Abstract Are managers necessary for organizations? Could organizations function without them? To answer, we must separate between two questions: are top managers necessary? And are middle managers necessary? I argue that larger organizations are prone to need someone to have oversight of the wholeness and to take responsibility for its design and development. Given the dedication and time commitment needed to fulfill that role, it is virtually impossible to have a larger organization without any top management. However, a large organization with top management and frontline employees—but no managerial layers in between—is already a much more realistic possibility. It typically requires having autonomous, self-managing teams empowered to make all the necessary decisions related to their own work, accompanied by certain structural solutions (often enhanced by ICT) solving key information- and coordination-related tasks that are traditionally taken care of by middle managers. Often specific coach roles also emerge. In principle, if working substitutes are found to all tasks traditionally taken care of by middle managers, an organization can be functional and successful without any managerial layers. I examine a few successful examples of such organizations, Buurtzorg and Reaktor, while also highlighting key boundary conditions for when, where, and how self-managing organizations can succeed. I conclude by distinguishing between structure and hierarchy, arguing that while self-managing organizations are characterized by high levels of decentralization, their functionality is ensured through having enough structure, thus combining low hierarchy with adequate structure to find the most functional form of organizing in a particular context.
Benjamin Kraner, Shengnan Li, Andreia Sofia Teixeira, Claudio J. Tessone
Trust is key to the efficient functioning of any fiat or crypto-currency and so is for the consensus algorithm behind the functioning of blockchain systems. By an arbitrary design choice, Bitcoin and most Proof-of- Work (PoW) blockchains have a limited supply. Once block rewards vanish, only transaction fees will remain as an incentive for miners to partake in the verification process. In this paper, we analyse the impact that miners bargaining over block composition has on consensus in the absence of block rewards: in this situation, competing blocks at the same height may be more attractive to peers by including less transactions (i.e. sharing the mempool). The mining and acceptance of blocks can be modelled as an Ulti-matum Game, where miners' strategies represent their fairness sentiment. Extending previous Literature, our study focuses on the effect of the transaction arrival rate on global consensus in the system and whether local consensus is formed under certain assumptions about the strategies of miners. We find that consensus is threatened when the supply of transactions is low and stable consensus only emerges when the amount of unconfirmed transactions remains sufficient. In addition, when miners are set with randomised strategies, it is more difficult for the system to achieve consensus. Our research suggests that transitioning from a block reward incentive to a transaction fee incentive may weaken and even destroy the consensus of PoW-based systems.
Matthias Lohr, Kenneth Skiba, Marco Konersmann, Jan Jürjens · 5 authors
Existing fair exchange protocols usually neglect consideration of cost when assessing their fairness. However, in an environment with non-negligible transaction cost, e.g., public blockchains, high or unexpected transaction cost might be an obstacle for wide-spread adoption of fair exchange protocols in business applications. For example, as of 2021-12-17, the initialization of the FairSwap protocol on the Ethereum blockchain requires the selling party to pay a fee of approx. 349.20 USD per exchange. We address this issue by defining cost fairness, which can be used to assess two-party exchange protocols including implied transaction cost. We show that in an environment with non-negligible transaction cost where one party has to initialize the exchange protocol and the other party can leave the exchange at any time cost fairness cannot be achieved.
In the emerging realm of decentralized finance (DeFi), most of the existing Automated Market Maker (AMM) protocols used by major platforms like Uniswap and Curve are governed by a static mathematical equation, such as the constant product curve. One major shortcoming of these curves is that they require external forces to maintain the price of the liquidity pool (LP), subjecting the LP to loss due to arbitrage. A novel solution, the dynamic curve AMM, was recently proposed to ensure that the pool price always matches the market price, making the LP invulnerable to arbitrageurs. Dynamic curves, however, have a path-dependent trading problem, meaning that the number of trades and the distribution of trades affect the trader’s gain. We show how to find the optimal trading policy for a dynamic AMM curve under several settings. We first show that in a zero-transaction-fee setting the optimal trading policy is to place infinitesimally small trades, resulting in zero slippage. Then, we present an algorithm that computes the optimal policy in a fixed-number-of-trade setting. Though the problem has an exponentially large search space, our algorithm utilizes dynamic programming to achieve a polynomial run-time. Finally, we generalize the solution to more complex settings, including a per-order-fee setting and a percentage-fee setting.
