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.

Synopsis

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 one likes.

Directions

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:

 

 

Cournot Ltd.

Bertrand Ltd.

High Price

Low Price

High Price

(10, 10)

(1, 15)

Low Price

(15, 1)

(4,4)

Hint

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.