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Noam Nisan

Publications and source records attributed to Noam Nisan.

At least 19 recordsLinked to original sources
arXiv2026

Complexity of Unambiguous Problems in $Σ^P_2$

Various practical problems within the class $Σ_{2}^P$ possess an unambiguity property, meaning that yes-instances correspond with a unique witness. The semantic class containing all unambiguous $Σ_{2}^P$ problems is denoted $UΣ_{2}^P$. Examples include the existence of (1) a dominating strategy in a game, (2) a Condorcet winner, (3) a strongly popular partition in hedonic games, and (4) a winner (source) in a tournament. The computational complexity of unambiguous problems is not well understood, leaving many questions unresolved. We address this gap in a broad complexity-theoretic sense; our main contributions consist of the following. - We identify three syntactic subclasses of $UΣ_{2}^P$ associated with general properties of problems that guarantee uniqueness: Polynomial Tournament Winner (PTW), Polynomial Condorcet Winner (PCW), and Polynomial Majority Argument (PMA). - We establish complexity upper and lower bounds for our proposed classes. In particular, we show that they are all contained in $S_2^P$ and are thus significantly easier than the immediate $Σ_{2}^P$ upper bound. - We characterize the complexity of various practical problems using this framework.

cs.CC↗
arXiv2026

Online Block Packing and Multidimensional EIP-1559

We consider the online algorithmic challenge that is faced by blockchains that have multidimensional block constraints and serve quasi-patient bidders. We first provide online approximation algorithms for the important special cases of small transactions or a small number of dimensions; this solves open problems left by [Babaioff and Nisan, EC 2025]. Second, we study multidimensional variants of Ethereum's EIP-1559 protocol. We show that if the block builders manage to approximately optimize each block's welfare myopically, then an approximation to the global offline optimal welfare is obtained. On the other hand, we show that, unlike in the single-dimensional case, EIP-1559 by itself does not guarantee any good approximation.

cs.DS↗
arXiv2026

Domination-Avoiding Learning Agents Cannot Collude

An influential paper of Calvano et al. empirically demonstrated that Q-learning agents spontaneously collude when placed as sellers that compete on prices in a natural market model. More recent results of Fish et al. empirically demonstrated that similar collusion happens with commercial LLMs. We formally prove that such collusion can also happen with external-regret-minimizing agents. We identify a very general class of agents, which we term Domination-Avoiding agents, that provably do not collude in such markets. This class contains all Mean-Based agents and all internal-regret-minimizing agents, as well as others such as Multiplicative-Weight agents with variable learning rate and contextual variants thereof. More generally we show that, in any game, this class of agents is guaranteed to jointly learn to almost never play strategies that are eliminated by repeated elimination of purely dominated strategies.

cs.GT↗
arXiv2026

On the Welfare of EIP-1559 with Patient Bidders

The ``EIP-1599 algorithm'' is used by the Ethereum blockchain to assemble transactions into blocks. While prior work has studied it under the assumption that bidders are ``impatient'', we analyze it under the assumption that bidders are ``patient'', which better corresponds to the fact that unscheduled transactions remain in the mempool and can be scheduled at a later time. We show that with ``patient'' bidders, this algorithm produces schedules of near-optimal welfare, provided it is given a mild resource augmentation (that does not increase with the time horizon). We prove some generalizations of the basic theorem, establish lower bounds that rule out several candidate improvements and extensions, and propose several questions for future work.

cs.GT↗
arXiv2026

The Root of Revenue Continuity

In the setup of selling one or more goods, various papers have shown, in various forms and for various purposes, that a small change in the distribution of a buyer's valuations may cause only a small change in the possible revenue that can be extracted. We prove a simple, clean, convenient, and general statement to this effect: let $X$ and $Y$ be random valuations on $k$ additive goods, and let $W(X,Y)$ be the Wasserstein (or "earth mover's") distance between them; then $$\left\vert \sqrt{Rev(X)}-\sqrt{Rev(Y)}\right\vert \le \sqrt{W(X,Y)}.$$ This further implies that a simple explicit modification of any optimal mechanism for $X$, namely, "uniform discounting," is guaranteed to be almost optimal for any $Y$ that is close to $X$ in the Wasserstein distance.

cs.GT↗
arXiv2025

Does Your Blockchain Need Multidimensional Transaction Fees?

