Pooling equilibrium

{{Short description|Equilibrium outcome of a signaling game}}

{{More citations needed|date=February 2024}}

A pooling equilibrium in game theory is an equilibrium outcome of a signaling game.Ellison, Glenn. "[https://ocw.mit.edu/courses/14-122-microeconomic-theory-ii-fall-2002/0c77aa544ed2ea3d26fed6f9e4460551_pbe.pdf Game Theory 14.122: Handout #l Finding PBE in Signaling Games]", [https://ocw.mit.edu/courses/14-122-microeconomic-theory-ii-fall-2002/ Microeconomic Theory II]. MIT OpenCourseWare.[https://www.oxfordreference.com/display/10.1093/oi/authority.20110803100336941#:~:text=An%20equilibrium%20in%20which%20agents,choosing%20the%20same%20insurance%20contract pooling equilibrium]. Oxford Reference. Retrieved 6 Feb. 2024.

In a signaling game, players send actions called "signals" to other players. These signals are based on privately held information, which is not known to others in the game.{{Cite journal |last1=Bergstrom |first1=Carl T. |last2=Számadó |first2=Szabolcs |last3=Lachmann |first3=Michael |date=2002-11-29 |editor-last=Johnstone |editor-first=R. A. |editor2-last=Dall |editor2-first=S. R. X. |title=Separating equilibria in continuous signalling games |journal=Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences |language=en |volume=357 |issue=1427 |pages=1595–1606 |doi=10.1098/rstb.2002.1068 |issn=0962-8436 |pmc=1693066 |pmid=12495516}} These actions do {{em|not}} reveal a player's "type" to other players, who then choose their strategies accordingly. In a pooling equilibrium, all types of a given sender send the same signal. Some senders represent their true type, while others correctly mimic the type of others, having no incentive to differentiate themselves. As a result, the receiver acts as if they have received no information, maximizing their utility according to their prior beliefs.{{Citation |last=Sobel |first=Joel |title=Signaling Games |date=2020 |work=Complex Social and Behavioral Systems : Game Theory and Agent-Based Models |pages=251–268 |editor-last=Sotomayor |editor-first=Marilda |url=https://doi.org/10.1007/978-1-0716-0368-0_481 |access-date=2024-06-30 |place=New York, NY |publisher=Springer US |language=en |doi=10.1007/978-1-0716-0368-0_481 |isbn=978-1-0716-0368-0 |editor2-last=Pérez-Castrillo |editor2-first=David |editor3-last=Castiglione |editor3-first=Filippo|url-access=subscription }}