Zero-Sum Game
What is a Zero-Sum
Game?
Zero-sum is a situation
in
game theory
in which
one person’s gain is
equivalent to another’s
loss, so the net change
in wealth or benefit is
zero. A zero-sum game
may have as few as two
players, or millions of
participants.
Zero-sum games are found in
game theory, but are less common
than non-zero sum games. Poker
and gambling are popular
examples of zero-sum games
since the sum of the amounts won
by some players equals the
combined losses of the others.
Games like chess and tennis,
where there is one winner and one
loser, are also zero-sum games. In
the financial markets, options and
futures are examples of zero-sum
games, excluding transaction
costs. For every person who gains
on a contract, there is a counter-
party who loses.
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Non-Zero Sum Game
What is a Non Zero Sum Game?
A non zero sum game is a situation where there is
a net benefit or net loss to the system based
on out the outcome of the game.
An example of what should not be considered a
non zero sum game is a contest between a
trade ship and a pirate ship, although it may
look like
one at first glance. Here, a victory for the pirates
would mean gain of wealth, resources, and
men (probably as prisoners),
whereas a win for the trade ship would only mean
a defeat of the challenge by the pirates. Here,
the prize and losses being different for both
the contesting parties do not qualify it as an
example of a non zero sum game.
Another example could be in financial markets,
where competing firms collaborate to expand
the overall size of their market. Creating an
industry-wide organization would increase
confidence in the industry and result in more
profit for all competitors.
Non zero sum games don’t have to create a net
positive result, it could also be negative as
well.
In the pirate example above, there is a
case where the pirates win and it’s a net
negative for the whole system.
Typical Example
The Battle of the Sexes is a simple
example of a typical non-zero-sum
game. In this example a man and his
wife want to go out for the evening.
They have decided to go either to a
ballet or to a boxing match. Both
prefer to go together rather than
going alone. While the man prefers
to go to the boxing match, he would
prefer to go with his wife to the ballet
rather than go to the fight alone.
Similarly, the wife would prefer to go
to the ballet, but she too would rather
go to the fight with her husband than
go to the ballet alone. The matrix
representing the game is given
below:
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The wife's payoff matrix is represented by the first element of the
ordered pair while the husband's payoff matrix is represented by the
second of the ordered pair.
From the matrix above, it can be seen that the situation represents a
non-zero-sum, non-strictly competitive conflict. The common interest
between the husband and wife is that they would both prefer to be
together than to go to the events separately. However, the opposing
interests is that the wife prefers to go to the ballet while her husband
prefers to go to the boxing match.10
Husband
Wife
Boxing Match Ballet
Boxing Match 2, 3 1, 1
Ballet 1, 1 3, 2