2. Consider the following three variants, A, B, and C,of the grade game Column C
ID: 1137416 • Letter: 2
Question
2. Consider the following three variants, A, B, and C,of the grade game Column Column !Row a 8,8 12,3 6,1210,10 Row a 8,8 5,3 10,10 Column 1 Row a 8,8 5,5 | b 1 312 | 10,10 l ). Does each game (A, B, or C) have a dominant strategy for a player? il). Is there a game (A, B, or C) that continues to be the same game (in principle) as the original grade game? Why or why not? ill) Consider game C ili 1) does (a rational) Row player ever choose to play b? Why or why not? íi.2) does Row player have a dominant strategy? Why or why not? ill 3) are your answers to ii.1) and ii 2) contradictory to each other? Why or why not?Explanation / Answer
i)
Game A
Best Responses
Row Player
BRR(a) = a
BRR(b) = b
Column Player
BRC(a) = a
BRC(b) = b
None of the two player have a dominant strategy.
Game B
Best Responses
Row Player
BRR(a) = a
BRR(b) = a
Column Player
BRC(a) = b
BRC(b) = b
Both row and column playes have dominant strategy “a” and “b” respectively.
Game C
Best Responses
Row Player
BRR(a) = a
BRR(b) = b
Column Player
BRC(a) = a
BRC(b) = a
Only column player have dominant strategy “b”.
ii) Do not have knowledge about grade game.
iii)
1 ) Best Responses
Row Player
BRR(a) = a
BRR(b) = b
Column Player
BRC(a) = a
BRC(b) = a.
Yes, row player will choose b when column player choose a because payoof to row player by choosing “b” is more than by choosing “a”.
2) No, row player does not have a dominant strategy because he chooses different strategy foe strategies chosen by column player.
3) No, they are not because both suggests that row player does not have a dominant strategy.
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