arXiv subjects

Akaki Mamageishvili

Publications and source records attributed to Akaki Mamageishvili.

34 records · Page 2Linked to original sources

arXiv2023

Efficient Rollup Batch Posting Strategy on Base Layer

We design efficient and robust algorithms for the batch posting of rollup chain calldata on the base layer chain, using tools from operations research. We relate the costs of posting and delaying, by converting them to the same units and adding them up. The algorithm that keeps the average and maximum queued number of batches tolerable enough improves the posting costs of the trivial algorithm, which posts batches immediately when they are created, by 8%. On the other hand, the algorithm that only cares moderately about the batch queue length can improve the trivial algorithm posting costs by 29%. Our findings can be used by layer two projects that post data to the base layer at some regular rate.

cs.CR↗

arXiv2023

Axioms for Constant Function Market Makers

We study axiomatic foundations for different classes of constant-function automated market makers (CFMMs). We focus particularly on separability and on different invariance properties under scaling. Our main results are an axiomatic characterization of a natural generalization of constant product market makers (CPMMs), popular in decentralized finance, on the one hand, and a characterization of the Logarithmic Scoring Rule Market Makers (LMSR), popular in prediction markets, on the other hand. The first class is characterized by the combination of independence and scale invariance, whereas the second is characterized by the combination of independence and translation invariance. The two classes are therefore distinguished by a different invariance property that is motivated by different interpretations of the numéraire in the two applications. However, both are pinned down by the same separability property. Moreover, we characterize the CPMM as an extremal point within the class of scale invariant, independent, symmetric AMMs with non-concentrated liquidity provision. Our results add to a formal analysis of mechanisms that are currently used for decentralized exchanges and connect the most popular class of DeFi AMMs to the most popular class of prediction market AMMs.

cs.GT↗

arXiv2022

Staking Pools on Blockchains

On several proof-of-stake blockchains, agents engaged in validating transactions can open a pool to which others can delegate their stake in order to earn higher returns. We develop a model of staking pool formation in the presence of malicious agents and establish existence and uniqueness of equilibria. We then identify potential and risk of staking pools. First, allowing for staking pools lowers blockchain security. Yet, honest stake holders obtain higher returns. Second, by choosing welfare optimal distribution rewards, staking pools prevent that malicious agents receive large rewards. Third, when pool owners can freely distribute the returns from validation to delegators, staking pools disrupt blockchain operations, since malicious agents attract most delegators by offering generous returns.

cs.GT↗

arXiv2022

On-Chain Auctions with Deposits

Second-price auctions with deposits are frequently used in blockchain environments. An auction takes place on-chain: bidders deposit an amount that fully covers their bid (but possibly exceeds it) in a smart contract. The deposit is used as insurance against bidders not honoring their bid if they win. The deposit, but not the bid, is publicly observed during the bidding phase of the auction. The visibility of deposits can fundamentally change the strategic structure of the auction if bidding happens sequentially: Bidding is costly since deposit are costly to make. Thus, deposits can be used as a costly signal for a high valuation. This is the source of multiple inefficiencies: To engage in costly signalling, a bidder who bids first and has a high valuation will generally over-deposit in equilibrium, i.e.~deposit more than he will bid. If high valuations are likely there can, moreover, be entry deterrence through high deposits: a bidder who bids first can deter subsequent bidders from entering the auction. Pooling can happen in equilibrium, where bidders of different valuations deposit the same amount. The auction fails to allocate the item to the bidder with the highest valuation.

cs.GT↗

arXiv2021

Vote Delegation with Unknown Preferences

We examine vote delegation when preferences of agents are private information. One group of agents (delegators) does not want to participate in voting and abstains under conventional voting or can delegate its votes to the other group (voters) who decide between two alternatives. We show that free delegation favors minorities, that is, alternatives that have a lower chance of winning ex-ante. The same occurs if the number of voting rights that actual voters can have is capped. When the number of delegators increases, the probability that the ex-ante minority wins under free and capped delegation converges to the one under conventional voting--albeit non-monotonically. Our results are obtained in a private value setting but can be readily translated into an information aggregation setting when voters receive a signal about the ''correct" alternative with some probability.

cs.GT↗

arXiv2021

FileBounty: Fair Data Exchange

Digital contents are typically sold online through centralized and custodian marketplaces, which requires the trading partners to trust a central entity. We present FileBounty, a fair protocol which, assuming the cryptographic hash of the file of interest is known to the buyer, is trust-free and lets a buyer purchase data for a previously agreed monetary amount, while guaranteeing the integrity of the contents. To prevent misbehavior, FileBounty guarantees that any deviation from the expected participants' behavior results in a negative financial payoff; i.e. we show that honest behavior corresponds to a subgame perfect Nash equilibrium. Our novel deposit refunding scheme is resistant to extortion attacks under rational adversaries. If buyer and seller behave honestly, FileBounty's execution requires only three on-chain transactions, while the actual data is exchanged off-chain in an efficient and privacy-preserving manner. We moreover show how FileBounty enables a flexible peer-to-peer setting where multiple parties fairly sell a file to a buyer.

