1

December 2017
ACM Transactions on Economics and Computation (TEAC) - Special Issue on Wine'15: Volume 5 Issue 4, December 2017

**Publisher:** ACM

**Bibliometrics**:

Citation Count: 0

Downloads (6 Weeks): 20, Downloads (12 Months): 20, Downloads (Overall): 20

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The Stackelberg equilibrium is a solution concept that describes optimal strategies to commit to: Player 1 ( the leader ) first commits to a strategy that is publicly announced, then Player 2 ( the follower ) plays a best response to the leader’s choice. We study the problem of computing ...

**Keywords**:
Algorithmic game theory, Extensive-Form Correlated Equilibrium, extensive-form games, finite sequential games, stackelberg equilibrium

2

December 2016
WINE 2016: Proceedings of the 12th International Conference on Web and Internet Economics - Volume 10123

**Publisher:** Springer-Verlag New York, Inc.

We study the truthful facility assignment problem, where a set of agents with private most-preferred points on a metric space are assigned to facilities that lie on the metric space, under capacity constraints on the facilities. The goal is to produce such an assignment that minimizes the social cost, i.e., ...

3

December 2015
WINE 2015: Proceedings of the 11th International Conference on Web and Internet Economics - Volume 9470

**Publisher:** Springer-Verlag New York, Inc.

The Stackelberg equilibrium is a solution concept that describes optimal strategies to commit to: Playerï��1 the leader first commits to a strategy that is publicly announced, then Playerï��2 the follower plays a best response to the leader's choice. We study Stackelberg equilibria in finite sequential i.e., extensive-form games and provide ...

4

February 2015
Information and Computation: Volume 240 Issue C, February 2015

**Publisher:** Academic Press, Inc.

We initiate a comprehensive study of the complexity of computing Boolean functions by polynomial threshold functions (PTFs) on general Boolean domains (as opposed to domains such as { 0 , 1 } n or { - 1 , 1 } n that enforce multilinearity). A typical example of such a ...

**Keywords**:
Communication complexity, Polynomial threshold functions, Threshold circuits

5

August 2014
Theory of Computing Systems: Volume 55 Issue 2, August 2014

**Publisher:** Springer-Verlag New York, Inc.

Two standard algorithms for approximately solving two-player zero-sum concurrent reachability games are value iteration and strategy iteration . We prove upper and lower bounds of $2^{m^{\varTheta(N)}}$ on the worst case number of iterations needed by both of these algorithms for providing non-trivial approximations to the value of a game with ...

**Keywords**:
Strategy iteration, Concurrent reachability games, Value iteration, Analysis of algorithms

6

August 2014
Theory of Computing Systems: Volume 55 Issue 2, August 2014

**Publisher:** Springer-Verlag New York, Inc.

Boolean functions that have constant degree polynomial representation over a fixed finite ring form a natural and strict subclass of the complexity class ACC 0 . They are also precisely the functions computable efficiently by programs over fixed and finite nilpotent groups. This class is not known to be learnable ...

**Keywords**:
Membership queries, Modular gates, Polynomials over finite rings, Exact learning

7

November 2013
Discrete Applied Mathematics: Volume 161 Issue 16-17, November, 2013

**Publisher:** Elsevier Science Publishers B. V.

For matrix games we study how small nonzero probability must be used in optimal strategies. We show that for nxn win-lose-draw games (i.e. (-1,0,1) matrix games) nonzero probabilities smaller than n^-^O^(^n^) are never needed. We also construct an explicit nxn win-lose game such that the unique optimal strategy uses a ...

**Keywords**:
Nonnegative inverse, Ill-conditioned matrices, Matrix games

8

October 2013
IEEE Transactions on Information Theory: Volume 59 Issue 10, October 2013

**Publisher:** IEEE Press

We bound the minimum number $w$ of wires needed to compute any (asymptotically good) error-correcting code $C:\{0,1\}^{\Omega (n)}\to\{0,1\}^{n}$ with minimum distance $\Omega (n)$ , using unbounded fan-in circuits of depth $d$ with arbitrary gates. Our main results are: 1) if $d=2$ , then $w=\Theta (n ({\lg n/\lg\lg n})^{2})$ ; 2) ...

9

October 2012
SAGT 2012: Proceedings of the 5th International Symposium on Algorithmic Game Theory - Volume 7615

**Publisher:** Springer-Verlag New York, Inc.

We consider the problem of approximating the minmax value of a multi-player game in strategic form. We argue that in three-player games with 0-1 payoffs, approximating the minmax value within an additive constant smaller than ï�ź/2, where $\xi = \frac{3-\sqrt5}{2} \approx 0.382$, is not possible by a polynomial time algorithm. ...

