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. receiving $500 or receiving nothing B. receiving $100 or receiving $50 C. answering honestly or answering with a lie D. playing the game or not playing the game

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. receiving​ $500 or receiving nothing B. receiving​ $100 or receiving​ $50 C. answering honestly or answering with a lie D. playing the game or not playing the game

BlackTom AI · Accepted Answer

We start by restating the prompt to ensure the options are analyzed in context. The question asks about a two-player game where each player can either answer honestly or lie, with payoffs as described, and it asks to describe the strategies and the equilibrium, and to compare to the Prisoner’s Dilemma. The provided answer choices for Part 1 say the strategies are:

Option A: receiving $500 or receiving nothing
Option B: receiving $100 or receiving $50
Option C: answering honestly or answering with a lie
Option D: playing the game or not playing the game

Option A asserts that the strategies concern payoffs rather than actions. In game theory, strategies refer to the actions players can choose, not the resulting payoffs. This makes A mischaracterize what the strategic options are.

Option B centers on payoff outcomes (100 or 50) rather than the actions themselves. While payoffs are what result from strategies, the strategic choice available to each player is not about selecting a payoff directly but about choosing to answer honestly or lie. Thus B is misdirected.

Option C identifies the strategies as the actions available to each player: either answer honestly or lie. This correctly captures the strategic choices each player can make in the described game. It aligns with the problem’s framing of two players, each choosing between two actions, which defines the strategy set.

Option D suggests the choice is between playing the game or not playing the game. In the described setup, both players participate in the game with the given payoffs, so deciding to play or not is not part of the strategic space presented. Therefore D does not describe the strategies consistent with the scenario.

Why Option C is the correct description hinges on standard game-theoretic terminology: a strategy specifies an action profile available to a player in a given game. Here, each player has two actions: answer honestly or lie. The combination of these choices by both players yields the payoff matrix described in the problem (100/100 if both honest, 0/500 or 500/0 if one lies and the other honest, and 50/50 if both lie). The other options conflate strategies with outcomes or with participation decisions, which are not the strategic choices defined by the game.

To further illustrate potential misunderstandings:
- If one thought of Strategy A (payoff options) as the strategy, they would be mixing the concept of outcomes with the actions that lead to them, which is backward in standard analysis.
- If one insisted on B (payoff levels) as strategy, they would ignore the players’ available actions and the strategic interaction that produces those payoffs.
- If one proposed D (play or not) as strategy, they would be introducing a pre-game decision not present in the problem’s description, effectively altering the game’s structure.

In summary, analyzing the problem through the lens of actions available to each player confirms that the true description of the strategies is: the players choose between honesty and lying. This corresponds to Option C. The other options misidentify what constitutes a strategy in this game, either by focusing on payoffs instead of actions or by introducing participation as a strategic decision.

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