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In Gift game 1, why do not we have equilibria where the receiver accepts the gift with probability 1/2?

The info box states that the PBE was proposed by Cho and Kreps.

As far as I understand, Cho and Kreps proposed the "intuitive criterion" for selection of "reasonable" equilibria in 1987 (probably a somewhat imprecise description). However, the PBE as a solution method has been used in economics way earlier than this. Spence's model on education as signalling (1973) and Milgrom and Roberts model on limit pricing (1982) are just two examples.

I'm genuinely curious about the history of PBE as a solution concept in economics. Would be happy if someone with more knowledge on the topic than myself could extent the article to include this. Cheers. — Preceding unsigned comment added by 193.157.252.221 (talk) 09:52, 18 January 2017 (UTC)[reply]

In "A PBE is always an NE but may not be an SPE." PBE is Perfect Bayesian Equilibrium and SPE is subgame perfect equilibrium but what is NE? --Jid~enwiki (talk) 08:53, 3 April 2018 (UTC)[reply]

@Jid~enwiki: Nash Equilibrium. --Erel Segal (talk) 16:51, 3 May 2021 (UTC)[reply]

If indeed "A PBE is a refinement of both Bayesian Nash equilibrium (BNE) and subgame perfect equilibrium (SPE)," then the sentence "A PBE is always an NE but may not be an SPE" is incorrect (assuming that NE means Nash Equilibrium). Pegasusgr (talk) 20:22, 6 April 2018 (UTC)[reply]

This is fixed as of 2020.

--editeur24 (talk) 21:31, 7 December 2020 (UTC)[reply]

"On paths of zero probability, known as off-equilibrium paths, the beliefs must be specified but can be arbitrary." — The beliefs can only be arbitrary in weak perfect Bayesian equilibrium (originally known as weak sequential equilibrium, Myerson 1997 "Game Theory: Analysis of Conflict"). In perfect Bayesian equilibrium there is an extra requirement that beliefs must satisfy Bayes' rule "wherever possible", which essentially means that they can only be "made up" right after a zero-probability event and must then be maintained (Bayes-updated) forever until another zero-probability event occurs. Curious Mr. EZ (talk) 01:07, 22 March 2023 (UTC)[reply]