0
$\begingroup$

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?

$\endgroup$

1 Answer 1

3
$\begingroup$

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.

$\endgroup$
6
  • $\begingroup$ Do Gale and Shapley establish the existence of a core? $\endgroup$ Dec 7, 2020 at 9:00
  • 1
    $\begingroup$ 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. $\endgroup$
    – Bayesian
    Dec 7, 2020 at 9:01
  • $\begingroup$ Does Shapley and Shubik (1971) use quasi-linear preferences? $\endgroup$ Dec 7, 2020 at 9:06
  • $\begingroup$ I edited my answer. $\endgroup$
    – Bayesian
    Dec 7, 2020 at 9:17
  • $\begingroup$ Thanks so much!! $\endgroup$ Dec 7, 2020 at 9:19

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.