<p>Gale and Shapley barely make any assumptions about preferences. They don't need a functional form, simply an ordinal ranking of the options. Moreover, there are no transfers in this setting, only the discrete matching options.</p>
<p>Even Kelso and Crawford do not use quasi-linear utility. They assume some utility function that is increasing and continuous in salary, but not necessarily linearly increasing.</p>
<p>In Shapley and Shubik (1971) monetary transfers enter linearly.
However, I wouldn't call this quasi-linear utility, because in quasi-linear utility most people have the following functional form over a good <span class="math-container">$x$</span> and money <span class="math-container">$m$</span> in mind: <span class="math-container">$u(x,m) = v(x) - m$</span>, where <span class="math-container">$v$</span> is a continuous function.
In their model, the <span class="math-container">$v(x)$</span> is simply the money value of house <span class="math-container">$x$</span>, where the houses are district options.</p>

CC BY-SA 4.0
2020-12-07T09:00:02.550Z
Do Gale and Shapley establish the existence of a core?
Friendlyperson2020
CC BY-SA 4.0
2020-12-07T09:01:43.303Z
They may not mention it as "the core." However, they prove the existence of stable allocations, which is the same as "the core" in their setting.
Bayesian
CC BY-SA 4.0
2020-12-07T08:56:37.453Z
2020-12-07T09:17:47.743Z
2020-12-07T09:17:47.743Z
Bayesian
<p>Is it correct to say that preferences in the classic Gale and Shapley College Admissions problem are quasi-linear?</p>
<p>Or is this something thats introduced later in the literature, vis a vis Shapley and Shubik (1971), Kelso and Crawford (1982), etc?</p>

<microeconomics><game-theory><preferences><search-and-matching><matching>
Question regarding preferences in Gale and Shapley (1962)
Friendlyperson2020
# Question regarding preferences in Gale and Shapley (1962)

(Asked by: username_0 on 2020-12-07)

Is it correct to say that preferences in the classic Gale and Shapley College Admissions problem are quasi-linear?

Or is this something thats introduced later in the literature, vis a vis Shapley and Shubik (1971), Kelso and Crawford (1982), etc?

**Tags:** microeconomics, game-theory, preferences, search-and-matching, matching

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## 1 answers

### Answer by username_1 on 2020-12-07. Score: 3 | Accepted answer

Gale and Shapley barely make any assumptions about preferences. They don't need a functional form, simply an ordinal ranking of the options. Moreover, there are no transfers in this setting, only the discrete matching options.

Even Kelso and Crawford do not use quasi-linear utility. They assume some utility function that is increasing and continuous in salary, but not necessarily linearly increasing.

In Shapley and Shubik (1971) monetary transfers enter linearly.
However, I wouldn't call this quasi-linear utility, because in quasi-linear utility most people have the following functional form over a good $x$ and money $m$ in mind: $u(x,m) = v(x) - m$, where $v$ is a continuous function.
In their model, the $v(x)$ is simply the money value of house $x$, where the houses are district options.

> **Comments:**
> **username_0**: Do Gale and Shapley establish the existence of a core?  
> **username_1**: They may not mention it as "the core." However, they prove the existence of stable allocations, which is the same as "the core" in their setting.  

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