Part 1Novo and Pharm, the only two producers of cold medication, play a research and development (R&D) gameThe table shows their economic profit in a payoff matrix for the game they play. At the Nash equilibrium, what is Novo's economic profit and what is Pharm's economic profit? Part 1At the Nash equilibrium, Novo's economic profit is _______ million and Pharm's economic profit is _______ million. A. minus−$3; $50 B. $15; $15 C. $10; $10 D. $50; minus−$3 Part 1[table]
| | Novo's strategies (red squares) | | R&D | | No R&D Pharm's strategies (blue squares) | R&D | | $10m | | | minus−$3m $10m | | | $50m | | | | | | No R&D | | $50m | | | $15m minus−$3m | | | $15m |
[/table]

Question

Part 1Novo and​ Pharm, the only two producers of cold​ medication, play a research and development​ (R&D) gameThe table shows their economic profit in a payoff matrix for the game they play. At the Nash​ equilibrium, what is​ Novo's economic profit and what is​ Pharm's economic​ profit? Part 1At the Nash​ equilibrium, Novo's economic profit is​ _______ million and​ Pharm's economic profit is​ _______ million. A. minus−​$3; ​$50 B. ​$15; $15 C. ​$10; $10 D. ​$50; minus−​$3 Part 1[table]
|  | ​Novo's strategies ​(red squares) |  | ​ R&D |  | No​ R&D ​Pharm's strategies ​(blue squares) | ​R&D |  | ​$10m |  |  | minus−​$3m ​$10m |  |  | ​$50m |  |  |  |  |  |  No​ R&D |  | ​$50m |  |  | ​$15m minus−​$3m |  |  | ​$15m | 
[/table]

BlackTom AI · Accepted Answer

Here is the problem restated and analyzed option by option to understand which outcome is consistent with a Nash equilibrium in the given R&D game.

Option A: 'minus $3; $50' — This would imply Novo earns -3 and Pharm earns 50 at the Nash equilibrium. To reach such a pairing, the matrix would need to place Novo's best response to Pharm’s equilibrium choice at a negative payoff for Novo while Pharm secures a very high payoff. However, in most R&D coordination games, such a highly asymmetric outcome at equilibrium is unusual unless one player has a dominant strategy that leads to a negative payoff for the other. Without seeing the exact best-response structure that yields Novo negative profit while Pharm earns 50, this option seems inconsistent with typical Nash equilibria in symmetric bi-matrix payoff tables like this one, where both firms have comparable payoff ranges.

Option B: '$15; $15' — This corresponds to a symmetric equilibrium where both Novo and Pharm earn 15. Symmetry is plausible in a two-player R&D payoff table, but we must check whether 15 is the surplus each player would receive in a Nash equilibrium given the other player's strategy. If either player could increase their payoff by unilaterally changing strategies (from R&D to No R&D or vice versa) while the other keeps theirs fixed, then 15 would not be a Nash equilibrium payoff. The existence of larger payoffs in some cells (like 50) can affect incentives to deviate. Therefore, unless both players’ best responses line up exactly at 15, this option may not be the equilibrium outcome.

Option C: '$10; $10' — A symmetric outcome where both Novo and Pharm earn 10. This is a common shape for a Nash equilibrium in symmetric payoff matrices, especially when each player’s best response to the other’s strategy results in the same payoff for both. If, given the rival’s move, each firm’s optimal reply yields 10, then neither firm benefits by deviating unilaterally. This aligns with the typical Nash equilibrium idea where both players settle at a mutually consistent payoff that is not improvable by unilateral deviation.

Option D: '$50; -$3' — This would have Novo earning 50 while Pharm loses 3. A highly asymmetric equilibrium like this would require Pharm to have no profitable unilateral deviation that would push Pharm’s payoff up from -3, and Novo to have no profitable deviation that would be worse for Novo than 50. In many payoff structures, such a lopsided outcome is unlikely to be stable as the disadvantaged player would have a strong incentive to change strategy to improve their own payoff. Without a justification from the best-response curves that preserves both parties at (50, -3), this option seems unlikely to be the Nash equilibrium.

Putting the reasoning together, and considering the symmetry and payoff possibilities shown in typical R&D payoff tables, the equilibrium coordinates that balance best responses for both firms are the equal payoffs, reflecting a mutual best response given the other’s action. Therefore, the pair that matches this symmetry and common equilibrium outcome is the one where both firms receive 10. The other options involve drastic asymmetries or potential deviations that would violate the Nash equilibrium condition in most interpretations of this table.

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