We often overlook the fact that our communication consists of full of implicit messages; for example, "Maybe next time" often means a polite way to say "no"; "Could you pass me the salt?" isn't usually a question; even mere silence could convey the meaning of "as usual." The elusive idea of implicit meaning has attracted the attention of prominent philosophers such as Wittgenstein, Austin, and Grice, whereas it has been largely neglected in the literature of communication games. If many economic activities rely on a natural language, which heavily utilizes implicit communication, why haven't economists studied them much?
One of the main reasons is that economists usually use game theory to model communication, and an implicit message is just another message in communication games. Specifically, each equilibrium message is just a label, and whether a message is implicit or explicit is an irrelevant detail in the standard cheap talk game in Crawford and Sobel (1982).
Is there an economic interaction in which the distinction between implicit and explicit messages plays a substantial role? If so, how can we describe implicit messages in a formal model?
So far, I proposed three ways to incorporate implicit communication into economic models and demonstrated the potential benefits of studying implicit communication formally.
To describe my first approach, suppose that a speaker has two dimensional-aspects to communicate, and one of the aspects can be interpreted as the primary information given a context. Then, the informational content of a message about the primary aspect can be interpreted as the denotation of the message, whereas the content of the message about the secondary aspect can be interpreted as the implicit meaning of the message.
My paper Directives, Expressives and Motivation, Theoretical Economics (2017) is based on the above approach. In this paper, the denotation of a principal's message is an instruction to the agent, and the secondary information is the principal's belief about the agent. Thus, the principal's instruction could implicitly express her belief about the agent through her instructions. It is shown that a sensible principal could fail to provide useful instructions if the instruction could convey the implicit meaning of distrust to the agent.
The second approach is based on the fact that one can remind of something specific by explicitly referring it, whereas one cannot do it by being silent. Thus, if a listener has limited memory, the difference between explicit and implicit messages is not an irrelevant detail anymore.
My paper Reminder Game: Indirectness in Persuasion, Games and Economic Behavior (2016) is built on the above observation. A decision maker forms her consideration set given her memory capacity based on noisy information about each alternative. A "persuader" who wants her to select a particular choice regardless of the value decides whether to send her a reminder. It is found that the persuader's reminder could backfire; the fact that he sends the reminder conveys the negative information about the recommended choice. Thus, in this context, remaining silent is an implicit yet persuasive message for the persuader.
The thrid approach is based on a simple fact that if messaging is costly, implicit and explicit messages are distinctive economic activities. Then, if the communication rule, i.e., pragmatics, is determined by a fictituous linguistic designer to economize cooperative communiation, the meaning of informative silence should be determined by the efficient communication rule.
My paper Efficient Communication and Indexicality Mathematical Social Sciences shows that, when the notion of context is defined as the finrest mutally self-evident event, the meaning of informative silence in the efficient communication rule is the "most common situation" given the context. That is, while silence has no fixed meaning, it conveys the information systematically once the context is fixed. A sign that refers to an object systematically given a context is called indexical in lingusitics. For example, "I" is an indexical since it does not refer to any person by itself but once the contextual information "the spekaer" is given, "I" refers to the specific person. My paper shows that informative silence exhbits indeixicality in any efficient communication rule.