Part 1Consider a game with two players who cannot communicate, and in which each player is asked a question. The players can either answer honestly or lie. If both answer honestly, each receives $100. If one answers honestly and the other lies, the liar receives $500 and the honest player gets nothing. If both lie, then each receives $50.Describe the strategies and the payoffs.What is the equilibrium of this game?Compare this game to the prisoners' dilemma. Are the games similar or different? Explain. Part 1The strategies are _______. A. answering honestly or answering with a lie B. receiving $500 or receiving nothing C. playing the game or not playing the game D. receiving $100 or receiving $50

Question

Part 1Consider a game with two players who cannot​ communicate, and in which each player is asked a question. The players can either answer honestly or lie. If both answer​ honestly, each receives​ $100. If one answers honestly and the other​ lies, the liar receives​ $500 and the honest player gets nothing. If both​ lie, then each receives​ $50.Describe the strategies and the payoffs.What is the equilibrium of this​ game?Compare this game to the​ prisoners' dilemma. Are the games similar or​ different? Explain. Part 1The strategies are​ _______. A. answering honestly or answering with a lie B. receiving​ $500 or receiving nothing C. playing the game or not playing the game D. receiving​ $100 or receiving​ $50

BlackTom AI · Accepted Answer

We begin by restating the question and all answer options to set the stage for analysis:
Question: In a two-player game where each player can either answer honestly or lie, with payoffs as described, what are the strategies and payoffs, what is the equilibrium, and how does it compare to the prisoners' dilemma? Part 1: The strategies are _______.
Options:
A. answering honestly or answering with a lie
B. receiving $500 or receiving nothing
C. playing the game or not playing the game
D. receiving $100 or receiving $50

Now, evaluate each option
Option A: "answering honestly or answering with a lie". This correctly identifies the strategic choices each player can make: honest or lie. It captures the strategic decision space that defines the game. Therefore this option describes the actual strategies players choose from, making it the correct characterization of strategies.
Option B: "receiving $500 or receiving nothing". This describes payoffs, not the set of strategic actions. While these payoffs are part of the outcomes, they are not the strategic options available to a player. So this option mislabels payoffs as strategies and is incorrect.
Option C: "playing the game or not playing the game". In this setup, both players participate in the game; there is no option to abstain or to not play described in the model. Therefore this option does not reflect the actual strategic choices and is incorrect.
Option D: "receiving $100 or receiving $50". These are payoff outcomes under certain profiles (HH yields 100 each; LL yields 50 each) but again they are not the players’ strategic actions. The prompt asks for the strategies, not the payoffs, so this option is incorrect.

To deepen the analysis, consider the strategic form briefly: each player has two strategies (Honest, Lie). The payoff matrix has HH = (100,100); HL = (0,500); LH = (500,0); LL = (50,50). We can further reason about best responses: if the other player chooses Honest, lying yields 500 vs honest yields 100, so Lie is better. If the other player lies, lying yields 50 vs honest yields 0, so Lie is still better. Thus Lie is the dominant strategy for both players, making (Lie, Lie) the Nash equilibrium with payoffs (50,50). The question’s prompt, however, asks specifically for the strategies, which are the two options each player can select: honest or lie, matching Option A.

In summary, among the presented choices, only Option A correctly names the strategic choices available to the players. Options B, C, and D refer to payoffs or to participation factors, not to the actual strategy set, and therefore are incorrect.

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