Noam Nisan

Noam Nisan, Emmanuel Zerah

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.

Moshe Babaioff, Noam Nisan

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.

Matan Gilboa, Paul W. Goldberg, Elias Koutsoupias et al.

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. In particular, we resolve an open question by Brandt and Bullinger (JAIR '22) and Bullinger and Gilboa (IJCAI '25) concerning strong-popularity in additive hedonic games.

Moshe Babaioff, Amitai Frey, Noam Nisan

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.

Yoav Kolumbus, Noam Nisan

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.

Yoav Kolumbus, Noam Nisan

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.