concessions to be made. A
positive sum game would be a situation in which everybody gains or everybody
loses. These are usually referred to as “win-win” or sometimes “lose-lose”. The latter
often results from a situation in which two opposing parties spend more time
arguing then compromising and their negotiations result in a stalemate in which
nothing gets accomplished. A win- win scenario occurs when the amount of benefits
that can come out of a negotiation is not fixed. A win- win cannot occur when there
is a fixed price on an item or a fixed budget for one project, but when there are many
funds that the two parties are able to pull from and use at their disposal. The winwin approach also assumes that there are multiple interests at stake so there exists
room for concessions to be made.
The goal of negotiations is to win in the short term, but more importantly to
be successful in the long run. Long-term success depends on one’s ability to control
the negotiation process and the ability to maintain the correct perspective. The best
perspective is always the winning perspective, which is defined by the attitudes and
behaviors that result in a win. One visual tool that is useful for evaluating options
during a negotiation is the “Negotiation Matrix” that can be seen in the figure below.
This table helps one to determine their most desirable outcome.
You
Them
Desirable
WIN
WIN
Undesirable
LOSE
LOSE
The way it works is actually very simple. Each of the four quadrants represents an
outcome of either you or your opponent. When you prepare for any sort of
negotiation you can list the options available and place them in their respective
quadrant. This is a concise and organized way to visually evaluate your choices.
The skills necessary to win a good negotiation hold many parallels to a
simple two person game as shown in this paper. When you look at the strategies it
takes to analyze the options of each choice given, and weigh the wins and losses of
each opponent it boils down to a simple scenario of classic game theory. While real
world pressures often can complicate things, it could benefit anyone to learn the
suggested strategies listed above.
Bibliography
http://www.digitaltonto.com/2009/game-theory-guide-to-negotiations/
http://www.worldwidenegotiation.org/imgpro/File/Appling%20game%20theory
%20to%20negotiation.pdf
http://www.faculty.haas.berkeley.edu/rjmorgan/mba211/Course%20Overview.pp
t
http://www.profitclinic.com/SmallBiz/ResInfo/DntGo/Win.html