arXiv subjects

Noam Nisan

Publications and source records attributed to Noam Nisan.

At least 55 records · Page 3Linked to original sources

arXiv2017

A "Quantal Regret" Method for Structural Econometrics in Repeated Games

We suggest a general method for inferring players' values from their actions in repeated games. The method extends and improves upon the recent suggestion of (Nekipelov et al., EC 2015) and is based on the assumption that players are more likely to exhibit sequences of actions that have lower regret. We evaluate this "quantal regret" method on two different datasets from experiments of repeated games with controlled player values: those of (Selten and Chmura, AER 2008) on a variety of two-player 2x2 games and our own experiment on ad-auctions (Noti et al., WWW 2014). We find that the quantal regret method is consistently and significantly more precise than either "classic" econometric methods that are based on Nash equilibria, or the "min-regret" method of (Nekipelov et al., EC 2015).

cs.GT↗

arXiv2017

Correlated and Coarse equilibria of Single-item auctions

We study correlated equilibria and coarse equilibria of simple first-price single-item auctions in the simplest auction model of full information. Nash equilibria are known to always yield full efficiency and a revenue that is at least the second-highest value. We prove that the same is true for all correlated equilibria, even those in which agents overbid -- i.e., bid above their values. Coarse equilibria, in contrast, may yield lower efficiency and revenue. We show that the revenue can be as low as 26% of the second-highest value in a coarse equilibrium, even if agents are assumed not to overbid, and this is tight. We also show that when players do not overbid, the worst-case bound on social welfare at coarse equilibrium improves from 63% of the highest value to 81%, and this bound is tight as well.

cs.GT↗

arXiv2016

Networks of Complements

We consider a network of sellers, each selling a single product, where the graph structure represents pair-wise complementarities between products. We study how the network structure affects revenue and social welfare of equilibria of the pricing game between the sellers. We prove positive and negative results, both of "Price of Anarchy" and of "Price of Stability" type, for special families of graphs (paths, cycles) as well as more general ones (trees, graphs). We describe best-reply dynamics that converge to non-trivial equilibrium in several families of graphs, and we use these dynamics to prove the existence of approximately-efficient equilibria.

cs.GT↗

arXiv2015

Smooth Boolean functions are easy: efficient algorithms for low-sensitivity functions

A natural measure of smoothness of a Boolean function is its sensitivity (the largest number of Hamming neighbors of a point which differ from it in function value). The structure of smooth or equivalently low-sensitivity functions is still a mystery. A well-known conjecture states that every such Boolean function can be computed by a shallow decision tree. While this conjecture implies that smooth functions are easy to compute in the simplest computational model, to date no non-trivial upper bounds were known for such functions in any computational model, including unrestricted Boolean circuits. Even a bound on the description length of such functions better than the trivial $2^n$ does not seem to have been known. In this work, we establish the first computational upper bounds on smooth Boolean functions: 1) We show that every sensitivity s function is uniquely specified by its values on a Hamming ball of radius 2s. We use this to show that such functions can be computed by circuits of size $n^{O(s)}$. 2) We show that sensitivity s functions satisfy a strong pointwise noise-stability guarantee for random noise of rate O(1/s). We use this to show that these functions have formulas of depth O(s log n). 3) We show that sensitivity s functions can be (locally) self-corrected from worst-case noise of rate $\exp(-O(s))$. All our results are simple, and follow rather directly from (variants of) the basic fact that that the function value at few points in small neighborhoods of a given point determine its function value via a majority vote. Our results confirm various consequences of the conjecture. They may be viewed as providing a new form of evidence towards its validity, as well as new directions towards attacking it.

cs.CC↗

arXiv2015

Public projects, Boolean functions and the borders of Border's theorem

Border's theorem gives an intuitive linear characterization of the feasible interim allocation rules of a Bayesian single-item environment, and it has several applications in economic and algorithmic mechanism design. All known generalizations of Border's theorem either restrict attention to relatively simple settings, or resort to approximation. This paper identifies a complexity-theoretic barrier that indicates, assuming standard complexity class separations, that Border's theorem cannot be extended significantly beyond the state-of-the-art. We also identify a surprisingly tight connection between Myerson's optimal auction theory, when applied to public project settings, and some fundamental results in the analysis of Boolean functions.

