Nonzero-sum Games Explained
Most of the games businesses play are nonzero-sum games where
the total gains vary depending on the players’ actions. In most
business games the size of the pie is determined by the players’
actions so that seeking a larger share of the pie might result in
reducing the total size of the pie. In a zero-sum game the total
gains are constant; what one wins, the other loses. A zero-sum game
is a game of pure conflict in which players’ actions affect only
the allocation, not the size, of the pie.
A major part of any negotiation consists of identifying
potential gains from trade. This involves looking for win-win
situations. If the realized gains from trade are as large as is
feasible, we call the transaction efficient. Efficient means that
it would have been impossible to have restructured the transaction
so as to make some participants better off and none worse off. It
is tempting to suggest that all transactions must be efficient.
Unfortunately, they are not. The individually rational pursuit of a
large share of the pie often sabotages efficiency. A tension
between cooperation and conflict is present in most games. Rational
actions by each of the individuals can result in an outcome that no
Consider the following stylized representation of competition
between two firms. The tension between conflict and cooperation is
illustrated by the decisions of two firms competing to sell the
same product. Cournot Ltd. and Bertrand Ltd., purveyors of mineral
water, compete by choosing one of the two possible prices – high or
low. Each firm’s profit depends also on the price of its rival. A
firm earns the highest possible profit when it charges the low
price while its rival charges the high price; moderately high
profit when both firms charge the high price; moderately low profit
when both charge the low price; and the lowest possible profit when
it charges the high price and its rival charges the low price.
What price will each charge?
See the table below with Cournot’s profit being the first number
in each pair and Bertrand’s the second:
Analyze the given situation from both competitor’s
perspective, and present either one solution or compare several
possible solutions in your written answer. Your submission
should not exceed 1000 words excluding the title page, possible
table of contents, references, and appendices. The submission is
expected to follow an essay-style but you may, of course, include
figures and tables in your paper. You are expected to link your
analysis to course readings and additional research, meaning a
current APA style and in-text citations must be used.
The pursuit of individual gain results in both players being
worse off than they need to be. Try to place yourself in the shoes
of your competitor. By the very nature of a game, players’ actions
affect not only themselves but also the other players (or
competitors in this case). If you don’t take into account your
effects on others when choosing the competitive action, the
business game often has inefficient outcomes. Gains from trade
exists but the logic of the situation can mean that the maximum
gains from trade are not realized.
Can the players somehow achieve legal cooperation and
overcome conflict? Using contracts could solve, at least
in some cases, your dilemma.
What changes if the game is played repeatedly?
The game now has a history and a future. Thus the players can make
their actions contingent on what their rivals did in the past. They
can reward or punish rivals’ past behavior.
What will happen in terms of profits if each firm
threatens the other with a price war? It can’t be in
either firm’s interest to cut its price, can it? The concern for
the future can generate cooperation but what are the three
caveats that must be appended to the idea that cooperation can
occur in the ongoing competitive relationship?
I will let you in on a little secret; a huge number of
laboratory experiments have been done, putting subjects, usually
undergraduate students, in a repeated competitive situation and
letting them play for real money. Typically, they cooperate in the
early plays of the game and then revert to non-cooperative play
toward the end of the experiment.
Save and submit your assignment using a naming convention that
includes your first and last name and the activity number (or
description). Do not add punctuation or use special characters.
Submit it by the posted due date.
Competition vs. Cooperation, please assume the U.S. market and
keep in mind U.S. anti-trust laws, specifically the Sherman Act of
1890, which forbids price fixing.
For more on U.S. anti-trust laws please visit:
(Links to an external site.)Links to an external site.