Optimal Communication Schemes for Utility Maximizing Teens: Essays on the Economic Design of Communicative Structures

Designing communication systems and protocols in the real-world often involves various subproblems such as: a) “what information should be sent?”, b)“how to syntactically encode this information to messages?”, c) “how to reliably transmit these messages?” among other similar questions, and d) since communication is often means to some end, “how can the communicated information be used at destination?”. While information theory and communication engineering allow us to approach a significant half of these problems, aspects such as ”what should be communicated?” and ”how should the information be used?” often demand accounting for the context and underlying objectives of designing communication systems. Building upon economic theories of communication and signaling, we approach the problem of engineering of communicative structures within an economic paradigm, and discuss various algorithmic and game-theoretic issues that emerge from this exploration. We first study the problem of optimal lossy compressions – of comparing different ways to compress a piece of information on the basis of economic utility – when communication takes place between cooperating agents. Using ideas from combinatorial optimization, we present approximation algorithms for the simple version of the problem, as well as in the presence of side-information and in presence of uniform noise. We then study the problem of designing communicative structures in presence of strategic behaviour from Sender and Receiver. We discuss three forms of design problems in this model: a) Sender-led design, b) Receiver-led design, and c) Design by some third-party principal. For the first two, we discuss the general model, Best Response characterizations, Stackelberg (or leader-follower) equilibriums, and the relevant versions of revelation principle. We also present the associated linear programs for solving them under unbounded communication and noiseless conditions, and discuss the relationship with related ideas in Persuasion and Mechanism Design. We also show the existence of instances of Sender-led (or Receiver-led) design problem where the presence of exogenous (stochastic) noise has gainful (or welfare-positive) effects for the Receiver (or the Sender respectively).

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