cs.GT↗

arXiv2015

Welfare Maximization with Limited Interaction

We continue the study of welfare maximization in unit-demand (matching) markets, in a distributed information model where agent's valuations are unknown to the central planner, and therefore communication is required to determine an efficient allocation. Dobzinski, Nisan and Oren (STOC'14) showed that if the market size is $n$, then $r$ rounds of interaction (with logarithmic bandwidth) suffice to obtain an $n^{1/(r+1)}$-approximation to the optimal social welfare. In particular, this implies that such markets converge to a stable state (constant approximation) in time logarithmic in the market size. We obtain the first multi-round lower bound for this setup. We show that even if the allowable per-round bandwidth of each agent is $n^{ε(r)}$, the approximation ratio of any $r$-round (randomized) protocol is no better than $Ω(n^{1/5^{r+1}})$, implying an $Ω(\log \log n)$ lower bound on the rate of convergence of the market to equilibrium. Our construction and technique may be of interest to round-communication tradeoffs in the more general setting of combinatorial auctions, for which the only known lower bound is for simultaneous ($r=1$) protocols [DNO14].

cs.GT↗

arXiv2014

Economic Efficiency Requires Interaction

We study the necessity of interaction between individuals for obtaining approximately efficient allocations. The role of interaction in markets has received significant attention in economic thinking, e.g. in Hayek's 1945 classic paper. We consider this problem in the framework of simultaneous communication complexity. We analyze the amount of simultaneous communication required for achieving an approximately efficient allocation. In particular, we consider two settings: combinatorial auctions with unit demand bidders (bipartite matching) and combinatorial auctions with subadditive bidders. For both settings we first show that non-interactive systems have enormous communication costs relative to interactive ones. On the other hand, we show that limited interaction enables us to find approximately efficient allocations.

cs.GT↗

arXiv2014

Sampling and Representation Complexity of Revenue Maximization

We consider (approximate) revenue maximization in auctions where the distribution on input valuations is given via "black box" access to samples from the distribution. We observe that the number of samples required -- the sample complexity -- is tightly related to the representation complexity of an approximately revenue-maximizing auction. Our main results are upper bounds and an exponential lower bound on these complexities.

cs.GT↗

arXiv2014

Mechanisms for Multi-Unit Auctions

We present an incentive-compatible polynomial-time approximation scheme for multi-unit auctions with general k-minded player valuations. The mechanism fully optimizes over an appropriately chosen sub-range of possible allocations and then uses VCG payments over this sub-range. We show that obtaining a fully polynomial-time incentive-compatible approximation scheme, at least using VCG payments, is NP-hard. For the case of valuations given by black boxes, we give a polynomial-time incentive-compatible 2-approximation mechanism and show that no better is possible, at least using VCG payments.

cs.GT↗

arXiv2014

Mixed Strategies in Combinatorial Agency

In many multiagent domains a set of agents exert effort towards a joint outcome, yet the individual effort levels cannot be easily observed. A typical example for such a scenario is routing in communication networks, where the sender can only observe whether the packet reached its destination, but often has no information about the actions of the intermediate routers, which influences the final outcome. We study a setting where a principal needs to motivate a team of agents whose combination of hidden efforts stochastically determines an outcome. In a companion paper we devise and study a basic combinatorial agency model for this setting, where the principal is restricted to inducing a pure Nash equilibrium. Here we study various implications of this restriction. First, we show that, in contrast to the case of observable efforts, inducing a mixed-strategies equilibrium may be beneficial for the principal. Second, we present a sufficient condition for technologies for which no gain can be generated. Third, we bound the principals gain for various families of technologies. Finally, we study the robustness of mixed equilibria to coalitional deviations and the computational hardness of the optimal mixed equilibria.

cs.GT↗

arXiv2014

Price Competition in Online Combinatorial Markets

We consider a single buyer with a combinatorial preference that would like to purchase related products and services from different vendors, where each vendor supplies exactly one product. We study the general case where subsets of products can be substitutes as well as complementary and analyze the game that is induced on the vendors, where a vendor's strategy is the price that he asks for his product. This model generalizes both Bertrand competition (where vendors are perfect substitutes) and Nash bargaining (where they are perfect complements), and captures a wide variety of scenarios that can appear in complex crowd sourcing or in automatic pricing of related products. We study the equilibria of such games and show that a pure efficient equilibrium always exists. In the case of submodular buyer preferences we fully characterize the set of pure Nash equilibria, essentially showing uniqueness. For the even more restricted "substitutes" buyer preferences we also prove uniqueness over {\em mixed} equilibria. Finally we begin the exploration of natural generalizations of our setting such as when services have costs, when there are multiple buyers or uncertainty about the the buyer's valuation, and when a single vendor supplies multiple products.