Pietro Ferraro, Andreas Penzkofer, Christopher King, Robert Shorten
In this article, we present a feedback approach to the design of an attack mitigation policy for directed acyclic graph (DAG)-based distributed ledgers. We develop a model to analyze the behavior of the ledger under the so-calledTips Inflation Attack, which endangers the liveness of transactions, and we design a control strategy to counteract this attack strategy. The efficacy of this approach is showcased through a theoretical analysis, in the form of two theorems about the stability properties of the ledger with and without the controller, and extensive Monte Carlo simulations of an agent-based model of the distributed ledger.
Matthias Lohr, Kenneth Skiba, Marco Konersmann, Jan Jürjens · 5 authors
Existing fair exchange protocols usually neglect consideration of cost when assessing their fairness. However, in an environment with non-negligible transaction cost, e.g., public blockchains, high or unexpected transaction cost might be an obstacle for wide-spread adoption of fair exchange protocols in business applications. For example, as of 2021-12-17, the initialization of the FairSwap protocol on the Ethereum blockchain requires the selling party to pay a fee of approx. 349.20 USD per exchange. We address this issue by defining cost fairness, which can be used to assess two-party exchange protocols including implied transaction cost. We show that in an environment with non-negligible transaction cost where one party has to initialize the exchange protocol and the other party can leave the exchange at any time cost fairness cannot be achieved.
We study a scenario where an adjudication task (e.g., the resolution of a binary dispute) is outsourced to a set of agents who are appointed as jurors. This scenario is particularly relevant in a Web3 environment, where no verification of the adjudication outcome is possible, and the appointed agents are, in principle, indifferent to the final verdict. We consider simple adjudication mechanisms that use (1) majority voting to decide the final verdict and (2) a payment function to reward the agents with the majority vote and possibly punish the ones in the minority. Agents interact with such a mechanism strategically: they exert some effort to understand how to properly judge the dispute and cast a yes/no vote that depends on this understanding and on information they have about the rest of the votes. Eventually, they vote so that their utility (i.e., their payment from the mechanism minus the cost due to their effort) is maximized. Under reasonable assumptions about how an agent's effort is related to her understanding of the dispute, we show that appropriate payment functions can be used to recover the correct adjudication outcome with high probability. Our findings follow from a detailed analysis of the induced strategic game and make use of both theoretical arguments and simulation experiments.
Dimitris Karakostas, Aggelos Kiayias, Thomas Zacharias
We study Nash-dynamics in the context of blockchain protocols. We introduce a formal model, within which one can assess whether the Nash dynamics can lead utility-maximizing participants to defect from the "honest" protocol operation, towards variations that exhibit one or more undesirable infractions, such as abstaining from participation and producing conflicting protocol histories. Blockchain protocols that do not lead to such infraction states are said to be compliant. Armed with this model, we evaluate the compliance of various Proof-of-Work (PoW) and Proof-of-Stake (PoS) protocol families, with respect to different utility functions and reward schemes, leading to the following results: i) PoS ledgers under resource-proportional rewards can be compliant if costs are negligible, but non-compliant if costs are significant; ii) PoW and PoS under block-proportional rewards exhibit different compliance behavior, depending on the lossiness of the network; iii) PoS ledgers can be compliant w.r.t. one infraction, i.e., producing conflicting messages, but non-compliant (and non-equilibria) w.r.t. abstaining or an attack we call selfish signing; iv) taking externalities, such as exchange rate fluctuations, into account, we quantify the benefit of economic penalties, in the context of PoS protocols, in disincentivizing particular infractions.
