<p>In the revenue-maximizing auction as defined by Myerson '81 there are two sources of inefficiency. The optimal allocation awards the good to the buyer with the highest virtual value, given this virtual value is non-negative. The virtual value is defined as <span class="math-container">$\theta_i  - \frac{1-F_i(\theta_i)}{f_i(\theta_i)}$</span>, using the standard notation.</p>
<ol>
<li><p>The good may not be allocated although trade is efficient. This case cannot occur if the virtual values are always positive. Intuitively, if the lowest possible value weighted by the density at that point is sufficiently high.</p>
</li>
<li><p>The good may not be allocated to the agent with the highest value (if the ranking of virtual values and actual values does not coincide). This case cannot occur if all values are drawn from the same distribution.</p>
</li>
</ol>

CC BY-SA 4.0
2023-04-05T12:18:00.823Z
2023-04-05T12:18:00.823Z
Bayesian
<p>Is it true that in the design of the expected revenue maximizing auction in the standard independent private value setting, the allocation of the object may be ex-post inefficient?</p>

<auctions><expected-utility>
Expected revenue maximizing auction & ex-post efficiency
Michael
# Expected revenue maximizing auction & ex-post efficiency

(Asked by: username_0 on 2022-11-10)

Is it true that in the design of the expected revenue maximizing auction in the standard independent private value setting, the allocation of the object may be ex-post inefficient?

**Tags:** auctions, expected-utility

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## 1 answers

### Answer by username_1 on 2023-04-05. Score: 0

In the revenue-maximizing auction as defined by Myerson '81 there are two sources of inefficiency. The optimal allocation awards the good to the buyer with the highest virtual value, given this virtual value is non-negative. The virtual value is defined as $\theta\_i - \frac{1-F\_i(\theta\_i)}{f\_i(\theta\_i)}$, using the standard notation.

1. The good may not be allocated although trade is efficient. This case cannot occur if the virtual values are always positive. Intuitively, if the lowest possible value weighted by the density at that point is sufficiently high.
2. The good may not be allocated to the agent with the highest value (if the ranking of virtual values and actual values does not coincide). This case cannot occur if all values are drawn from the same distribution.


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