# Abstract

John Nash won the 1994 Nobel in Economics for his work on what came to be known as “Nash Equilibrium”, where two or more competing entities “cooperate” (without illegally colluding) to reach a “Nash Bargain”. A Nash Bargain is reached when two or more competitors produce optimal quantities of the same or similar product or service to maximize their own self- interest, assuming others are rational and will do the same. The book and movie “A Beautiful Mind” dramatized Nash’s life story and work.

A relatively simple Excel-based tool helps you calculate a Nash Bargain in a competitive situation. It is available for FREE.

## What Can the Nash Bargain Advisor Do For You?

**can handle a competitive situation where you know: 1) The “Demand Curve” data for the market, namely the relationship between market price and quantity of product on the market, 2) Your own Cost Structure, namely the non-recurring investment to set up your production facilities and the recurring production cost of each item sold, and 3) An estimate of your competitor(s) Cost Structures.**

*Nash Bargain Advisor**at:*

**Nash Bargain Advisor**http://sites.google.com/site/bigira/stuff-ira-knows/NashBargainAdvisor.xls?attredirects=0&d=1

(or at) http://polaris.umuc.edu/~iglickst/swen603/NashBargainAdvisor.xls

**will compute the optimal quantity, market price, and estimated profit (or loss) you are likely to make if you follow the given advice, and if your competitors independently do the same.**

*Nash Bargain Advisor*## About “Elastic” Markets

The heavy black line is the Demand Curve that indicates how the market price declines from about $12 per unit to $4 when the quantity on the market increases from 10 million to 100 million units. (You can change the Demand Curve by entering different numbers on the SETUP sheet of the * Nash Bargain Advisor*.)

*.)*

**Nash Bargain Advisor****allows you to enter and compare two different sets of Cost Structures.**

*Nash Bargain Advisor***may result in situations where overall profits increase or decrease monotonically as production quantities increase. However, it is much more typical for profits to maximize with a moderate number of units on the market and for there to be lower profits (or net losses) for very low or very high production quanities.**

*Nash Bargain Advisor*## About Competitive Markets

**assuming others are rational and will do the same.**(The

**highlighted**part of the previous sentence is the most important part. If competitors are not rational, or if they try to “cheat” by producing too many units, the Nash Bargain will not work.)

**calculates the optimal quanities each competitor should produce to maximize their own self-interest, assuming others “cooperate” by doing the same in a rational way. The**

*Nash Bargain Advisor***also calculates the consequences if one or more producers “cheat” and over-produce more than their optimal quanitiy, or, if one or more producers under-produce due to miscalculation or disruption in supplies or production facilities.**

*Nash Bargain Advisor*## How to Use the Nash Bargain Advisor

The first four entries define the Demand Curve. In the real world, that data would come from marketing surveys or actual experience with sales volume at various outlets with different prices. It is assumed we are working in the relatively linear portion of the Demand Curve, where market price and quantity available vary inversely.

**minimum**reasonable number of units that may be on the market in the first cell. In the above example, that number is 10 million units. With that number of units available, market demand will support a price of about $12 per unit, entered into the second cell.

**maximum**reasonable number of units and the estimated price market demand will support. In the example, 100 million units will drive the price down to about $4 per unit.

*calculates that Alpha should optimally produce about 32 million units and Beta about 31 million, for a total of about 63 million units on the market.*

**Nash Bargain Advisor**Note that Beta could increase their profits by producing about 40 million units, about 9 million more than the Nash Bargain calls for. However, doing so will reduce Alpha’s profits to nearly zero, making Alpha, in game theory terms, the “SUCKER”. That would most likely prompt Alpha to retalliate by also over-producing in the next production cycle. If Beta produces fewer than the Nash Bargain quantity, their profits will decrease. Beta will lose money if they decrease below about 24 million units. If Beta under-produces, Alpha, the cooperator, will see the market price go up and Alpha will earn greater profits.

So, for their long-term self-interest, both Alpha and Beta should refrain from cheating and avoid getting into a “price war”.

**also calculates nine examples for the cases where both Alpha and Beta cooperate and where one or both competitors over- or under-produce.**

*Nash Bargain Advisor*- BOTH COOPERATE: Market price is $7.24, Alpha makes a net profit of $40M and Beta $46M.
- ALPHA CHEATS (over-produces by 50%): Market price drops to $5.80, Alpha (Cheater) makes a hefty net profit of $64M and Beta (the SUCKER) is driven down to a profit of $1M.
- BETA CHEATS (over-produces by 50%): Market price drops to $5.86, Beta (Cheater) makes a hefty net profit of $65M and Alpha (the SUCKER) is driven down to a
*loss*of $5M - BOTH CHEAT: Market Price drops to $4.42, both Alpha and Beta
*lose*about $3M each. - ALPHA UNDER-PRODUCES (by 50%): Market price is driven up to $8.68. Beta (Cooperator) makes a hefty profit of $91M and Alpha (under-producer) takes a
*loss*of $32M. - BETA UNDER-PRODUCES (by 50%): Market price is driven up to $8.62. Alpha (Cooperator) makes a hefty profit of $84M and Beta (under-producer) takes a
*loss*of $15M. - BOTH UNDER-PRODUCE (by 50%): Market price is driven up to $10.06. Alpha takes a loss of $9M and Beta’s profits go down to only $7M.
- ALPHA CHEATS (over-produces by 50%) and BETA UNDER-PRODUCES (by 50%): Market price is $7.18, Alpha (Cheater) makes a hefty profit of $130M and Beta (under-producer) takes a loss of $31M.
- BETA CHEATS (over-produces by 50%) and ALPHA UNDER-PRODUCES (by 50%): Market price is $7.30, Beta (Cheater) makes a hefty profit of $132M and Alpha (under-producer) takes a loss of $54M.

*Therefore, it appears that the best long-term situation for consumers and producers is a competitive market where producers meet their Nash Bargain quantities and do not cheat. Consumers benefit from reasonable and relatively stable prices while producers make a fair profit.*## How to Use Nash Bargain Advisor for More Than Two Producers

**may be used for more than two producers by combining additional producers into Alpha or Beta. For example, say there are four producers in a given market and two have advanced production facilities while the other two basic facilities. You could use Alpha for the two advanced facility and Beta for the two basic facilities, combining their non-recurring costs and dividing their Nash Bargain quantities.**

*Nash Bargain Advisor*