Consider the location game we covered in Lecture 3. Now assume there are three players (vendors). As we assumed in the lecture, consumers in each area choose the closest vendor and if there are multiple closest vendors then these vendors receive equal share of consumers in the area. Notice Si = {1, 2, 3, ...., 9} for i = 1, 2, 3. Here are some examples of payoffs: u1(1, 1, 1) = 3, u1(1, 1, 9) = u2(1, 1, 9) = 2.25, u3(1, 1, 9) = 4.5, u1(1, 5, 9) = u3(1, 5, 9) = 2.5 and u2(1, 5, 9) = 4. (a) Is s′1 = 1 strictly dominated by s′′1 = 2 for player 1? (b) Is s′1 = 1 weakly dominated by s′′1 = 2 for player 1? (c) Can you find a Nash equilibrium in pure strategies?
Consider the location game we covered in Lecture 3. Now assume there are three players (vendors). As we assumed in the lecture, consumers in each area choose the closest vendor and if there are multiple closest vendors then these vendors receive equal share of consumers in the area. Notice Si = {1, 2, 3, ...., 9} for i = 1, 2, 3. Here are some examples of payoffs: u1(1, 1, 1) = 3, u1(1, 1, 9) = u2(1, 1, 9) = 2.25, u3(1, 1, 9) = 4.5, u1(1, 5, 9) = u3(1, 5, 9) = 2.5 and u2(1, 5, 9) = 4. (a) Is s′1 = 1 strictly dominated by s′′1 = 2 for player 1? (b) Is s′1 = 1 weakly dominated by s′′1 = 2 for player 1? (c) Can you find a Nash equilibrium in pure strategies?
Chapter15: Oligopoly And Strategic Behavior
Section: Chapter Questions
Problem 17P
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Question
Consider the location game we covered in Lecture 3. Now assume there are
three players (vendors). As we assumed in the lecture, consumers in each area choose
the closest vendor and if there are multiple closest vendors then these vendors receive
equal share of consumers in the area. Notice Si = {1, 2, 3, ...., 9} for i = 1, 2, 3. Here are
some examples of payoffs: u1(1, 1, 1) = 3, u1(1, 1, 9) = u2(1, 1, 9) = 2.25, u3(1, 1, 9) =
4.5, u1(1, 5, 9) = u3(1, 5, 9) = 2.5 and u2(1, 5, 9) = 4.
three players (vendors). As we assumed in the lecture, consumers in each area choose
the closest vendor and if there are multiple closest vendors then these vendors receive
equal share of consumers in the area. Notice Si = {1, 2, 3, ...., 9} for i = 1, 2, 3. Here are
some examples of payoffs: u1(1, 1, 1) = 3, u1(1, 1, 9) = u2(1, 1, 9) = 2.25, u3(1, 1, 9) =
4.5, u1(1, 5, 9) = u3(1, 5, 9) = 2.5 and u2(1, 5, 9) = 4.
(a) Is s′1 = 1 strictly dominated by s′′1 = 2 for player 1?
(b) Is s′1 = 1 weakly dominated by s′′1 = 2 for player 1?
(c) Can you find a Nash equilibrium in pure strategies?
(b) Is s′1 = 1 weakly dominated by s′′1 = 2 for player 1?
(c) Can you find a Nash equilibrium in pure strategies?
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