Blockchains have block-size limits to ensure the entire cluster can keep up with the tip of the chain. These block-size limits are usually single-dimensional, but richer multidimensional constraints allow for greater throughput. The potential for performance improvements from multidimensional resource pricing has been discussed in the literature, but exactly how big those performance improvements are remains unclear. In order to identify the magnitude of additional throughput that multi-dimensional transaction fees can unlock, we introduce the concept of an $α$-approximation. A constraint set $C_1$ is $α$-approximated by $C_2$ if every block feasible under $C_1$ is also feasible under $C_2$ once all resource capacities are scaled by a factor of $α$ (e.g., $α=2$ corresponds to doubling all available resources). We show that the $α$-approximation of the optimal single-dimensional gas measure corresponds to the value of a specific zero-sum game. However, the more general problem of finding the optimal $k$-dimensional approximation is NP-complete. Quantifying the additional throughput that multi-dimensional fees can provide allows blockchain designers to make informed decisions about whether the additional capacity unlocked by multidimensional constraints is worth the additional complexity they add to the protocol.

cs.GT↗
arXiv2024

Learning to Maximize Gains From Trade in Small Markets

We study the problem of designing a two-sided market (double auction) to maximize the gains from trade (social welfare) under the constraints of (dominant-strategy) incentive compatibility and budget-balance. Our goal is to do so for an unknown distribution from which we are given a polynomial number of samples. Our first result is a general impossibility for the case of correlated distributions of values even between just one seller and two buyers, in contrast to the case of one seller and one buyer (bilateral trade) where this is possible. Our second result is an efficient learning algorithm for one seller and two buyers in the case of independent distributions which is based on a novel algorithm for computing optimal mechanisms for finitely supported and explicitly given independent distributions. Both results rely heavily on characterizations of (dominant-strategy) incentive compatible mechanisms that are strongly budget-balanced.

cs.GT↗
arXiv2024

Monotonic Mechanisms for Selling Multiple Goods

Maximizing the revenue from selling two or more goods has been shown to require the use of $nonmonotonic$ mechanisms, where a higher-valuation buyer may pay less than a lower-valuation one. Here we show that the restriction to $monotonic$ mechanisms may not just lower the revenue, but may in fact yield only a $negligible$ $fraction$ of the maximal revenue; more precisely, the revenue from monotonic mechanisms is no more than k times the simple revenue obtainable by selling the goods separately, or bundled (where k is the number of goods), whereas the maximal revenue may be arbitrarily larger. We then study the class of monotonic mechanisms and its subclass of allocation-monotonic mechanisms, and obtain useful characterizations and revenue bounds.

cs.GT↗
arXiv2024

Asynchronous Proportional Response Dynamics in Markets with Adversarial Scheduling

We study Proportional Response Dynamics (PRD) in linear Fisher markets where participants act asynchronously. We model this scenario as a sequential process in which in every step, an adversary selects a subset of the players that will update their bids, subject to liveness constraints. We show that if every bidder individually uses the PRD update rule whenever they are included in the group of bidders selected by the adversary, then (in the generic case) the entire dynamic converges to a competitive equilibrium of the market. Our proof technique uncovers further properties of linear Fisher markets, such as the uniqueness of the equilibrium for generic parameters and the convergence of associated best-response dynamics and no-swap regret dynamics under certain conditions.

cs.GT↗
arXiv2023

Serial Monopoly on Blockchains

We study the following problem that is motivated by Blockchains where ``miners'' are serially given the monopoly for assembling transactions into the next block. Our model has a single good that is sold repeatedly every day where new demand for the good arrives every day. The novel element in our model is that all unsatisfied demand from one day remains in the system and is added to the new demand of the next day. Every day there is a new monopolist that gets to sell a fixed supply $s$ of the good and naturally chooses to do so at the monopolist's price for the combined demand. What will the dynamics of the prices chosen by the sequence of monopolists be? What level of efficiency will be obtained in the long term? We start with a non-strategic analysis of users' behavior and our main result shows that prices keep fluctuating wildly and this is an endogenous property of the model and happens even when demand is stable with nothing stochastic in the model. These price fluctuations underscore the necessity of an analysis under strategic behavior of the users, which we show results in the prices being stable at the market equilibrium price.

cs.GT↗
arXiv2023

How and Why to Manipulate Your Own Agent: On the Incentives of Users of Learning Agents

The usage of automated learning agents is becoming increasingly prevalent in many online economic applications such as online auctions and automated trading. Motivated by such applications, this paper is dedicated to fundamental modeling and analysis of the strategic situations that the users of automated learning agents are facing. We consider strategic settings where several users engage in a repeated online interaction, assisted by regret-minimizing learning agents that repeatedly play a "game" on their behalf. We propose to view the outcomes of the agents' dynamics as inducing a "meta-game" between the users. Our main focus is on whether users can benefit in this meta-game from "manipulating" their own agents by misreporting their parameters to them. We define a general framework to model and analyze these strategic interactions between users of learning agents for general games and analyze the equilibria induced between the users in three classes of games. We show that, generally, users have incentives to misreport their parameters to their own agents, and that such strategic user behavior can lead to very different outcomes than those anticipated by standard analysis.

