14. You have baked a cake, but your two dear daughters won't stop fightingon who gets the biggest slice. To settle the dispute, to ask your deardaughter one (DD1) to cut the cake and your dear daughter two (DD2)to choose which piece she wants.(a) Draw the extensive form of the game. Let dear daughter one'sstrategies be "Cut Evenly" or "Cut Unevenly"; depending onwhat is on the platter, dear daughter two's strategies might in-clude "Take Big Slice", "Take Small Slice", or "Take Equal Slice".Assign payoffs to dear daughter one and dear daughter two thatgrow with the size of the slice that they receive.(b) Use backward induction to find the equilibrium outcome of thisgame.(c) Is the promise to take a small slice by DD2, if DD1 cuts unevenly,credible? Explain carefully.(d) After the rules are announced, dear daughter two says "It is notfair! I want to be the one who gets to cut the cake, not the onewho chooses the slice!". Is dear daughter two's complaint valid?You are determined to teach your dear daughters that they shouldnot fight. You cut the cake in one large slice and several smallslices and you warn them that if they both attempt to grab thelarge slice, you will destroy the cake and give them nothing. Ifonly one of them goes for the large slice, she can enjoy it. Describethe interaction between your two dear daughters as a simultaneousmove game where each of them can either go for the large slice orfor a small one. As above, assign payoffs that grow with the sizeof the slice that they receive. What is the Nash equilibrium (orNash equilibria) of this game? If the game is played sequentially,does the first mover have an advantage? Explain your answer.

A decision tree is a graphical representation of a sequential game. The decision tree provides an…

(a) Draw the extensive form of the game. Let dear daughter one's strategies be "Cut Evenly" or "Cut Unevenly"; depending on what is on the platter, dear daughter two's strategies might in- clude "Take Big Slice", "Take Small Slice", or "Take Equal Slice". Assign payoffs to dear daughter one and dear daughter two that grow with the size of the slice that they receive. (b) Use backward induction to find the equilibrium outcome of this game. (c) Is the promise to take a small slice by DD2, if DD1 cuts unevenly, credible? Explain carefully.

(a) Draw the extensive form of the game. Let dear daughter one's strategies be "Cut Evenly" or "Cut Unevenly"; depending on what is on the platter, dear daughter two's strategies might in- clude "Take Big Slice", "Take Small Slice", or "Take Equal Slice". Assign payoffs to dear daughter one and dear daughter two that grow with the size of the slice that they receive. (b) Use backward induction to find the equilibrium outcome of this game. (c) Is the promise to take a small slice by DD2, if DD1 cuts unevenly, credible? Explain carefully.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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