CO 759 : Algorithmic Game Theory — Fall 2010

CMSC 858F: Algorithmic Game Theory Fall 2010 Achieving Byzantine Agreement and Broadcast against Rational Adversaries

1 Overview In this presentation, we describe byzantine agreement and broadcast with respect to rational adversaries with particular preferences on the output of the honest players.

CMSC 858 F : Algorithmic Game Theory Fall 2010 Complexity of finding Nash equilibrium : PPAD completeness results

Nash’s theorem guarantees the presence of mixed nash equilibrium in every finite game. We are concerned here with the problem of finding such an equilibrium efficiently. In other words, does there exist an algorithm to find the mixed nash equilibrium in polynomial time? The answer to this question is not known but it is known finding mixed Nash equilibrium is PPAD complete, which implies some s...

CMSC 858 F : Algorithmic Game Theory Fall 2010 Market Clearing with Applications

We will look at MARKET CLEARING or MARKET EQUILIBRIUM prices. We will consider two models with linear utilities : FISHER model and ARROWDEBREU model. See [1] and chapter 5 of [2] for more details. Finally we see an application of the FISHER model to wireless networks. I have also used as reference the scribe notes for this same lecture when this course was taught by Prof. Hajiaghayi at Rutgers ...

CMSC 858F: Algorithmic Game Theory Fall 2010 Frugality & Profit Maximization in Mechanism Design

Recall from the previous lecture that in combinatorial auction each bidder has an associated real-valued valuation function V defined for each subset of items S. An allocation of items S1, S2, . . . , Sn among the bidders with valuation function V1, V2, . . . , Vn respectively is socially efficient if the allocation maximizes the social welfare ∑ i Vi(Si). Combinatorial auction is a very genera...

Algorithmic game theory