(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.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
Transcribed Image Text:14. You have baked a cake, but your two dear daughters won't stop fighting
on who gets the biggest slice. To settle the dispute, to ask your dear
daughter 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'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.
(d) After the rules are announced, dear daughter two says "It is not
fair! I want to be the one who gets to cut the cake, not the one
who chooses the slice!". Is dear daughter two's complaint valid?
You are determined to teach your dear daughters that they should
not fight. You cut the cake in one large slice and several small
slices and you warn them that if they both attempt to grab the
large slice, you will destroy the cake and give them nothing. If
only one of them goes for the large slice, she can enjoy it. Describe
the interaction between your two dear daughters as a simultaneous
move game where each of them can either go for the large slice or
for a small one. As above, assign payoffs that grow with the size
of the slice that they receive. What is the Nash equilibrium (or
Nash equilibria) of this game? If the game is played sequentially,
does the first mover have an advantage? Explain your answer.
Expert Solution
Step 1: Introduce the concept of decision tree.
A decision tree is a graphical representation of a sequential game. The decision tree provides an overview of all the possible choices for players as well as specific details on the consequences of any particular choices. The decision tree is used to analyze the game and determine optimal strategies.
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