<p>If we align all buyers in ascending order according to their willingness to pay, a buyer will buy the product only if his willingness to pay matches the price or is above it, set by market,in case of perfect competition, or a firm(s), in case of any of externality in the market.
So the expected number of buyers using your said setup can only be calculated if we happen to know the price existing in the market, since we happen to all other factors required to calculate expectation, i.e., range and a probability distribution function.</p>

CC BY-SA 4.0
2023-05-31T18:17:29.077Z
2023-05-31T18:17:29.077Z
Aditya Agarwal
<p>There is a continuum of players who want to buy a product. The utility to each player from that product is <span class="math-container">$q$</span>. If he does not buy the product, his utility is zero. The random variable, <span class="math-container">$q$</span>, has a uniform distribution over the interval <span class="math-container">$[x_1,y_1]$</span>, where <span class="math-container">$x_1&lt;y_1$</span>. The players use a mixed strategy <span class="math-container">$z=\frac{1-\frac{q}{y_1}}{a-q}$</span> to buy the product, where <span class="math-container">$a&gt;y_1$</span> is a constant and <span class="math-container">$x_1 \leq q \leq y_1$</span>, i.e. a player buys the product with probability <span class="math-container">$z$</span>. How can one calculate the expected number of buyers using this setup? If yes, how do we do that? If not, what other information is required?</p>

<microeconomics><game-theory>
Expected number of players buying a product
Ramandeep
# Expected number of players buying a product

(Asked by: username_0 on 2023-05-31)

There is a continuum of players who want to buy a product. The utility to each player from that product is $q$. If he does not buy the product, his utility is zero. The random variable, $q$, has a uniform distribution over the interval $[x\_1,y\_1]$, where $x\_1. The players use a mixed strategy $z=\frac{1-\frac{q}{y\_1}}{a-q}$ to buy the product, where $a>y\_1$ is a constant and $x\_1 \leq q \leq y\_1$, i.e. a player buys the product with probability $z$. How can one calculate the expected number of buyers using this setup? If yes, how do we do that? If not, what other information is required?

**Tags:** microeconomics, game-theory

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## 1 answers

### Answer by username_1 on 2023-05-31. Score: 1

If we align all buyers in ascending order according to their willingness to pay, a buyer will buy the product only if his willingness to pay matches the price or is above it, set by market,in case of perfect competition, or a firm(s), in case of any of externality in the market.
So the expected number of buyers using your said setup can only be calculated if we happen to know the price existing in the market, since we happen to all other factors required to calculate expectation, i.e., range and a probability distribution function.


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