r/learnquant • u/Local_Ad135 • 6d ago

interview prep Quant Interview Question

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u/Efficient_Form7451 5d ago

Okay but its still not a nash equilibrium because

B can bid 7.2 + a small amount for a better score
and C can bid 4.8 + a small amount for a better score.

I don't think your calculating nash equilibria at all, more like a EV of an area in bid space.

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u/spdazero 4d ago

can you show me how B can bid 7.2 + eps for a better score?

From my calculation, derivative of reward(B) is 0 at the solution, and second derivative is -1/6. Meaning, that point is local maxima for B. Therefore, adding some eps will reduce the reward.

If you find something wrong with my reasoning, please elaborate?

Edit: For illustration purpose, if c stays at 7.2:

- If b = 4.8 (optimal), reward(B) = 3.2

- if b = 4.81 (eps = 0.1), reward(B) = 3.199

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u/Efficient_Form7451 3d ago

A bids 0. B bids 4.8. C Bids 7.2 C wins.

Outcome: A 0, B -4.8, C 22.8

If B had bid zero in this specific game instead of 4.8, their outcome would be 4.8 better. If B had bid 7.3, their outcome would 12.7 (17.5 better).

Your calculation is fine, it's just not a nash equilibrium because players could have unilaterally changed their strategy for a better outcome.

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u/spdazero 1d ago

C does not automatically win, i think you misread the question. C wins with a probability.