Language Games: Correlation through Non-Understanding,Dialogue, Inarticulateness, and Misunderstanding (This Version -- May 2024)
Abstract: A language game is a finite complete-information game preceded by pre-play communication with explicit constraints on players' ability to produce and understand messages and on their knowledge of each other's constraints. Players communicate directly and publicly but may not understand or may misunderstand each other's messages. The paper gives conditions under which it is possible to implement correlated equilibria outside the convex hull of the set of Nash equilibria through language games. These conditions can be satisfied in games with any numbers of players, including two. In the game of Chicken it is possible to induce the entire set of correlated equilibria via a language game.
Strategic Information Transmission in the Employment Relationship (This Version -- April 2024)
Abstract: Formal procedures for dealing with information in organizations may be costly to set up. Informal ones may be more vulnerable to opportunism. We study the tradeoffs by introducing strategic communication a la Crawford and Sobel (1982) into Simon’s (1951) model of the employment relationship. A contract specifies the principal’s “range of authority” and a fixed wage for the agent. With extreme conflict, optimal contracts minimize the range of authority and preclude communication. With little conflict they maximize the range of authority and induce influential communication. They divide the state space into approximately equal-sized topics. Topics are bounded by actions over which the principal has authority and contain approximately equal numbers of cheap-talk actions.
Meaning in Communication Games (This Version -- May 2024)
Abstract: This paper investigates the strategic use of a pre-existing language. It proposes an iterative procedure, interpreted as a mental process on part of the sender, that associates a set of Bayesian Nash equilibria, which we dub language equilibria, with every combination of a sender-receiver game and a pre-existing language. Every sender-receiver game has a language equilibrium when there is no uncertainty about language. Language equilibrium makes sharp predictions about equilibrium outcomes (taken to be joint distributions over types and actions) in common-interest games, in games with sender-ideal equilibria, and in games with partial incentive alignment. This is the case when, as is frequently assumed, the language is rich, but also when the language is impoverished. Importantly, unlike earlier suggestions for how to invoke the role of a pre-existing language in sender-receiver games, language equilibrium makes predictions about language use, i.e., joint distributions over types, actions, and messages.