- The first survey of the use of game theory as an analytical tool for blockchain networks, focused on security issues such as pool block withholding, majority attacks, and denial of service attacks.
- Key findings show different security issues may require different game theory approaches to accurately examine potential outcomes; the assumption of a singular Nash equilibrium for any given situation may limit the applicability and accuracy of using game theory as an analytical tool; and that different mechanisms may result in substantially different outcomes when utilizing game theory.
- They also find the majority of existing literature focuses on permissionless networks, research can also be applied to permissioned networks.
- Z. Liu et al., “A Survey on Blockchain: A Game Theoretical Perspective,” IEEE Access, vol. 7, pp. 47615–47643, 2019, doi: 10.1109/ACCESS.2019.2909924.
Core Research Question
- How can game theory be applied as an analytical tool to help address some common security issues in blockchain networks, and what are some of the potential advantages/disadvantages of doing so?
Overview & Fundamentals of Blockchain
- A blockchain provides four specific advantages over other networks; decentralization, a tamper-proof ledger, transparent transactions, and trustless but secure trading.
- Nodes are essential for blockchain networks to function. They broadcast transactions, store data into blocks, verify transactions, and reach consensus regarding the ordering of transactions/blocks.
- Different consensus protocols regulate who can operate a node and are typically classified as permissionless (public) or permissioned (private) networks. Permissionless blockchains essentially allow anyone to operate a node while a permissioned blockchain relies on a “small” group of authenticated nodes.
- Blockchain consensus incentives, such as mining, are used in an attempt to ensure node operators do not deviate from the blockchain’s consensus protocol. However, nodes may deviate from the protocol to increase individual utility which is referred to as “forking.”
Overview & Fundamentals of Game Theory
- Game theory provides a set of mathematical tools to analyze interactions among rational actors. Imagine player β has two choices to make, X or Y, with each having a different expected outcome. Player β will have a strategy on how to realize their desired expected outcome, but other players may or may-not also be participating, and have their own strategy and desired outcomes. Assuming all players are rational, game theory provides mathematical tools to analyze the choices and potential payoffs of these actors. The four specific game theory models analyzed in this paper are as follows:
- Non-cooperative games: Players have spontaneous strategies intended to maximize individual utility. No communication takes place between players so no cooperation may be planned, however, cooperation may occur naturally if cooperation results in Nash equilibrium.
- Extensive-form game: This game is made up of multiple non-cooperative subgames for which the player can explicitly map key aspects, such as sequencing potential moves. Backward induction is commonly used to find subgame equilibrium, potentially resulting in Nash equilibrium.
- Stackelberg game: Players are grouped into two categories; leaders and followers. Leaders make the first move in the game and followers decide their strategies after seeing the strategies of the leaders. Both attempt to maximize individual utility.
- Stochastic game: This is conducted in a sequence of stages, with each stage acting as a static non-cooperative subgame. At the start of the stage players select actions and receive a payoff related to the current state of the game and the chosen actions. The game then moves to a new stage where this is repeated, so on and so forth.
Other Specific Background Terms
- Utility: an economic concept modeling value or worth. Rational individuals always want to maximize their value/worth, so they always attempt to maximize utility.
- Nash equilibrium: a concept in game theory where actors have no incentive to change their strategy. If no other actor changes their strategy then an individual cannot receive an incremental benefit from changing theirs.
- Selfish mining: a subversive strategy in proof-of-work (PoW) blockchain systems where malicious miners do not release newly mined blocks. This causes good faith miners to use computing power to continue mining blocks already completed by the malicious miner. This allows the malicious miner to focus on unmined blocks and increases their chances of completing the next block, and receiving the reward first.
- Majority attack: when a miner possesses relatively large computational power compared to the rest of the miners they may be able to achieve results similar to a 51% attack without needing more than 50% of the network’s computational power. The amount of computational power necessary to successfully perform the attack varies.
- Goldfinger attack: attackers receive compensation to devalue a cryptocurrency
- Prisoners dilemma: a common term in game theory showing how two rational actors acting in their own self-interests may not produce the optimal outcome compared to if they were to cooperate.
- Pool Block WithHolding (PBWH): a type of selfish mining attack where miners in a pool do not submit blocks they find to the pool. This may cause the profitability of the pool overall, and thus participating miners as well, to drop.
- The researchers provide an overview and fundamental look at blockchain technology on a macro scale.
- They define the basic advantages, data organization and workflow, and cover a brief explanation of the compatibility of nodes and incentives.
- An overview and fundamental discussion of game theory is then provided.
