Agreeing to agree and Dutch books

• Main Authors: CHEN, Yi-Chun, LEHRER, Ehud, LI, Jiangtao, SAMET, Dov, SHMAYA, Eran
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2015
• Subjects: Agreement theorem; Common knowledge; Common prior; Dutch book; No trade theorem; Economic Theory
• Online Access: https://ink.library.smu.edu.sg/soe_research/2199; https://ink.library.smu.edu.sg/context/soe_research/article/3198/viewcontent/1_s20_S0899825615001141_main.pdf
• Institution: Singapore Management University

We say that agreeing to agree is possible for an event E if there exist posterior beliefs of the agents with a common prior such that it is common knowledge that the agents' posteriors for E coincide. We propose a notion called Dutch book which is a profile of interim contracts between an outsider and the agents based on the occurrence of E, such that the outsider makes positive profit in all states. We show that in a finite state space, when the agents cannot tell whether Eoccurred or not, agreeing to agree is possible for E if and only if there is no Dutch book on E. This characterization also holds in countable state spaces with two agents. We weaken the notion of Dutch book to characterize agreeing to agree in a countable state space with multiple agents, when each set in each agent's information partition is finite.