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Session 8University of Southern California
ISE544 June 18, 2009
Geza P. Bottlik Page 1
Outline
• Two party distributive negotiations (Win/Lose)
– Case history
– Basic Problem Definition
– Class exercise – known distributions
– Equilibrium demonstration
– Uncertainty
– Time
– Auctions
Session 8University of Southern California
ISE544 June 18, 2009
Geza P. Bottlik Page 2
Case history - Elmtree House
If you were the Mrs. Peters what would you have done?
What advice would you have given Steve about approaching
the potential buyer?
Where should Steve hold the talks?
Do you think both parties were satisfied with the outcome?
Session 8University of Southern California
ISE544 June 18, 2009
Geza P. Bottlik Page 3
Reserve Value Distribution
Session 8University of Southern California
ISE544 June 18, 2009
Geza P. Bottlik Page 4
Basic Problem Definition
Distributive allocation
Two bargainers(buyer/seller) – make a joint decision which is
enforceable
Single deal
Ignore the effects of time
The alternative is the status quo
Each has a predetermined alternative to a settlement
Session 8University of Southern California
ISE544 June 18, 2009
Geza P. Bottlik Page 5
Basic Problem Definition - continued
Reservation Prices:
s : minimum the seller is willing to settle for
b : maximum the buyer is willing to pay
X* : final contract value (if any)
X* - s : Seller’s surplus
b – X*: Buyer’s surplus
In general these are unknown to each other (one is known – one’s own, and the other is a random variable)
Reservation prices generally do not become public
The more they lie, the more it pays to be honest and vice versa
Session 8University of Southern California
ISE544 June 18, 2009
Geza P. Bottlik Page 6
Zone of Possible Agreement
Session 8University of Southern California
ISE544 June 18, 2009
Geza P. Bottlik Page 7
Input
In the box 9.1 “Select the best candidate”, there is another approach to proof the solution. You can see it in the book “Introduction to Probability Models, Eight edition, Sheldon M. Ross” on Page 123-125. For those of you who are interested in probability, you might be interested in ISE538, stochastic process, instructed by Prof. Ross.
In the sequential decision problem, let’s assume it is a real-world problem. If I were the seller of the house,
I would set 130% of my RP for the first half of the month.
I would set the first half average of buyer’s offer that is higher than my RP to be my RP for the second half.
Anyone who breaks my desirability first gets my house.
However, my RP have to be reasonable in the market. I add my desirability value to the monetary value on the first half, so the percentage should be changed time by time.
TN (that’s assuming you are in a sellers market!! GPB)
Session 8University of Southern California
ISE544 June 18, 2009
Geza P. Bottlik Page 8
Class exercise – known distributions
This exercise involves negotiation between a buyer and a seller
(e.g. the buyer is a program manager and the seller is the controller, this could also be about completion dates between customer and provider)
The reservation price distributions are known to both.
In this case they are uniformly distributed (every value in the range has equal probability)
Buyer $100 to $200
Seller $50 to $150
This means there is a 87.5% chance of being able to come to an agreement (See next page)
Session 8University of Southern California
ISE544 June 18, 2009
Geza P. Bottlik Page 9
Class exercise – known distributions
ZOPA – Zone of possible agreement – overlap of the ranges of the buyer’s and seller’s reservation values
Session 8University of Southern California
ISE544 June 18, 2009
Geza P. Bottlik Page 10
Equilibrium demonstration
Session 8University of Southern California
ISE544 June 18, 2009
Geza P. Bottlik Page 11
Equilibrium demonstration - continued
1234567
102103104105106107
A B C D E F G H
Min Max Min Max50$ 150$ 100$ 200$
s s' b b' X* S surplus B surplus126$ 150$ 143$ 128$ -$ -$ -$ 92$ 100$ 193$ 150$ 125$ 33$ 68$ 90$ 100$ 102$ 101$ 101$ 11$ 2$ 72$ 100$ 125$ 116$ 108$ 36$ 17$
111$ 136$ 147$ 131$ -$ -$ -$ 100$ 125$ 176$ 150$ 138$ 38$ 39$
Average 98$ 121$ 147$ 129$ 68$ 22$ 19$ % agreement 59%
Seller Buyer
Session 8University of Southern California
ISE544 June 18, 2009
Geza P. Bottlik Page 12
Uncertainty
Tree diagrams
Cumulative probability distributions
Utility Curves
Session 8University of Southern California
ISE544 June 18, 2009
Geza P. Bottlik Page 13
Cumulative Distribution
Session 8University of Southern California
ISE544 June 18, 2009
Geza P. Bottlik Page 14
Tree Diagram
Session 8University of Southern California
ISE544 June 18, 2009
Geza P. Bottlik Page 15
The effects of time
Timing concessions
Sequential search, select the best candidate
Strike game
Escalation game
Virtual strike
Session 8University of Southern California
ISE544 June 18, 2009
Geza P. Bottlik Page 16
The effects of time
We must choose when to come to an agreement
It requires patience
Sometimes there are deadlines
Self-imposed penalties
Real penalties
Most people are too impatient
Session 8University of Southern California
ISE544 June 18, 2009
Geza P. Bottlik Page 17
The effects of time – Select the best candidate
A series of sequential candidates are presented to the selector
He/She has a choice of either selecting the current candidate or going on to the next one. One cannot go back to a rejected candidate
You can tell which candidates are better
Before discussing the answer, we will play the game in class I will present a series of numbers
Session 8University of Southern California
ISE544 June 18, 2009
Geza P. Bottlik Page 18
The effects of time – Select the best candidate
You have to decide when to select a candidate. Write down your answer. I will continue to show new candidates as long as there are any candidates left.
Class results:
Session 8University of Southern California
ISE544 June 18, 2009
Geza P. Bottlik Page 19
Auctions
Distributive negotiation with 3 or more parties
It is distributive between the auctioneer and an individual bidder
It is competitive among bidders – it gets in the way of the distributive aspect
1. Open, ascending, outcry (English)
2. Open, descending, outcry (Dutch)
3. Sealed bids
4. High bidders wins, pays second price (Philatelic)
5. Reciprocal (buy, sell)
6. Silent Auction