- Four specific game theory models are outlined: non-cooperative games, extensive-form games, Stackelberg games, and stochastic games. Each is briefly put in terms of their applicability to blockchains.
- Applications of game theory and blockchains are then analyzed through a security lens.
- Specifically, the authors analyze selfish mining attacks, majority attacks, denial of service (DoS) attacks, false data sharing, distrustful goods trading, and cyber-insurance.
- The authors then discuss game theory applicability to mining-management and actions on blockchains.
- The authors discuss challenges and future directions of game theory and blockchains.
- Researchers use a literature-review style survey of multiple current blockchain-related issues and use game theory as an analytical framework to map potential outcomes.
- The authors use multiple game theory models explained above as follows:
- Potential actors are defined. There can be two or more actors depending on the game model used and situation.
- Each actor can take different defined actions.
- Theoretical payoffs or outcomes are defined in relation to each action.
- Using the foundational assumptions in each game model, the authors are able to infer which action may be the optimal choice for each actor to attempt to maximize their utility.
- Pool Block WithHolding (PBWH)
- The authors use a two-player non-cooperative game to show it is always optimal for both parties to decide to individually launch a PBWH. However, when both parties choose this, the utility of each pool is lower than if neither launched the attack. The game demonstrates the only way a PBWH results in improved utility for one party is if said party controls the majority of computational power. This is similar to the “prisoner’s dilemma” in game theory.
- At times, large mining pools may be divided into small pools simultaneously. If this happens, malicious miners may improve their utility by attacking larger pools rather than smaller pools. However, this may be costly as it has been shown utility only increases while using PBWH if the malicious actor has the majority of computational power.
- Majority attack
- Using theoretical non-cooperative games, if more than 50% of a network’s total computational power is used to extend the longest chain, then an attacker trying to deviate from honest mining will be wasting their own computational power by deviating. Thus, honest mining maximizes their utility and creates Nash equilibrium.
- Defender scenario
- The authors show the interaction between an attacker and defender can be estimated using a stochastic model. A defender can choose to actively add honest nodes to the blockchain (defend) or let it run as usual (do nothing). If the probability of the attacker succeeding exceeds a certain level then it is optimal for the defender to take action, resulting in a Nash equilibrium.
- Goldfinger attack
- The authors demonstrate that by using non-cooperative games, with attackers and defenders as the two actors, the defender can maximize their utility by having their bid satisfy constraints associated with power distribution. In this situation the game is at Nash equilibrium, as the defender offers a high enough bid to result in the attackers utility being maximized by not attacking the currency’s value. If the bid is not sufficient the attacker may carry out the attack.
- Denial of Service (DoS) attack
- Using non-cooperative games and assuming the two actors are “large pools” and “small pools,” a payoff matrix shows that to maximize utility in the short-run pools have an incentive to attack larger pools. However, larger pools may have greater computational power making the attack difficult. Also, this game assumes static pool participation when in reality miners can jump between pools, consistently changing pool computational power. This may result in a continuously shifting Nash equilibrium.
- Using continuous games, a potential counter to DDoS attacks is to add a “reputation” score to miners evaluating their honesty when mining. This would theoretically encourage honest mining as miners maximized their reputations to become more desirable for mining pools. When all miners maximize their utility by mining honestly, this would in a Nash equilibrium.
- From a game theory perspective there are two main challenges when using the theoretical models discussed:
- The assumption of a singular Nash equilibrium when in reality multiple exist. For example, a person can choose to participate in operating a node while simultaneously deciding if they will pay a transaction fee. This results in multiple Nash equilibria scenarios, demonstrating it is difficult to fully estimate results using game theory.
- Each game discussed in the paper has its own limitations, which may differ from the general structure of a blockchain, hindering the accuracy of the chosen game to estimate actors’ choices.
- More research should be done to analyze the choice of participating in different consensus mechanisms using game theory. Different mechanisms may result in different theoretical outcomes, depending on the potential incentives each mechanism utilizes.
- The majority of game theory research and blockchains has revolved around permissionless (public) blockchains. Game theory can also be applied to permissioned (private) blockchains as well and research should be conducted regarding this topic.
Game theory can be used as an analytical tool to model potential outcomes of multiple security threats to blockchain networks. Understanding the actor, action, and payoff structure of game theory models allows for the development of other related games to help predict potential scenarios. One such example is that of using game theory to analyze blockchain based secure edge networks. Another example illustrates how mining pool inequality may decrease the fairness and efficiency of a pool by using a Nash equilibria equation.