Elias Koutsoupias

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.

Aggelos Kiayias, Elias Koutsoupias, Aikaterini-Panagiota Stouka

Proof-of-Stake (PoS) blockchain systems, especially those that allow stakeholders to organize themselves in ``stake-pools'', have emerged as a compelling paradigm for the deployment of large scale distributed ledgers. A stake-pool operates a node that engages in the PoS protocol and potentially represents a large number of smaller stakeholders. While such pooled PoS operation is attractive from various angles, it also exhibits a significant shortcoming that, so far and to the best of our knowledge, has not been sufficiently understood or investigated. Pooled PoS operation, to be effective and not lead to sub-optimal dictatorial or cartel-like configurations, should enable the stakeholders to revoke and re-delegate their stake in a way that is aligned with their incentives. However, given that stake-pool operators are exactly those entities who determine what transactions are to be recorded in the ledger, they are quite likely to form a cartel and censor any transaction they want, such as those that attempt to adjust the current stake-pool lineup. In this way, a power grab takes place, where the stake-pool cartel perpetuates its control over the PoS system. We first model and observe formally the emergence of the above problem in pooled PoS systems, and then we describe an anti-censorship mechanism that takes advantage of the underlying cryptographic functions of the ledger and the nature of peer-to-peer networks to diffuse information without suppression. We provide a thorough game-theoretic analysis of this mechanism discovering various types of Nash equilibria which demonstrate that the ``revolution'', i.e., the strategic decision of pool members to withdraw support from a censoring cartel as well as the pool operators to step down, can be incentivized, under suitable and plausible conditions in the utility functions of the involved participants.

Georgios Birmpas, Elias Koutsoupias, Philip Lazos et al.

Bitcoin is a decentralised digital currency that serves as an alternative to existing transaction systems based on an external central authority for security. Although Bitcoin has many desirable properties, one of its fundamental shortcomings is its inability to process transactions at high rates. To address this challenge, many subsequent protocols either modify the rules of block acceptance (longest chain rule) and reward, or alter the graphical structure of the public ledger from a tree to a directed acyclic graph (DAG). Motivated by these approaches, we introduce a new general framework that captures ledger growth for a large class of DAG-based implementations. With this in hand, and by assuming honest miner behaviour, we (experimentally) explore how different DAG-based protocols perform in terms of fairness, i.e., if the block reward of a miner is proportional to their hash power, as well as efficiency, i.e. what proportion of user transactions a ledger deems valid after a certain length of time. Our results demonstrate fundamental structural limits on how well DAG-based ledger protocols cope with a high transaction load. More specifically, we show that even in a scenario where every miner on the system is honest in terms of when they publish blocks, what they point to, and what transactions each block contains, fairness and efficiency of the ledger can break down at specific hash rates if miners have differing levels of connectivity to the P2P network sustaining the protocol.

Elias Koutsoupias, Philip Lazos, Paolo Serafino et al.

We study the strategic implications that arise from adding one extra option to the miners participating in the bitcoin protocol. We propose that when adding a block, miners also have the ability to pay forward an amount to be collected by the first miner who successfully extends their branch, giving them the power to influence the incentives for mining. We formulate a stochastic game for the study of such incentives and show that with this added option, smaller miners can guarantee that the best response of even substantially more powerful miners is to follow the expected behavior intended by the protocol designer.

Aggelos Kiayias, Elias Koutsoupias, Maria Kyropoulou et al.

We study the strategic considerations of miners participating in the bitcoin's protocol. We formulate and study the stochastic game that underlies these strategic considerations. The miners collectively build a tree of blocks, and they are paid when they create a node (mine a block) which will end up in the path of the tree that is adopted by all. Since the miners can hide newly mined nodes, they play a game with incomplete information. Here we consider two simplified forms of this game in which the miners have complete information. In the simplest game the miners release every mined block immediately, but are strategic on which blocks to mine. In the second more complicated game, when a block is mined it is announced immediately, but it may not be released so that other miners cannot continue mining from it. A miner not only decides which blocks to mine, but also when to release blocks to other miners. In both games, we show that when the computational power of each miner is relatively small, their best response matches the expected behavior of the bitcoin designer. However, when the computational power of a miner is large, he deviates from the expected behavior, and other Nash equilibria arise.