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Therese's strategy_

Therese's strategy_

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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4. Fleeing a Dangerous Conflict Violence, caused by a conflict over scarce water resources, broke out last week between herders and farmers in Cameroon's Far North region, causing more than 30,000 people to flee to the neighboring country of Chad, most of them women and children. Martine and Therese are cousins fleeing together, and they each care about the other's welfare. Martine is willing to share food with Therese, who has little, but Martine knows that Therese is not trustworthy and may ask for food even if she is not hungry. They both need energy, so if Martine shares food, her strength decreases but Therese's increases. The increase in strength Therese gets is greater if she eats when she is truly hungry. Therese can signal her hunger by helping to carry Martine's baby. Because doing this takes energy, Martine may be more likely to believe Therese when she says she is hungry if she has been carrying the baby. Because they had to leave suddenly, Martine is uncertain whether her cousin is hungry; let p be the probability of her being hungry. Martine's energy level is 1 when she keeps all of her food and S if she shares it, for some 0 < S < 1. Therese has either low, medium, or high levels of energy (L, M, or H, where 0 < L < M <H < 1), depending on whether she is hungry and if she is given food, and she exerts energy e if she helps to carry the baby. Let r be a factor that represents the extent to which each cousin values the energy of the other. Consequently, the payoffs are shown in the following diagram, where x, y represents a payoff of x and Therese and y to Martine:
Transcribed Image Text:4. Fleeing a Dangerous Conflict Violence, caused by a conflict over scarce water resources, broke out last week between herders and farmers in Cameroon's Far North region, causing more than 30,000 people to flee to the neighboring country of Chad, most of them women and children. Martine and Therese are cousins fleeing together, and they each care about the other's welfare. Martine is willing to share food with Therese, who has little, but Martine knows that Therese is not trustworthy and may ask for food even if she is not hungry. They both need energy, so if Martine shares food, her strength decreases but Therese's increases. The increase in strength Therese gets is greater if she eats when she is truly hungry. Therese can signal her hunger by helping to carry Martine's baby. Because doing this takes energy, Martine may be more likely to believe Therese when she says she is hungry if she has been carrying the baby. Because they had to leave suddenly, Martine is uncertain whether her cousin is hungry; let p be the probability of her being hungry. Martine's energy level is 1 when she keeps all of her food and S if she shares it, for some 0 < S < 1. Therese has either low, medium, or high levels of energy (L, M, or H, where 0 < L < M <H < 1), depending on whether she is hungry and if she is given food, and she exerts energy e if she helps to carry the baby. Let r be a factor that represents the extent to which each cousin values the energy of the other. Consequently, the payoffs are shown in the following diagram, where x, y represents a payoff of x and Therese and y to Martine:
L - e +r, 1+r(L – e) Н —е + rS, S + r(H — е) М —е+ r, 1+ r(M — е) Н —е + rS, S + r(H — е) Кеp Share Кеep Share Carry Carry Hungry Not Hungry 1- p Don't Carry Don't Carry Keep Share Кeep Share L +r, 1+ rL H + rS, S+ rH M +r, 1+rM H + rS, S+ rH Suppose there is a separating equilibrium where Therese helps carry the baby if she is hungry and does not help if she is not hungry, and Miriam shares food when Therese helps but keeps all the food when Therese does not help. a) In order for these strategies to be an equilibrium, neither cousin can have incentive to deviate. Given Therese's strategy, what conditions must hold for Martine to have no incentive to deviate? Express any condition as a bound on the value of r as a function of the other parameters. b) Given Martine's strategy, what conditions must hold for Therese to have no incentive to deviate? Express any condition as a bound on the value of r as a function of the other parameters. c) Explain these conditions conceptually by interpreting the meaning of the expressions you found for the bounds on r. Now consider a potential pooling equilibrium where Therese never helps carry the baby and Martine never shares her food. d) What conditions must hold for this to be an equilibrium? Hint: don't forget to consider actions and beliefs off the equilibrium path.
Transcribed Image Text:L - e +r, 1+r(L – e) Н —е + rS, S + r(H — е) М —е+ r, 1+ r(M — е) Н —е + rS, S + r(H — е) Кеp Share Кеep Share Carry Carry Hungry Not Hungry 1- p Don't Carry Don't Carry Keep Share Кeep Share L +r, 1+ rL H + rS, S+ rH M +r, 1+rM H + rS, S+ rH Suppose there is a separating equilibrium where Therese helps carry the baby if she is hungry and does not help if she is not hungry, and Miriam shares food when Therese helps but keeps all the food when Therese does not help. a) In order for these strategies to be an equilibrium, neither cousin can have incentive to deviate. Given Therese's strategy, what conditions must hold for Martine to have no incentive to deviate? Express any condition as a bound on the value of r as a function of the other parameters. b) Given Martine's strategy, what conditions must hold for Therese to have no incentive to deviate? Express any condition as a bound on the value of r as a function of the other parameters. c) Explain these conditions conceptually by interpreting the meaning of the expressions you found for the bounds on r. Now consider a potential pooling equilibrium where Therese never helps carry the baby and Martine never shares her food. d) What conditions must hold for this to be an equilibrium? Hint: don't forget to consider actions and beliefs off the equilibrium path.
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