Refer to figure 6: A single fishing firm and the rest of the fishing industry simultaneously choose how intensively to fish in a shared fishery. Higher fishing effort raises short‑run profits for each player but reduces the overall fish stock, affecting the profits of others.

Refer to fig 6 above and select the correct statement:

Question

Refer to figure 6: A single fishing firm and the rest of the fishing industry simultaneously choose how intensively to fish in a shared fishery. Higher fishing effort raises short‑run profits for each player but reduces the overall fish stock, affecting the profits of others.

Refer to fig 6 above and select the correct statement:

BlackTom AI · Accepted Answer

This is a classic tragedy-of-the-commons (prisoner’s dilemma) structure: each fisher’s immediate best response is to increase effort, but mutual overfishing reduces the total stock and lowers everyone’s payoffs.

1) Relevant knowledge points and concepts
- Nash equilibrium: a strategy profile where no player can unilaterally increase payoff.
- Dominant strategy: a strategy that is best regardless of the other player’s action.
- Pareto efficiency: an outcome is Pareto efficient if no other outcome makes some players better off without making others worse off.
- Common-pool resource/tragedy of the commons: individual incentives to extract more lead to overexploitation and collectively worse outcomes.

2) Step-by-step reasoning
- Compare payoffs: raising effort always increases a single firm’s short-run profit, irrespective of the other players’ effort, while higher total effort reduces stock and hence other players’ payoffs.
- Therefore for each player “high effort” strictly dominates “low effort” (the immediate private payoff from choosing high effort is larger whether the other chooses high or low).
- If both players choose high effort, neither can improve by switching to low effort unilaterally, so (high, high) is a Nash equilibrium.
- Consider the joint payoff from (low, low): because stock is preserved, both obtain higher long-run payoffs than at (high, high). Thus (low, low) Pareto-dominates (high, high).

3) Intermediate steps / payoff logic
- Unilateral deviation: from (low, low) one player gains by increasing effort → incentive to deviate.
- From (high, high) unilateral deviation to low reduces that player’s short-run profit → no profitable deviation.

4) Why the correct answer is correct
- There is a unique Nash equilibrium: both choose high effort. That equilibrium is Pareto inferior to the cooperative (low, low) outcome, so it is not Pareto efficient.

5) Why other options are incorrect
- “Coordination game with no clear outcome”: incorrect because incentives point clearly to overfishing; there is a single predictable equilibrium.
- “One of the Nash Equilibria is pareto efficient”: incorrect because the only Nash equilibrium (high, high) is Pareto dominated.
- “There is one Nash Equilibrium which is a Dominant equilibrium”: misleading here — while the equilibrium arises from dominant strategies, the important and correct characterization emphasized by the figure is that this unique equilibrium is not Pareto efficient; the provided option about dominance does not capture that key inefficiency.

6) Conclusion
The unique Nash equilibrium is (both choose high effort) and it is not Pareto efficient; therefore the correct choice is: There is one Nash Equilibrium which is not pareto efficient. This matches the provided answer.

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