Session 8 University 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 8 University 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 8 University of Southern California ISE544 June 18, 2009 Geza P. Bottlik Page 3 Reserve Value Distribution

Session 8 University 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 8 University 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 8 University of Southern California ISE544 June 18, 2009 Geza P. Bottlik Page 6 Zone of Possible Agreement

Session 8 University 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 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 8 University 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 8 University 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 8 University of Southern California ISE544 June 18, 2009 Geza P. Bottlik Page 10 Equilibrium demonstration

Session 8 University of Southern California ISE544 June 18, 2009 Geza P. Bottlik Page 11 Equilibrium demonstration - continued

Session 8 University of Southern California ISE544 June 18, 2009 Geza P. Bottlik Page 12 Uncertainty Tree diagrams Cumulative probability distributions Utility Curves

Session 8 University of Southern California ISE544 June 18, 2009 Geza P. Bottlik Page 13 Cumulative Distribution

Session 8 University of Southern California ISE544 June 18, 2009 Geza P. Bottlik Page 14 Tree Diagram

Session 8 University 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 8 University 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 8 University 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 8 University 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 8 University 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