We introduce the SPRIG (Smart Proofs via Recursive Information Gathering) protocol. SPRIG allows agents to propose, question, and defend mathematical proofs in a decentralized fashion. A structure of stakes and bounties aims at producing debates in good faith and if those persist, they must go down to machine-level details, where they can be settled automatically. This combination of economic incentives and an oracle is designed to promote succinct and informative proofs. SPRIG can run autonomously as a smart contract on a blockchain platform, and hence it does not rely on a central trusted institution. We translate SPRIG into a general game-theoretic model and prove that the protocol satisfies two desirable properties: no spamming and monotonicity. We then characterize analytically the equilibrium of a simple two-player specification of the model: this provides important insights into the impact of the protocol’s parameters on the probabilities that it induces type I/II errors. We conclude by discussing the main attacks SPRIG’s designers will need to take into account.
We propose and study a new class of polynomial voting rules for a general decentralized decision/consensus system, and more specifically for the proof-of-stake protocol. The main idea, inspired by the Penrose square-root law and the more recent quadratic voting rule, is to differentiate a voter’s voting power and the voter’s share (fraction of the total in the system). We show that, whereas voter shares form a martingale process that converges to a Dirichlet distribution, their voting powers follow a supermartingale process that decays to zero over time. This prevents any voter from controlling the voting process and, thus, enhances security. For both limiting results, we also provide explicit rates of convergence. When the initial total volume of votes (or stakes) is large, we show a phase transition in share stability (or the lack thereof), corresponding to the voter’s initial share relative to the total. We also study the scenario in which trading (of votes/stakes) among the voters is allowed and quantify the level of risk sensitivity (or risk aversion) in three categories, corresponding to the voter’s utility being a supermartingale, a submartingale, and a martingale. For each category, we identify the voter’s best strategy in terms of participation and trading. Funding: W. Tang gratefully acknowledges financial support through the National Science Foundation [Grants DMS-2113779 and DMS-2206038] and through a start-up grant at Columbia University. D. D. Yao’s work is part of a Columbia–City University/Hong Kong collaborative project that is supported by InnoHK Initiative, the Government of Hong Kong Special Administrative Region, and the Laboratory for AI-Powered Financial Technologies.
A decentralized blockchain is a distributed ledger that is often used as a platform for exchanging goods and services. This ledger is maintained by a network of nodes that obeys a set of rules, called a consensus protocol, which helps to resolve inconsistencies among local copies of a blockchain. In this paper, we build a mathematical framework for the consensus protocol designer, specifying (a) the measurement of a resource which nodes strategically invest in and compete for to win the right to build new blocks in the blockchain; and (b) a payoff function for such efforts. Thus, the equilibrium of an associated stochastic differential game can be implemented by selecting nodes in proportion to this specified resource and penalizing dishonest nodes by its loss. This associated, induced game can be further analyzed using mean field games. The problem can be broken down into two coupled PDEs, where an individual node's optimal control path is solved using a Hamilton-Jacobi-Bellman equation, and where the evolution of states distribution is characterized by a Fokker-Planck equation. We develop numerical methods to compute the mean field equilibrium for both steady states at the infinite time horizon and evolutionary dynamics. As an example, we show how the mean field equilibrium can be applied to the Bitcoin blockchain mechanism design. We demonstrate that a blockchain can be viewed as a mechanism that operates in a decentralized setup and propagates properties of the mean field equilibrium over time, such as the underlying security of the blockchain.
The recently proposed Uniswap v3 replaces the fungible liquidity provider token (LP token) into non-fungible ones, making the design for liquidity mining more difficult. In this paper, we propose a flexible liquidity mining scheme that realizes the overall liquidity distribution through the fine control of local rewards. From the liquidity provider's point of view, the liquidity provision strategy forms a multiplayer zero-sum game. We analyze the Nash Equilibrium and the corresponding strategy, approximately, deploying the liquidity proportional to the reward distribution, in some special cases and use it to guide the general situations. Based on the strategic response above, such a scheme allows the mining rewards provider to optimize the distribution of liquidity for the purpose such as low slippage and price stabilization.
