Final Report Summary - ALGAME (Algorithms, Games, Mechanisms, and the Price of Anarchy) The project aimed to advance important research directions of algorithmicgame theory. Our group managed to substantially extend the state of theart in multiple fronts of this multi-faceted research area. Thisincludes the following specific advances.We developed a novel theory for designing and analyzing incentivecompatible mechanisms and auctions. For this, we developed a duality frameworkfor partial differential constraints, which is based in extending thetheory of linear programming to infinite programs. Combining it withthe theory of matchings and using multidimensional geometricisoperimetric inequalities, we succeeded in extending Myerson's theoryof optimal auctions to two items and to the important special case ofuniform distributions of multiple items. This has been an open problemfor 35 years and one of the most fundamental and difficult questionsin auction theory.In other fronts, we made significant progress progress inunderstanding the limitations of incentive compatible algorithmic environments, thatis, when the input to an algorithm is provided by selfish agentsthat are have a stake in the outcome. This question is nicely capturedby the Nisan-Ronen conjecture for the scheduling problem, a majoropen problem of the last two decades. We managed to make progress inthis question by generalizing it and showing that incentivecompatibility substantially limits the power of algorithms for domainsthat differ very little from scheduling.The dual research direction to incentive compatibility asks about thelimitations of algorithms that are executed by selfishagents. Blockchains provide the best example of such distributedalgorithms. Our work on blockchains includes a rigorous approach andanalysis of blockchain mining games, as well as the study of theirextensions when the agents can pay forward other agents or manipulatethe energy that they expend for mining.
