Lal and Bhattacharjya Theorem 4. Contracting the Short, Pruning the Deep. Optimization in the Private Value Model: How good is the Chord algorithm? The minimum number of colors in a proper distinguish coloring of a graph is called the distinguishing chromatic number of the graph. Nikhil devanur thesis of Applied Probability, 21 3: If a class of games is known to have a Nash equilibrium with probability values that are either zero or Omega 1 and thus with support of bounded sizethen obviously this equilibrium can be found exhaustively in polynomial time.
By extending these techniques we prove a general theorem, showing that, for a far more general class of families of succinctly representable multiplayer games, the Nash equilibrium problem can also be reduced to the two-player case. Therefore, every graph has the same distinguishing number as its complement.
Our result, when combined with the junction tree algorithm for statistical inference, yields a unified proof of all previously known tractable cases of the NP-complete problem of finding pure Nash equilibria in graphical games, but also implies efficient algorithms for new classes, such as the games with O log n treewidth.
Dimakis, Richard Karp and Martin Wainwright: In each of these cycles, assigning a unique color to each of two adjacent vertices and using the third color for all remaining vertices results in a three-color distinguishing coloring. Sequential Mechanisms with Ex-post Participation Guarantees.
Adversarial Training using Generative Models. In view of the intractability of finding a Nash equilibrium, it is important to understand the limits of approximation in this context.
In particular, we show that bounded degree graphs have Nash equilibria with exponentially small probability in the size of the graph and provide a simple algorithm that finds small non-existence certificates for a large family of graphs.
Our proof uses ideas from the recently-established equivalence between polynomial-time solvability of normal-form games and graphical games, and shows that these kinds of games can implement arbitrary members of a PPAD-complete class of Brouwer functions.
We study how the structure of graphical games affects the existence of Nash equilibria. Potanka Virginia Polytechnic University, Reducing Revenue to Welfare Maximization. Fundamental algorithms and algorithmic game theory.
Probability Theory and Related Fields, 3: The sample complexity of auctions with side information. In particular, we are interested to answer whether pure Nash equilibria exist for games played on a given graph; and we study this question over all possible graphical games played on the given graph in the probabilistic sense, by considering the random measure defined by assigning random utility tables to the player-nodes.
In view of empirically successful algorithms available for this problem, this is in essence a positive result even though, due to the complexity of the reductions, it is of no immediate practical significance.
These hardness results suggest that, in some sense, our PTAS is as strong a positive result as one can expect. Phylogenies without Branch Bounds: Mechanism Design becomes Algorithm Design. UW theory group MSR.
The two- and three-dimensional hypercube graphs the 4-cycle and the graph of a cube, respectively have distinguishing number three.This thesis would not exist if not for the help of my numerous coauthors in graduate school: thank you, Pranjal Awasthi, Avrim Blum, Steven Brams, Simina Brnzei, Ioannis Caragian- nis, Nikhil Devanur, Michal Feldman, Deepak Garg, Sampath Kannan, Sean Kennedy, David.
Constantinos Daskalakis, Nikhil Devanur, S. Matthew Weinberg: Revenue Maximization and Ex-Post Budget Constraints.
In the 16th Annual ACM Conference on Economics and Computation. Thesis: Optimization in the Private Value Model: Competitive Analysis Applied to Auction Design Advisor: Anna Karlin. M.S.
in Computer Science. University of Washington, Seattle, WA. with Nikhil Devanur and Bach Ha. Prior-independent Mechanisms for Scheduling. STOC4 with Shuchi Chawla, David Malec, and Balu Sivan. Jason Hartline, Associate Professor.
with Nikhil Devanur and Bach Ha. EC Prior-independent Mechanisms for Scheduling, with Competitive Analysis Applied to Auction Design, Ph.D. Thesis, Aug.
Envy-Free Auctions for Digital Goods, with Andrew Goldberg, EC Nikhil R. Devanur is a researcher in the theory group at Microsoft Research, Redmond.
In this thesis, we examine resource allocation problems in online settings, focusing on problems in data-center scheduling and internet advertising. Our results are summarized as follows.Download