Blockchains have witnessed widespread adoption in the past decade in various fields. The growing demand makes their scalability and sustainability challenges more evident than ever. As a result, more and more blockchains have begun to adopt proof-of-stake (PoS) consensus protocols to address those challenges. One of the fundamental characteristics of any blockchain technology is its crypto-economics and incentives. Lately, each PoS blockchain has designed a unique reward mechanism, yet, many of them are prone to free-rider and nothing-at-stake problems. To better understand the ad-hoc design of reward mechanisms, in this paper, we develop a reward mechanism framework that could apply to many PoS blockchains. We formulate the block validation game wherein the rewards are distributed for validating the blocks correctly. Using evolutionary game theory, we analyze how the participants' behaviour could potentially evolve with the reward mechanism. Also, penalties are found to play a central role in maintaining the integrity of blockchains.
This study aims to solve the credit problems in the supply chain commodity and currency circulation links from the perspective of the ledger, while the game model method has been adopted. The research firstly reviews the relationship between distributed ledger technology and the essential functions of currency. Then, by constructing two-agent single-period and multi-period game models in the entire supply chain, the researchers analysed the incentive mechanism and equilibrium solution of distributed nodes of Central Bank Digital Currency (CBDC). The results of this study include the incentive mechanism and optimization of distributed nodes based on licensed distributed ledger technology, which is an important issue that CBDC faces when performing currency functions. The implications of this study mainly cover the limitations of the underlying technology of the public chain and its reward mechanism in the supply chain management and provide support for the rationality of the CBDC issuance mechanism based on state-owned commercial banks, which provides a reference for the CBDC practice. The main value of the research not only serves the decision-making department of the CBDC issuance but also provides ideas on the operation mode of digital currency for the field of digital currency research.
In the high-stakes race to develop more scalable blockchains, some platforms (Binance, Cosmos, EOS, TRON, etc.) have adopted committee-based consensus (CBC) protocols, whereby the blockchain's record-keeping rights are entrusted to a committee of elected block producers. In theory, the smaller the committee, the faster the blockchain can reach consensus and the more it can scale. What's less clear, is whether such protocols ensure that honest committees can be consistently elected, given blockchain users typically have limited information on who to vote for. We show that the approval voting mechanism underlying most CBC protocols is complex and can lead to intractable optimal voting strategies. We empirically characterize some simpler intuitive voting strategies that users tend to resort to in practice and prove that these nonetheless converge to optimality exponentially quickly in the number of voters. Exponential convergence ensures that despite its complexity, CBC exhibits robustness and has some efficiency advantages over more popular staked-weighted lottery protocols currently underlying many prominent blockchains such as Ethereum.
We propose a model for games in which the players have shared access to a blockchain that allows them to deploy smart contracts to act on their behalf. This changes fundamental game-theoretic assumptions about rationality since a contract can commit a player to act irrationally in specific subgames, making credible otherwise non-credible threats. This is further complicated by considering the interaction between multiple contracts which can reason about each other. This changes the nature of the game in a nontrivial way as choosing which contract to play can itself be considered a move in the game. Our model generalizes known notions of equilibria, with a single contract being equivalent to a Stackelberg equilibrium, and two contracts being equivalent to a reverse Stackelberg equilibrium. We prove a number of bounds on the complexity of computing SPE in such games with smart contracts. We show that computing an SPE is \(\textsf {PSPACE}\)-hard in the general case. Specifically, in games with k contracts, we show that computing an SPE is \(\varSigma _k^\textsf {P}\)-hard for games of imperfect information. We show that computing an SPE remains \(\textsf {PSPACE}\)-hard in games of perfect information if we allow for an unbounded number of contracts. We give an algorithm for computing an SPE in two-contract games of perfect information that runs in time \(O(m\ell )\) where m is the size of the game tree and \(\ell \) is the number of terminal nodes. Finally, we conjecture the problem to be \(\textsf {NP}\)-complete for three contracts.