Consider a simultaneous-move game with two players. The payoff table with order of payoffs (Player 1, Player 2) is provided above. Choose the statement that is consistent with it.

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Question restatement: In a simultaneous-move 2x2 game, identify which statements about Nash equilibria in pure strategies are consistent with the given payoff table. Options: a) Down and Left constitute Nash Equilibrium. b) Down and Right constitute Nash Equilibrium. c) Top and Right constitute Nash Equilibrium. d) There is no Nash Equilibrium in pure strategies.

Option a: Down and Left constitute Nash Equilibrium. To check if (Down, Left) is a Nash equilibrium, each player must be playing a best response to the other. If Player 2 plays Left, Player 1’s payoffs are Top=20 and Down=16, so the best response for Player 1 is Top, not Down. Therefore Down is not a best response to Left, so (Down, Left) is not a Nash equilibrium. This option is inconsistent with the payoff structure.

Option b: Down and Right constitute Nash Equilibrium. If Player 2 plays Right, Player 1’s payoffs are Top=18 and Down=19, so the best response for Player 1 is Down (not Top). So Down is a best response to Right. Now, if Player 1 plays Down, Player 2’s payoffs are Left=17 and Right=16, so the best response for Player 2 is Left (not Right). Therefore Right is not a best response to Down, and (Down, Right) is not a Nash equilibrium. This option is inconsistent with the best-response pattern.

Option c: Top and Right constitute Nash Equilibrium. If Player 2 plays Right, Player 1’s best response is Down (as just noted), not Top. Hence Top is not a best response to Right, so (Top, Right) cannot be a Nash equilibrium. This option is incorrect given the payoffs.

Option d: There is no Nash Equilibrium in pure strategies. Based on the best-response analyses above, no cell in the 2x2 payoff matrix satisfies both players playing a best response to the other at the same time. Player 1’s best responses depend on Player 2’s action, and Player 2’s best responses depend on Player 1’s action, and these do not align in any single outcome. Therefore, this option accurately reflects the absence of a pure-strategy Nash equilibrium in the given game.

SESS0007_24-25 LSA Test

Consider a simultaneous-move game with two players. The payoff table with order of payoffs (Player 1, Player 2) is provided above. Choose the statement that is consistent with it.

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