Outline

Session 8University of Southern California

ISE544 June 18, 2009

Geza P. Bottlik

Outline

• Two party distributive negotiations (Win/Lose)

– Case history

– Basic Problem Definition

– Class exercise – known distributions

– Equilibrium demonstration

– Uncertainty

– Time

– Auctions


ISE544 June 18, 2009

Geza P. Bottlik

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?


ISE544 June 18, 2009

Geza P. Bottlik

Reserve Value Distribution


ISE544 June 18, 2009

Geza P. Bottlik

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


ISE544 June 18, 2009

Geza P. Bottlik

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


ISE544 June 18, 2009

Geza P. Bottlik

Zone of Possible Agreement


ISE544 June 18, 2009

Geza P. Bottlik

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)


ISE544 June 18, 2009

Geza P. Bottlik

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)


ISE544 June 18, 2009

Geza P. Bottlik

Class exercise – known distributions

ZOPA – Zone of possible agreement – overlap of the ranges of the buyer’s and seller’s reservation values


ISE544 June 18, 2009

Geza P. Bottlik

Equilibrium demonstration


ISE544 June 18, 2009

Geza P. Bottlik

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


ISE544 June 18, 2009

Geza P. Bottlik

Uncertainty

Tree diagrams

Cumulative probability distributions

Utility Curves


ISE544 June 18, 2009

Geza P. Bottlik

Cumulative Distribution


ISE544 June 18, 2009

Geza P. Bottlik

Tree Diagram


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Geza P. Bottlik

The effects of time

Timing concessions

Sequential search, select the best candidate

Strike game

Escalation game

Virtual strike


ISE544 June 18, 2009

Geza P. Bottlik

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


ISE544 June 18, 2009

Geza P. Bottlik

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


ISE544 June 18, 2009

Geza P. Bottlik

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:


ISE544 June 18, 2009

Geza P. Bottlik

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

Outline

Documents

Transcript of Outline