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ConflictResolutionExample

# ConflictResolutionExample - Conflict Resolution Example Two...

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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 .

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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 .
decision space: Class work. Two corn production companies,

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ConflictResolutionExample - Conflict Resolution Example Two...

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