cs.GT↗

arXiv2013

Bertrand Networks

We study scenarios where multiple sellers of a homogeneous good compete on prices, where each seller can only sell to some subset of the buyers. Crucially, sellers cannot price-discriminate between buyers. We model the structure of the competition by a graph (or hyper-graph), with nodes representing the sellers and edges representing populations of buyers. We study equilibria in the game between the sellers, prove that they always exist, and present various structural, quantitative, and computational results about them. We also analyze the equilibria completely for a few cases. Many questions are left open.

cs.GT↗

arXiv2013

On the Efficiency of the Walrasian Mechanism

Central results in economics guarantee the existence of efficient equilibria for various classes of markets. An underlying assumption in early work is that agents are price-takers, i.e., agents honestly report their true demand in response to prices. A line of research in economics, initiated by Hurwicz (1972), is devoted to understanding how such markets perform when agents are strategic about their demands. This is captured by the \emph{Walrasian Mechanism} that proceeds by collecting reported demands, finding clearing prices in the \emph{reported} market via an ascending price tâtonnement procedure, and returns the resulting allocation. Similar mechanisms are used, for example, in the daily opening of the New York Stock Exchange and the call market for copper and gold in London. In practice, it is commonly observed that agents in such markets reduce their demand leading to behaviors resembling bargaining and to inefficient outcomes. We ask how inefficient the equilibria can be. Our main result is that the welfare of every pure Nash equilibrium of the Walrasian mechanism is at least one quarter of the optimal welfare, when players have gross substitute valuations and do not overbid. Previous analysis of the Walrasian mechanism have resorted to large market assumptions to show convergence to efficiency in the limit. Our result shows that approximate efficiency is guaranteed regardless of the size of the market.

cs.GT↗

arXiv2012

The AND-OR game: Equilibrium Characterization (Working Paper)

We consider a simple simultaneous first price auction for multiple items in a complete information setting. Our goal is to completely characterize the mixed equilibria in this setting, for a simple, yet highly interesting, {\tt AND}-{\tt OR} game, where one agent is single minded and the other is unit demand.

cs.GT↗

arXiv2012

Incentive Compatible Two Player Cake Cutting

We characterize methods of dividing a cake between two bidders in a way that is incentive-compatible and Pareto-efficient. In our cake cutting model, each bidder desires a subset of the cake (with a uniform value over this subset), and is allocated some subset. Our characterization proceeds via reducing to a simple one-dimensional version of the problem, and yields, for example, a tight bound on the social welfare achievable.

cs.GT↗

arXiv2012

Fair Allocation Without Trade

We consider the age-old problem of allocating items among different agents in a way that is efficient and fair. Two papers, by Dolev et al. and Ghodsi et al., have recently studied this problem in the context of computer systems. Both papers had similar models for agent preferences, but advocated different notions of fairness. We formalize both fairness notions in economic terms, extending them to apply to a larger family of utilities. Noting that in settings with such utilities efficiency is easily achieved in multiple ways, we study notions of fairness as criteria for choosing between different efficient allocations. Our technical results are algorithms for finding fair allocations corresponding to two fairness notions: Regarding the notion suggested by Ghodsi et al., we present a polynomial-time algorithm that computes an allocation for a general class of fairness notions, in which their notion is included. For the other, suggested by Dolev et al., we show that a competitive market equilibrium achieves the desired notion of fairness, thereby obtaining a polynomial-time algorithm that computes such a fair allocation and solving the main open problem raised by Dolev et al.

cs.GT↗

arXiv2012

Doubleclick Ad Exchange Auction

Display advertisements on the web are sold via ad exchanges that use real time auction. We describe the challenges of designing a suitable auction, and present a simple auction called the Optional Second Price (OSP) auction that is currently used in Doubleclick Ad Exchange.

cs.GT↗

arXiv2011

A Quantitative Version of the Gibbard-Satterthwaite Theorem for Three Alternatives

The Gibbard-Satterthwaite theorem states that every non-dictatorial election rule among at least three alternatives can be strategically manipulated. We prove a quantitative version of the Gibbard-Satterthwaite theorem: a random manipulation by a single random voter will succeed with a non-negligible probability for any election rule among three alternatives that is far from being a dictatorship and from having only two alternatives in its range.

math.CO↗