cs.CR↗

arXiv2021

Vote Delegation and Misbehavior

We study vote delegation with "well-behaving" and "misbehaving" agents and compare it with conventional voting. Typical examples for vote delegation are validation or governance tasks on blockchains. There is a majority of well-behaving agents, but they may abstain or delegate their vote to other agents since voting is costly. Misbehaving agents always vote. We compare conventional voting allowing for abstention with vote delegation. Preferences of voters are private information and a positive outcome is achieved if well-behaving agents win. We illustrate that vote delegation leads to quite different outcomes than conventional voting with abstention. In particular, we obtain three insights: First, if the number of misbehaving voters, denoted by f , is high, both voting methods fail to deliver a positive outcome. Second, if f takes an intermediate value, conventional voting delivers a positive outcome, while vote delegation fails with probability one. Third, if f is low, delegation delivers a positive outcome with higher probability than conventional voting. Finally, our results characterize worst-case outcomes that can happen in a liquid democracy.

cs.GT↗

arXiv2020

Mechanism Design and Blockchains

Game theory is often used as a tool to analyze decentralized systems and their properties, in particular, blockchains. In this note, we take the opposite view. We argue that blockchains can and should be used to implement economic mechanisms because they can help to overcome problems that occur if trust in the mechanism designer cannot be assumed. Mechanism design deals with the allocation of resources to agents, often by extracting private information from them. Some mechanisms are immune to early information disclosure, while others may heavily depend on it. Some mechanisms have to randomize to achieve fairness and efficiency. Both issues, information disclosure, and randomness require trust in the mechanism designer. If there is no trust, mechanisms can be manipulated. We claim that mechanisms that use randomness or sequential information disclosure are much harder, if not impossible, to audit. Therefore, centralized implementation is often not a good solution. We consider some of the most frequently used mechanisms in practice and identify circumstances under which manipulation is possible. We propose a decentralized implementation of such mechanisms, that can be, in practical terms, realized by blockchain technology. Moreover, we argue in which environments a decentralized implementation of a mechanism brings a significant advantage.

cs.GT↗

arXiv2020

Sequential Solutions in Machine Scheduling Games

We consider the classical machine scheduling, where $n$ jobs need to be scheduled on $m$ machines, and where job $j$ scheduled on machine $i$ contributes $p_{i,j}\in \mathbb{R}$ to the load of machine $i$, with the goal of minimizing the makespan, i.e., the maximum load of any machine in the schedule. We study inefficiency of schedules that are obtained when jobs arrive sequentially one by one, and the jobs choose themselves the machine on which they will be scheduled, aiming at being scheduled on a machine with small load. We measure the inefficiency of a schedule as the ratio of the makespan obtained in the worst-case equilibrium schedule, and of the optimum makespan. This ratio is known as the \emph{sequential price of anarchy}. We also introduce two alternative inefficiency measures, which allow for a favorable choice of the order in which the jobs make their decisions. As our first result, we disprove the conjecture of Hassin and Yovel claiming that the sequential price of anarchy for $m=2$ machines is at most 3. We show that the sequential price of anarchy grows at least linearly with the number $n$ of players, i.e., we show that $SPoA = Ω(n)$. Furthermore, we show that there exists an order of the jobs, resulting in makespan that is at most linearly larger than the optimum makespan. To the end, we show that if an authority can change the order of the jobs adaptively to the decisions made by the jobs so far (but cannot influence the decisions of the jobs), then there exists an adaptive ordering in which the jobs end up in an optimum schedule.

cs.GT↗

arXiv2018

No truthful mechanism can be better than $n$ approximate for two natural problems

This work gives the first natural non-utilitarian problems for which the trivial $n$ approximation via VCG mechanisms is the best possible. That is, no truthful mechanism can be better than $n$ approximate, where $n$ is the number of agents. The problems are the min-max variant of shortest path and (directed) minimum spanning tree mechanism design problems. In these procurement auctions, agents own the edges of a network, and the corresponding edge costs are private. Instead of the total weight of the subnetwork, in the min-max variant we aim to minimize the maximum agent cost.

cs.GT↗

arXiv2018

Assessment Voting in Large Electorates

We analyze Assessment Voting, a new two-round voting procedure that can be applied to binary decisions in democratic societies. In the first round, a randomly-selected number of citizens cast their vote on one of the two alternatives at hand, thereby irrevocably exercising their right to vote. In the second round, after the results of the first round have been published, the remaining citizens decide whether to vote for one alternative or to ab- stain. The votes from both rounds are aggregated, and the final outcome is obtained by applying the majority rule, with ties being broken by fair randomization. Within a costly voting framework, we show that large elec- torates will choose the preferred alternative of the majority with high prob- ability, and that average costs will be low. This result is in contrast with the literature on one-round voting, which predicts either higher voting costs (when voting is compulsory) or decisions that often do not represent the preferences of the majority (when voting is voluntary).