cs.GT↗
arXiv2022

Complexity of Public Goods Games on Graphs

We study the computational complexity of "public goods games on networks". In this model, each vertex in a graph is an agent that needs to take a binary decision of whether to "produce a good" or not. Each agent's utility depends on the number of its neighbors in the graph that produce the good, as well as on its own action. This dependence can be captured by a "pattern" $T:{\rm I\!N}\rightarrow\{0,1\}$ that describes an agent's best response to every possible number of neighbors that produce the good. Answering a question of [Papadimitriou and Peng, 2021], we prove that for some simple pattern $T$ the problem of determining whether a non-trivial pure Nash equilibrium exists is NP-complete. We extend our result to a wide class of such $T$, but also find a new polynomial time algorithm for some specific simple pattern $T$. We leave open the goal of characterizing the complexity for all patterns.

cs.GT↗
arXiv2022

Finding a Hidden Edge

We consider the problem of finding an edge in a hidden undirected graph $G = (V, E)$ with $n$ vertices, in a model where we only allowed queries that ask whether or not a subset of vertices contains an edge. We study the non-adaptive model and show that while in the deterministic model the optimal algorithm requires $\binom{n}{2}$ queries (i.e., querying for any possible edge separately), in the randomized model $\tildeΘ(n)$ queries are sufficient (and needed) in order to find an edge. In addition, we study the query complexity for specific families of graphs, including Stars, Cliques, and Matchings, for both the randomized and deterministic models. Lastly, for general graphs, we show a trade-off between the query complexity and the number of rounds, $r$, made by an adaptive algorithm. We present two algorithms with $O(rn^{2/r})$ and $\tilde{O}(rn^{1/r})$ sample complexity for the deterministic and randomized models, respectively.

cs.DS↗
arXiv2022

Auctions Between Regret-Minimizing Agents

We analyze a scenario in which software agents implemented as regret-minimizing algorithms engage in a repeated auction on behalf of their users. We study first-price and second-price auctions, as well as their generalized versions (e.g., as those used for ad auctions). Using both theoretical analysis and simulations, we show that, surprisingly, in second-price auctions the players have incentives to misreport their true valuations to their own learning agents, while in the first-price auction it is a dominant strategy for all players to truthfully report their valuations to their agents.

cs.GT↗
arXiv2021

Beyond Pigouvian Taxes: A Worst Case Analysis

In the early $20^{th}$ century, Pigou observed that imposing a marginal cost tax on the usage of a public good induces a socially efficient level of use as an equilibrium. Unfortunately, such a "Pigouvian" tax may also induce other, socially inefficient, equilibria. We observe that this social inefficiency may be unbounded, and study whether alternative tax structures may lead to milder losses in the worst case, i.e. to a lower price of anarchy. We show that no tax structure leads to bounded losses in the worst case. However, we do find a tax scheme that has a lower price of anarchy than the Pigouvian tax, obtaining tight lower and upper bounds in terms of a crucial parameter that we identify. We generalize our results to various scenarios that each offers an alternative to the use of a public road by private cars, such as ride sharing, or using a bus or a train.

econ.TH↗
arXiv2021

The Menu-Size Complexity of Revenue Approximation

Consider a monopolist selling $n$ items to an additive buyer whose item values are drawn from independent distributions $F_1,F_2,\ldots,F_n$ possibly having unbounded support. Unlike in the single-item case, it is well known that the revenue-optimal selling mechanism (a pricing scheme) may be complex, sometimes requiring a continuum of menu entries. Also known is that simple mechanisms with a bounded number of menu entries can extract a constant fraction of the optimal revenue. Nonetheless, whether an arbitrarily high fraction of the optimal revenue can be extracted via a bounded menu size remained open. We give an affirmative answer: for every $n$ and $\varepsilon>0$, there exists $C=C(n,\varepsilon)$ s.t. mechanisms of menu size at most $C$ suffice for obtaining $(1-\varepsilon)$ of the optimal revenue from any $F_1,\ldots,F_n$. We prove upper and lower bounds on the revenue-approximation complexity $C(n,\varepsilon)$ and on the deterministic communication complexity required to run a mechanism achieving such an approximation.

cs.GT↗
arXiv2020

Matching for the Israeli "Mechinot" Gap-Year Programs: Handling Rich Diversity Requirements

We describe our experience with designing and running a matching market for the Israeli "Mechinot" gap-year programs. The main conceptual challenge in the design of this market was the rich set of diversity considerations, which necessitated the development of an appropriate preference-specification language along with corresponding choice-function semantics, which we also theoretically analyze. Our contribution extends the existing toolbox for two-sided matching with soft constraints. This market was run for the first time in January 2018 and matched 1,607 candidates (out of a total of 3,120 candidates) to 35 different programs, has been run twice more since, and has been adopted by the Joint Council of the "Mechinot" gap-year programs for the foreseeable future.

cs.GT↗