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Complexity and Simplicity in Economic Mechanisms

Periodic Reporting for period 4 - COMPECON (Complexity and Simplicity in Economic Mechanisms)

Reporting period: 2021-11-01 to 2023-04-30

As more and more economic activity is moving the Internet, familiar economic mechanisms are being deployed at unprecedented scales of size, speed, and complexity. In many cases this new complexity becomes the defining feature of the deployed economic mechanism and the quantitative difference becomes a key qualitative one. A well-studied example of such situations is how the humble single-item auction suddenly becomes a billion-times repeated online ad auction, or even becomes a combinatorial auction with exponentially many possible outcomes. Similar complexity explosions occur with various markets, with information dissemination, with pricing structures, and with many other economic mechanisms.

The aim of this proposal is to study the role and implications of such complexity and to start developing a coherent economic theory that can handle it. We aim to identify various measures of complexity that are crucial bottlenecks and study them. Examples of such complexities include the amount of access to data, the length of the description of a mechanism, its communication requirements, the cognitive complexity required from users, and, of course, the associated computational complexity. On one hand we will attempt finding ways of effectively dealing with complexity, when needed, and on the other hand, attempt avoiding complexity, when possible, replacing it with ``simple'' alternatives without incurring too large of a loss.
We analyzed a host of economic scenarios where complexity plays a crucial role and studied to what extent can we mitigate said complexity. The answers are varied and nuanced. Some of the major models and scenarios that we have studied include:

(*) Complexity of multi-item auctions where we understand to a large extent the trade-off between complexity and revenue, as well as the required "information gathering" complexity involved.
(*) The complexities of communication, information exchange, and preference elicitation in several complex scenarios such as fair cake cutting, local equilibria, and fixed-point computation.
(*) Dynamics in Growing Markets.
(*) The dynamics and induced incentives of learning agents that participate in repeated games and auctions for their users.
This project achieved a host of new results that go beyond the state of the art in understanding the different the complex economic scenarios studied, in each case utilizing different techniques and achieving different results.

Beyond the many specific results obtained, an integrative "bigger picture" understanding emerged in three significant areas:

(*) Complexity of multi-item auctions: the trade-off between complexity and revenue
(*) Sample complexity needed for estimating value and bid distributions in auctions
(*) The role of communication in a multitude of complex market-like economic scenarios

New directions for research were opened regarding the dynamics and induced incentives of learning agents that participate in repeated games and auctions for their users.

Finally, our research that was motivated by economic scenarios has yielded back interesting questions in pure complexity.