ConflictResolutionExample - Conflict Resolution Example Two...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Conflict Resolution Example Two corn production companies, Crispy and Sweet , have continuous transportation flows of their corn to two processing facilities A and B . The fraction of corn that Crispy sends to A is p , while 1- p gets sent to B . The fraction of corn that Sweet sends to A is q , while 1- q gets sent to B . Interviews with the management of the two companies showed the following utilities: (i) both companies have a utility value of 200 if both companies send all their corn to A ; (ii) both companies have a utility value of 0 if both companies send all their corn to B ; (iii) if Crispy sends all to A and, at the same time, Sweet all to B , then Crispy has a utility of 100 and Sweet of 300; and (iv) if Crispy sends all to B and, at the same time, Sweet all to A , then Crispy has a utility of 300 and Sweet of 100. Assume that we see the fractions ( p and q ) as probabilities of shipping all corn to A . For example, if Crispy ships 20% to A , we have p =0.2. We now assume that p =0.2 is the probability that Crispy ships all to A . Let's further assume that Crispy and Sweet decide on their fractions independently of each other. Finally, let's assume that they want to maximize their expected utility, where u C is Crispy's expected utility and u S is Sweet's expected utility. a) Write down the formal model for u C and u S in terms of p and q . (e.g., u C = apq + bp (1- q ) + …, where a , b , and c are numbers). b) Draw the solution space in the u C - u S plane. Note that the solution space is defined by all u C - u S values for varying p and q values (between 0 and 1). c) What are the minimum and maximum u C and u S values, and for which p and q values are they obtained. d) Compute the fraction q , for which Crispy's expected utility, u C , is independent of its fraction p , what is Crispy's u C at this point? e) Compute the fraction p , for which Sweet's expected utility, u S , is independent of its fraction q , what is Sweet's u S at this point? f) Find the efficient (Pareto optimal) values u C = u S ; for which fractions p and q are they obtained? Solutions: a) u C = 200 pq + 100 p (1- q ) + 300(1- p ) q ; u S = 200 pq + 300 p (1- q ) + 100(1- p ) q .
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Uc = 100p + 300q - 200pq Us = 300p + 100q - 200pq b) Solution space in the u C - u S plane. b) The minimum is at (0,0) for p = q =0. The maximum expected utility is 300; Crispy reaches it if p =0, and q =1, and Sweet reaches it if p =1 and q =0. c) 200 q + 100(1- q ) = 300 q q =0.5 and u C =150. d) 200 p + 100(1- p ) = 300 p p =0.5 and u S =150. e) u C = u S =200, p = q =1. My answers: a: Uc = 100p + 300q - 200pq Us = 300p + 100q - 200pq b: utility space: u C = 200 pq + 100 p (1- q ) + 300(1- p ) q = 100p + 300q - 200pq ; u S = 200 pq + 300 p (1- q ) + 100(1- p ) q = 100q + 300p - 200pq .
Background image of page 2
decision space: Class work. Two corn production companies,
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/29/2009 for the course CEE 5930 taught by Professor Loucks during the Fall '00 term at Cornell University (Engineering School).

Page1 / 11

ConflictResolutionExample - Conflict Resolution Example Two...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online