10

October 2012
SAGT'12: Proceedings of the 5th international conference on Algorithmic Game Theory

**Publisher:** Springer-Verlag

We consider the problem of approximating the minmax value of a multi-player game in strategic form. We argue that in three-player games with 0-1 payoffs, approximating the minmax value within an additive constant smaller than ξ /2, where $\xi = \frac{3-\sqrt5}{2} \approx 0.382$, is not possible by a polynomial time ...

11

May 2012
STOC '12: Proceedings of the forty-fourth annual ACM symposium on Theory of computing

**Publisher:** ACM

**Bibliometrics**:

Citation Count: 1

Downloads (6 Weeks): 3, Downloads (12 Months): 9, Downloads (Overall): 198

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We bound the minimum number w of wires needed to compute any (asymptotically good) error-correcting code C:{0,1} Ω(n) -> {0,1} n with minimum distance Ω(n), using unbounded fan-in circuits of depth d with arbitrary gates. Our main results are: (1) If d=2 then w = Θ(n ({log n/ log log ...

**Keywords**:
bounded-depth circuits, error-correcting codes, hashing, lower bounds, superconcentrators

12

June 2011
CSR'11: Proceedings of the 6th international conference on Computer science: theory and applications

**Publisher:** Springer-Verlag

Two standard algorithms for approximately solving two-player zerosum concurrent reachability games are value iteration and strategy iteration. We prove upper and lower bounds of 2 m Θ( N ) on the worst case number of iterations needed for both of these algorithms to provide non-trivial approximations to the value of ...

13

June 2011
CSR'11: Proceedings of the 6th international conference on Computer science: theory and applications

**Publisher:** Springer-Verlag

Boolean functions that have constant degree polynomial representation over a fixed finite ring form a natural and strict subclass of the complexity class ACC 0 . They are also precisely the functions computable efficiently by programs over fixed and finite nilpotent groups. This class is not known to be learnable ...

14

June 2011
STOC '11: Proceedings of the forty-third annual ACM symposium on Theory of computing

**Publisher:** ACM

**Bibliometrics**:

Citation Count: 11

Downloads (6 Weeks): 5, Downloads (12 Months): 17, Downloads (Overall): 377

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Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games. When the number of positions of the game isbconstant, our algorithms run in polynomial time.

**Keywords**:
stochastic games, real algebraic geometry

15

October 2010
SAGT'10: Proceedings of the Third international conference on Algorithmic game theory

**Publisher:** Springer-Verlag

The king of refinements of Nash equilibrium is trembling hand perfection. We show that it is NP-hard and Sqrt-Sum-hard to decide if a given pure strategy Nash equilibrium of a given three-player game in strategic form with integer payoffs is trembling hand perfect. Analogous results are shown for a number ...

16

August 2010
MFCS'10: Proceedings of the 35th international conference on Mathematical foundations of computer science

**Publisher:** Springer-Verlag

We consider Boolean exact threshold functions defined by linear equations, and in general degree d polynomials. We give upper and lower bounds on the maximum magnitude (absolute value) of the coefficients required to represent such functions. These bounds are very close and in the linear case in particular they are ...

17

June 2010
CCC '10: Proceedings of the 2010 IEEE 25th Annual Conference on Computational Complexity

**Publisher:** IEEE Computer Society

We initiate a systematic study of constant depth Boolean circuits built using exact threshold gates. We consider both unweighted and weighted exact threshold gates and introduce corresponding circuit classes. We next show that this gives a hierarchy of classes that seamlessly interleave with the well-studied corresponding hierarchies defined using ordinary ...

**Keywords**:
Boolean Circuits, Threshold Functions, Exact Threshold Functions

18

May 2010
Computational Complexity - Selected papers from the 24th Annual IEEE Conference on Computational Complexity (CCC 2009): Volume 19 Issue 2, May 2010

**Publisher:** Springer-Verlag

Barrington, Straubing & Thérien (1990) conjectured that the Boolean A nd function can not be computed by polynomial size constant depth circuits built from modular counting gates, i.e. , by CC 0 circuits. In this work we show that the A nd function can be computed by uniform probabilistic CC ...

**Keywords**:
68Q15, 68Q17, 68Q87

19

December 2009
ISAAC '09: Proceedings of the 20th International Symposium on Algorithms and Computation

**Publisher:** Springer-Verlag

We study the following question, communicated to us by Miklós Ajtai: Can all explicit (e.g., polynomial time computable) functions f : ({0,1} w ) 3 �{0,1} w be computed by word circuits of constant size? A word circuit is an acyclic circuit where each wire holds a word (i.e., an ...

20

August 2009
CSR '09: Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications

**Publisher:** Springer-Verlag

We consider the class of constant depth AND/OR circuits augmented with a layer of modular counting gates at the bottom layer, i.e ${\bf AC}^{0} \circ {\bf MOD}_m$ circuits. We show that the following holds for several types of gates $\mathcal{G}$: by adding a gate of type $\mathcal{G}$ at the output, ...