a) Check each game for dominance solvability. Use Game 3 to explain why it is important to describe an equilibrium by using the strategies employed by other players, not merely the payoffs received in equilibrium. b) Find the Nash Equilibria of those games. Note that every equilibfium in domi- nated strategies that you found in a) is also a NE. This is generally the case: if an equilibrium is found by iterated elimination of (weakly) dominated strate- gies, it is also a Nash equilibrium. Can you explain why this must be the case?

a) Check each game for dominance solvability. Use Game 3 to explain why it is important to describe an equilibrium by using the strategies employed by other players, not merely the payoffs received in equilibrium. b) Find the Nash Equilibria of those games. Note that every equilibfium in domi- nated strategies that you found in a) is also a NE. This is generally the case: if an equilibrium is found by iterated elimination of (weakly) dominated strate- gies, it is also a Nash equilibrium. Can you explain why this must be the case?

Principles of Microeconomics (MindTap Course List)

8th Edition

ISBN:9781305971493

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter17: Oligopoly

Section: Chapter Questions

Problem 9PA

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GAME UUU B1 Player B B2 A1 7,13 5, 10 A2 3,8 9,16 Player A A3 5,8 4,7 In Game UUU (see table above), assuming players move simultaneously, Player A choosing A1 and Player B choosing B3 is a Nash equilibrium. Player A choosing A3 and Player B choosing B2 is a Nash equilibrium. Both Player A choosing A1 and Player B choosing B1 and Player A choosing A2 and player B choosing B2 are Nash equilibria in pure strategies Player A choosing A1 and Player B choosing B2 is a Nash equilibrium.
2. Consider the following two-player game with two players: Adam and Eve. Adam A1 A2 A3 A4 E1 6,3 5, 3 5, 0 2,0 E2 4,4 5, 4 3, 2 2, 3 Eve E3 4, 1 0,2 6, 1 3, 4 E4 3,0 5, 1 4,0 6₂ 1 a. Find the Iterated Elimination of Dominant Strategies Equilibrium for this game. Explain.
A R1 R2 C1 5,4 6,4 B C2 11,5 9, 2 In this game between players A and B, Only A has a dominant strategy O Only B has a dominant strategy Both players have a dominant strategy O Neither player has a dominant strategy
GAME 5 Player B B1 B2 Player A A1 7,3 | 5, 10 A2 3, 8| 9, 6 In Game 5 above, O Neither player has a dominant strategy. O Player B has a dominant strategy. O Player A has a dominant strategy. O Both players have dominant strategies.
ITERATIVE DOMINANCE Consider the following game in strategic form. a₁ 22 a3 bi 35,52 30,30 28,9 (9,11) (45,47) (47,28) (52,16) (28,9) (30,30) (16,45) (11,35) (35,52) b2 11,35 9,11 16,45 b3 52,16 45,47 47,28 Which of the following payoff profiles survive iterative deletion of strictly dominated strategies? (Mark all profiles that survive.)
4. Iterated Elimination Give an example of a game where iterated elimination of dominated strategies cannot eliminate any actions.
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