Our Gemara on Amud Beis discusses various psychological techniques when considering negotiating with those who kidnap for ransom. 

אֵין פּוֹדִין אֶת הַשְּׁבוּיִין יוֹתֵר עַל כְּדֵי דְמֵיהֶם, מִפְּנֵי תִּקּוּן הָעוֹלָם. הָא בִּכְדֵי דְמֵיהֶן פּוֹדִין, אַף עַל גַּב דְּפִרְקוֹנָהּ יוֹתֵר עַל כְּתוּבָּתָהּ.

One does not redeem captives at more than their value. This policy is for the betterment of the world, because if captives are ransomed at exorbitant prices, this will encourage their captors to kidnap more people. 

Halakha Le’maase, the poskim make distinctions between public policy and private action.  That is, the congregation should not feel burdened with excessive ransoms but family members and even the person himself might be able to pay whatever amount demanded upon them.  (See Shulkan Arukh YD:252:4 Shach and Bach.)

In a modern sense, Israel and America have often publicly declared that they “Do not negotiate with terrorists.”  While the logic of this is probably similar to our Gemara, namely that we do not want to encourage escalation of these tactics, what does the research actually show?

According to researcher Brian Michael Jennings, the findings are not as clear-cut ( Jenkins, Brian Michael, Does the U.S. No-Concessions Policy Deter Kidnappings of Americans?. Santa Monica, CA: RAND Corporation, 2018. https://www.rand.org/pubs/perspectives/PE277.html )

Here are the findings:

Deterrence is offered as the principal reason for the U.S. adherence to a no-concessions policy. Logically, a no-concessions policy should be a deterrent to kidnapping. No concessions means denying a reward to the kidnappers, thereby removing the incentive to kidnap Americans.

Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation cool

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