Question20 What are the individual equilibrium and social optimum in the following Tragedy of the Commons game? [table]
| | Player 2
Player 1 | | Conserve | Plunder Conserve | 100 , 100 | -100 , 200 Plunder | 200 , -100 | 0 , 0
[/table] Individual equilibrium is (Plunder, Plunder) and social optimum is (Conserve, Conserve) Both Individual equilibrium and social optimum is (Plunder, Plunder) Both Individual equilibrium and social optimum is (Conserve, Conserve) Individual equilibrium is (Conserve, Conserve) and social optimum is (Plunder, Plunder) ResetMaximum marks: 1 Flag question undefined

Question

Question20 What are the individual equilibrium and social optimum in the following Tragedy of the Commons game? [table]
|  | Player 2
Player 1 | | Conserve | Plunder Conserve | 100 , 100 | -100 , 200 Plunder | 200 , -100 | 0 , 0
[/table] Individual equilibrium is (Plunder, Plunder) and social optimum is (Conserve, Conserve) Both Individual equilibrium and social optimum is (Plunder, Plunder) Both Individual equilibrium and social optimum is (Conserve, Conserve) Individual equilibrium is (Conserve, Conserve) and social optimum is (Plunder, Plunder) ResetMaximum marks: 1 Flag question undefined

BlackTom AI · Accepted Answer

To tackle this Tragedy of the Commons setup, we first lay out the payoff matrix in a readable form. The table shows the four outcomes with each player's choices (Conserve or Plunder) and the corresponding payoffs for Player 1 and Player 2:

- If both Conserve: (100, 100)
- If Player 1 Conserve and Player 2 Plunder: (-100, 200)
- If Player 1 Plunder and Player 2 Conserve: (200, -100)
- If both Plunder: (0, 0)

Now, let’s assess each option option by option to see what it claims and whether that aligns with the logic of the game.

Option 1: Individual equilibrium is (Plunder, Plunder) and social optimum is (Conserve, Conserve)
- Examining individual incentives: If Player 2 chooses Plunder, Player 1’s payoffs are -100 for Conserve and 0 for Plunder. Therefore, Player 1’s best response to Plunder is Plunder. By symmetry, if Player 1 chooses Plunder, Player 2’s best response is also Plunder. Hence (Plunder, Plunder) is a Nash equilibrium (the stable outcome where neither can gain by unilateral deviation).
- Assessing social welfare: The total payoff is highest when both players Conserve (100 + 100 = 200) compared to (Plunder, Plunder) which yields 0 total. Therefore the social optimum is clearly (Conserve, Conserve).
- Verdict on this option: It correctly identifies the equilibrium but incorrectly labels the social optimum as Conserve/Conserve. This makes the statement partly accurate about the equilibrium but incorrect about the social optimum.

Option 2: Both Individual equilibrium and social optimum is (Plunder, Plunder)
- Recalling the earlier analysis, the Nash equilibrium is indeed (Plunder, Plunder) since each player’s best response to the other’s Plunder is Plunder.
- However, as shown, the social optimum is not (Plunder, Plunder) because the combined payoff is 0 there, whereas (Conserve, Conserve) yields a higher total of 200. Hence this option misidentifies the social optimum.
- Verdict on this option: The first part about the equilibrium is correct, but the social optimum claim is false, so the overall statement is incorrect.

Option 3: Both Individual equilibrium and social optimum is (Conserve, Conserve)
- This option asserts that Conserve/Conserve is the equilibrium. Yet, if Player 2 chooses Plunder, Player 1’s best response is Plunder (200 vs -100), and similarly for Player 2. Thus (Conserve, Conserve) is not a Nash equilibrium because each player has an incentive to deviate to Plunder when the other Conserves.
- Regarding social welfare, (Conserve, Conserve) is indeed the social optimum, but since the equilibrium claim is false, the overall statement is incorrect.

Option 4: Individual equilibrium is (Conserve, Conserve) and social optimum is (Plunder, Plunder)
- This flips the correct intuition: the equilibrium is not (Conserve, Conserve) for the reasons just discussed—the dominant strategy is Plunder for both players, making (Conserve, Conserve) not an equilibrium.
- The social optimum being (Plunder, Plunder) is also incorrect, since the best collective payoff occurs at (Conserve, Conserve) with a total of 200.
- Verdict on this option: Both parts are inconsistent with the game’s incentives and welfare analysis, so this option is false.

Summary of reasoning across options: The core ideas are that Plunder is the dominant strategy for each player, yielding the Nash equilibrium (Plunder, Plunder), while the highest combined payoff arises when both players Conserve, giving (Conserve, Conserve). Each option either misstates the equilibrium, the social optimum, or both, which makes them incorrect except for the allowed but incomplete accuracy in Option 1’s equilibrium part.

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