IIT JAM 2022 Question 29: Game theory and strategic behaviour
Which statement is CORRECT for Game A and Game B? Game A (Battle of the Sexes): Mary prefers a movie, John prefers football, both prefer being together. Payoffs (Mary, John): (Movie, Movie) = (2,1); (Movie, Football) = (0,0); (Football, Movie) = (0,0); (Football, Football) = (1,2). Game B (Prisoner's Dilemma), payoffs (Convict 1, Convict 2): (Do not confess, Do not confess) = (-1,-1); (Do not confess, Confess) = (-9,0); (Confess, Do not confess) = (0,-9); (Confess, Confess) = (-5,-5).
Tap an option to check your answer.
Answer and worked solution
Answer: (D)
In Game A the players want to coordinate, so the pure-strategy Nash equilibria are the two matched outcomes (Movie, Movie) with payoff (2,1) and (Football, Football) with payoff (1,2); the mismatched cells give (0,0) and are not equilibria.
In Game B confessing strictly dominates for each convict, so the unique Nash equilibrium is (Confess, Confess) at (-5,-5). Both descriptions match option (D).
The trap: (A) In Game A, (Movie, Football) and (Football, Movie) represent Nash equilibrium. In Game B, (Do not confess, Do not confess) is the Nash Equilibrium.
Options (A) and (B) put the Game A equilibria in the mismatched cells; coordination games have equilibria where the players' choices agree, not where they clash.
Game theory and strategic behaviour has come up 61 times in 6 exams since 2008.
What this question tests
This question is on Pure-strategy Nash equilibrium, part of Game theory and strategic behaviour in Game Theory.
Outcomes from which no player wants to deviate, and classic games that illustrate them.
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