# Project1 by stariya

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```									     MIME 6980                        PROJECT 1                       Fall 2006

This project is concerned with a negotiation between an inventor who is seeking
funding from an investor for a risky venture to develop a mechanism. The project
consists of two parts. In the first part, you will assume the role of an inventor and
find the best offer to make to the investor. In the second part you will assume the
role of the investor and you will set up some rule for accepting or rejecting an offer
from an inventor. The information available to you consists of ten measurements
of the stroke and imbalance angles of these mechanisms. On the basis of these
measurements, you will estimate the chance of success of the venture and its
worth, which will help you make a decision when playing the roles of the inventor
and the investor.

Part 1: Finding the best offer in a negotiation between an inventor and an
investor

An inventor has an idea about an automated factory mechanism but has no funds
to develop it. He proposes to share the potential revenue from a project to develop
the mechanism with an investor that in return will fund the project. The inventor
wants to select the fraction of the revenue that he will offer to the investor to
maximize the inventor's return from the project.

If the project is successful, it will generate revenue H, otherwise it will generate
revenue L (H>L). The project cost is I, which the inventor seeks from the investor.
The fraction of the share that the inventor will offer to the investor is e. The
investor has to either accept or reject the offer based on her perceived value of the
project -- no counteroffer is allowed. The opportunity cost of capital is i (current
rate of interest offered by other investments to the investor for the project
duration). If the inventor does not proceed with the project (because the investor
rejected his offer or because the inventor chose to do so) then the inventor can
make a certain amount of \$60 from a temporary job.

Figure 1 is a decision/event tree summarizing the game of the inventor and the
investor. In stage A, the inventor makes his offer. The investor either accepts of
rejects the offer. There are four outcomes of this game represented by the ends of
the arrows. Each pair of numbers next to each arrow represents the revenues of
the inventor and the investor.

1
Final Cash Position
(Inventor, Investor)
Investor accepts
B     offer                [H (1-e), He]
A    Inventor offers
fraction e

H
[J, (1+i)I]
Investor rejects
Nature                                                    offer
Investor accepts
A                          B      offer                [L(1-e), Le]
Inventor offers
fraction e

L
[J, (1+i)I]
Investor rejects
offer

Figure 1. Inventor-Investor game

Description of mechanism

The mechanism is a slider-crank mechanism that translates the rotary motion of
a crank to a translational motion of the slider (Fig. 2). The motion is transmitted
by a link called the coupling rod. Two main performance parameters of such a
mechanism are the stroke and time-ratio. The resulting mechanism should have a
stroke of 60 mm and a time ratio of 1.25 (which corresponds to an imbalance
angle of 20 degrees.)

Crank, r2               Connecting rod, r3

slider
e

Fig 2a. Crank-slider mechanism

2
Fig. 2b. Assembled mechanism

The inventor makes a mechanism to meet certain specifications for the stroke and
the time ratio (or equivalently for the imbalance angle). The venture is successful
if both the stroke and the imbalance angle are within acceptable ranges. Use the
following data to make the two decisions in this project:

    Acceptable range for stroke (mm): 57.5 to 62.5
    Acceptable range for the imbalance angle (degrees): 17 to 23
    Revenue if project is successful, H: \$1,000
    Revenue if project is successful, L: \$ 50
    Investment required to complete the project, I \$100
    Amount that inventor can make from temporary job: J: \$60
    Opportunity cost, i: 0.06

Table 1 below shows the stroke and imbalance angles of 10 mechanisms.
Information from this table can be used to estimate the chance of success of the
project.

Stroke      Imbalance Angle
(mm)             (deg)
1    61.49            20.45
2    78.59            18.70
3    52.25            23.25
4    58.29            20.27
5    65.10            22.20
6    51.49            15.86
7    56.77            30.44
8    66.55            28.48
9    59.59            19.69
10    57.53            21.38

Table 1. Properties of 10 mechanisms

3

Develop a decision approach for determining the inventor’s and the investor’s
decisions. This should consist of assumptions and a method to quantify your
preferences when you act as inventor or investor and of your estimate of the worth
of the risky venture. Describe and justify assumptions and the method.

Using your method determine the inventors and the investor’s decisions.
Specifically, determine the following:

a) Should the inventor make an offer to the investor or opt for the temporary
job with the fixed revenue J?
b) If the inventor makes an offer to the investor, specify the fraction of the
revenue, e.
c) When should the investor accept and when she should reject an offer? That
is, find a rule of procedure to determine if the investor should accept of
reject a given offer.

4

1. The project counts as two homework assignments, 200 points maximum.
Each part of the project carries equal weight.
2. 100 points will depend on your determination of the inventor’s and
investor’s decisions. You should justify your assumptions and your
decisions clearly. This includes the estimation of the value of the risky
venture. You should also show that you accounted for all information
available to you to make a decision.
a. There is no correct or wrong decision here. Since little information
is available about the likelihood of the project success, a risk averse
student may set up decision rules that are more likely to result in
the investor and the investor choosing the fixed revenue activities.
An ambitious student who wants to take risks to get a high grade in
this project may set - up decision rules that that result in one of
both players choosing the project frequently.
b. There is no single estimate of the probability of the project success
that can be used in this project because the data is scarce. You may
use the same estimate or different estimates of the probability of
success of the project when you act as the investor and as the
investor.
3. The remaining 100 points will be determined by finding the average
revenue of your decision using data from 133 mechanisms that are
available to the professor and by pairing your decisions with those of your
classmates as follows:
a. Using your decision rule for the inventor, the professor will simulate
eight decisions using your seven classmate’s rules plus your
decision rule for the investor.
b. The average revenue of the eight decisions will be calculated for the
133 mechanisms.
c. Using your decision rule for the inventor, eight decisions will be