econ.EM↗

arXiv2017

Sophisticated Attacks on Decoy Ballots: The Devil's Menu and the Market for Lemons

Decoy ballots do not count in election outcomes, but otherwise they are indistinguishable from real ballots. By means of a game-theoretical model, we show that decoy ballots may not provide effective protection against a malevolent adversary trying to buy real ballots. If the citizenry is divided into subgroups (or districts), the adversary can construct a so-called "Devil's Menu" consisting of several prices. In equilibrium, the adversary can buy the real ballots of any strict subset of districts at a price corresponding to the willingness to sell on the part of the citizens holding such ballots. By contrast, decoy voters are trapped into selling their ballots at a low, or even negligible, price. Blowing up the adversary's budget by introducing decoy ballots may thus turn out to be futile. The Devil's Menu can also be applied to the well-known "Lemons Problem".

cs.GT↗

arXiv2015

Tighter Bounds on the Inefficiency Ratio of Stable Equilibria in Load Balancing Games

In this paper we study the inefficiency ratio of stable equilibria in load balancing games introduced by Asadpour and Saberi [3]. We prove tighter lower and upper bounds of 7/6 and 4/3, respectively. This improves over the best known bounds in problem (19/18 and 3/2, respectively). Equivalently, the results apply to the question of how well the optimum for the $L_2$ -norm can approximate the $L_{\infty}$-norm (makespan) in identical machines scheduling.

cs.GT↗

arXiv2015

Multicast Network Design Game on a Ring

In this paper we study quality measures of different solution concepts for the multicast network design game on a ring topology. We recall from the literature a lower bound of 4/3 and prove a matching upper bound for the price of stability, which is the ratio of the social costs of a best Nash equilibrium and of a general optimum. Therefore, we answer an open question posed by Fanelli et al. in [12]. We prove an upper bound of 2 for the ratio of the costs of a potential optimizer and of an optimum, provide a construction of a lower bound, and give a computer-assisted argument that it reaches $2$ for any precision. We then turn our attention to players arriving one by one and playing myopically their best response. We provide matching lower and upper bounds of 2 for the myopic sequential price of anarchy (achieved for a worst-case order of the arrival of the players). We then initiate the study of myopic sequential price of stability and for the multicast game on the ring we construct a lower bound of 4/3, and provide an upper bound of 26/19. To the end, we conjecture and argue that the right answer is 4/3.

cs.GT↗

arXiv2014

An $H_{n/2}$ Upper Bound on the Price of Stability of Undirected Network Design Games

In the network design game with $n$ players, every player chooses a path in an edge-weighted graph to connect her pair of terminals, sharing costs of the edges on her path with all other players fairly. We study the price of stability of the game, i.e., the ratio of the social costs of a best Nash equilibrium (with respect to the social cost) and of an optimal play. It has been shown that the price of stability of any network design game is at most $H_n$, the $n$-th harmonic number. This bound is tight for directed graphs. For undirected graphs, the situation is dramatically different, and tight bounds are not known. It has only recently been shown that the price of stability is at most $H_n \left(1-\frac{1}{Θ(n^4)} \right)$, while the worst-case known example has price of stability around 2.25. In this paper we improve the upper bound considerably by showing that the price of stability is at most $H_{n/2} + ε$ for any $ε$ starting from some suitable $n \geq n(ε)$.

cs.GT↗

arXiv2013

Tree Nash Equilibria in the Network Creation Game

In the network creation game with n vertices, every vertex (a player) buys a set of adjacent edges, each at a fixed amount α > 0. It has been conjectured that for α >= n, every Nash equilibrium is a tree, and has been confirmed for every α >= 273n. We improve upon this bound and show that this is true for every α >= 65n. To show this, we provide new and improved results on the local structure of Nash equilibria. Technically, we show that if there is a cycle in a Nash equilibrium, then α < 65n. Proving this, we only consider relatively simple strategy changes of the players involved in the cycle. We further show that this simple approach cannot be used to show the desired upper bound α < n (for which a cycle may exist), but conjecture that a slightly worse bound α < 1.3n can be achieved with this approach. Towards this conjecture, we show that if a Nash equilibrium has a cycle of length at most 10, then indeed α < 1.3n. We further provide experimental evidence suggesting that when the girth of a Nash equilibrium is increasing, the upper bound on α obtained by the simple strategy changes is not increasing. To the end, we investigate the approach for a coalitional variant of Nash equilibrium, where coalitions of two players cannot collectively improve, and show that if α >= 41n, then every such Nash equilibrium is a tree.

cs.GT↗