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新论文 · v1arXiv:2611.14858

The Price of Anarchy in Markets for Lemons

Naveen Durvasula, Tim Roughgarden

原文摘要

We study the worst-case equilibrium gains from trade in simple bilateral trade mechanisms with interdependent valuations. Equilibria in such settings are typically complex, as proposed prices can convey private information held by the proposer. Such equilibria suffer lost gains from trade both due to the inefficiency introduced by screening (as in independent private value settings) and due to adverse selection. We identify broad conditions under which, nevertheless, sequential equilibria are guaranteed to achieve a constant fraction of the first-best gains from trade. Our bounds quantify the central role of rare pessimistic seller signals and rare optimistic buyer signals. The results apply to seller-proposer, buyer-proposer, and random-proposer mechanisms. The key idea in our analysis is to relate equilibrium gains from trade to proposer profits in an auxiliary market with independent private values.

cs.GT · cs.DS · econ.TH

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arXiv ↗PDF ↗
版本更新 · v4arXiv:2410.12755

Toward Optimal-Complexity Hash-Based Asynchronous MVBA with Optimal Resilience

Jovan Komatovic, Joachim Neu, Tim Roughgarden

原文摘要

Multi-valued validated Byzantine agreement (MVBA), a fundamental primitive of distributed computing, allows $n$ processes to agree on a valid $\ell$-bit value, despite $t$ faulty processes behaving maliciously. Among hash-based solutions for the asynchronous setting with adaptive faults, the state-of-the-art HMVBA protocol achieves optimal $O(n^2)$ message complexity, (near-)optimal $O(n \ell + n^2 λ\log n)$ bit complexity, and optimal $O(1)$ time complexity. However, it only tolerates $t < \frac15 n$ failures. In contrast, the best-known optimally-resilient protocol, SQ, incurs a higher bit complexity of $O(n^2 \ell + n^3 λ)$. This poses a fundamental question: Can a hash-based protocol be designed for the asynchronous setting with adaptive faults that simultaneously achieves optimal complexity and optimal resilience? This paper takes a significant step toward answering this question. Namely, we introduce Reducer, an MVBA protocol that retains HMVBA's optimal complexity while improving its resilience to $t < \frac14 n$. Like HMVBA and SQ, Reducer relies exclusively on collision-resistant hash functions. A key innovation in Reducer's design is its internal use of strong multi-valued Byzantine agreement (SMBA), a new variant of Byzantine agreement we introduce and construct, which ensures that the decided value was proposed by a correct process. To further advance resilience toward the optimal one-third bound, we then propose Reducer++, an MVBA protocol that tolerates up to $t < (\frac13 - ε)n$ adaptive failures, for any fixed constant $ε> 0$. Unlike Reducer, Reducer++ does not rely on SMBA. Instead, it employs a novel approach involving hash functions modeled as random oracles to ensure termination. Reducer++ maintains constant time complexity, quadratic message complexity, and quasi-quadratic bit complexity, with constants dependent on $ε$.

cs.DC

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arXiv ↗PDF ↗
版本更新 · v8arXiv:2501.06044

Beyond Optimal Fault Tolerance

Andrew Lewis-Pye, Tim Roughgarden

原文摘要

The optimal fault-tolerance achievable by any protocol has been characterized in a wide range of settings. For example, for state machine replication (SMR) protocols operating in the partially synchronous setting, it is possible to simultaneously guarantee consistency against $α$-bounded adversaries (i.e., adversaries that control less than an $α$ fraction of the participants) and liveness against $β$-bounded adversaries if and only if $α+ 2β\leq 1$. This paper characterizes to what extent "better-than-optimal" fault-tolerance guarantees are possible for SMR protocols when the standard consistency requirement is relaxed to allow a bounded number $r$ of consistency violations. We prove that bounding rollback is impossible without additional timing assumptions and investigate protocols that tolerate and recover from consistency violations whenever message delays around the time of an attack are bounded by a parameter $Δ^*$ (which may be arbitrarily larger than the parameter $Δ$ that bounds post-GST message delays in the partially synchronous model). Here, a protocol's fault-tolerance can be a non-constant function of $r$, and we prove, for each $r$, matching upper and lower bounds on the optimal "recoverable fault-tolerance" achievable by any SMR protocol. For example, for protocols that guarantee liveness against 1/3-bounded adversaries in the partially synchronous setting, a 5/9-bounded adversary can always cause one consistency violation but not two, and a 2/3-bounded adversary can always cause two consistency violations but not three. Our positive results are achieved through a generic "recovery procedure" that can be grafted on to any accountable SMR protocol and restores consistency following a violation while rolling back only transactions that were finalized in the previous $2Δ^*$ timesteps.

cs.DC

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.01323

Beyond Leaderless: Randomized Consensus Against Mobile Crashes

Ittai Abraham, Kaya Alpturer, Pranav Garimidi, Joachim Neu, Tim Roughgarden, Ertem Nusret Tas

原文摘要

Many consensus protocols fail to terminate under attack from an adversary that has the power to move between replicas and repeatedly crash one of them, even in synchrony. We present Multi-Leader Fixed-View Simplex (ML-FVS) to defend against such an adversary while keeping the simple structure and good-case latency of Simplex consensus. Our protocol extends fixed-view Simplex with multiple leaders, each of which may broadcast a proposal. At the voting deadline, each replica votes on the set of proposals it has seen so far. A hidden threshold beacon revealed after the votes gives a priority order on the multiple leaders, resolving each vote to its highest-priority proposal. Our model combines permanent adaptive Byzantine faults with mobile crashes. For a constant crash budget and $Δ$-delayed Byzantine corruption, we obtain $O(Δ)$ expected latency over repeated views whose leaders start honest. With immediate Byzantine corruptions, the protocol still achieves liveness. We also evaluate the protocol under random network delays and stochastic faults, finding that multiple leaders reduce view failures even when rational leaders delay their proposals to increase rewards.

cs.DC

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arXiv ↗PDF ↗