Game theory directly ties into the underlying framework of cryptocurrencies that exist as decentralized networks. In particular, cooperative game theory and its relevance to coordination games within the incentive and socially scalable structures of decentralized networks such as Bitcoin and Ethereum is vital to their security and long-term sustainability.
In a decentralized network without a centralized authority, cooperation among the players is necessary for the system to remain viable over the long term. But how does cooperation emerge? Further, how do you maintain cooperation among rational players motivated by self-interests?
These are questions that have been analyzed meticulously over the years and now have become an integral component of the sustained growth and functionality of entirely novel decentralized networks.
The Emergence of Cooperation in a Decentralized System
In a decentralized system, there is no centralized authority to deal out punishment or enforce the rules governing the parameters of the system. Naturally, a decentralized system needs some form of cooperation between the players to come to not only an agreement on the state of the network but also to ensure long-term sustainability and growth through mutual cooperation.
However, this becomes difficult as the players in a system are usually assumed to be rational and rely on their own-self interests as motivation for their actions. The potential for cooperation among players can arise when each player can help each other. The inherent dilemma that arises is when giving this help is costly. Therefore, achieving the right balance is necessary for cooperation to thrive, representing a state of equilibrium in the system.
As David Axelrod puts it in his famous book The Evolution of Cooperation, “Mutual cooperation can emerge in a world of egoists without central control by starting with a cluster of individuals who rely on reciprocity.” Before diving into this conclusion, it is important to understand the fundamental structure of cooperative game theory in cryptocurrencies.
As seen in a previous article outlining the classic example of a non-zero sum game, The Prisoner’s Dilemma, you can see that it is in the best interests of the two prisoners to both remain quiet and not rat out the other prisoner (for them to cooperate with each other).
The Prisoner’s Dilemma
However, this represents an unstable state since it assumes the players will not act out of their own self-interests and that they can communicate, which they can’t. What this example does not represent though is one of the most critical and invisible aspects governing a decentralized network such as Bitcoin, the shadow of the future.
While the stable state (Nash Equilibrium) in the classical Prisoner’s Dilemma is for both prisoners to defect in this one-time interaction, this is not the optimal solution for the Iterated Prisoner’s Dilemma. The Iterated Prisoner’s Dilemma represents a case where the scenario will play out over and over again, rather than just a one-time event between the prisoners. This creates a looming influence of future interactions of counterparts while also simultaneously allowing past interactions between players to become highly relevant to a future interaction since they know that they will be interacting with each other again and again. The implications of the Iterated Prisoner’s Dilemma are the focus of Axelrod’s book and can be applied to everything from international politics to cooperation based on mutual reciprocation between antagonists in war.
The Bitcoin Network
Thus, Bitcoin as a network represents a case of an Iterated Prisoner’s Dilemma since the players in the system will continually be using the system and interacting with each other in a coordination game aimed at maintaining and securing the network in the long-term. This is due to the inherent cost of mining. Since miners are responsible for securing the network and validating transactions, their investment in mining hardware ensures that they will (for the most part) continue to be a part of the system in the longer term, creating a shadow of the future sufficient enough to influence their short-term decision making.
With the reward for mining being in Bitcoin, the further incentive extenuates to an iterated dilemma since their received value for their efforts is invariably tied to the long-term success of the network. From this, mutual cooperation can emerge and become collectively stable.
The goal is to achieve a coordinated state of equilibrium between players that would otherwise be considered unstable in the classic non-iterated prisoner’s dilemma. An equilibrium state as such can only be achieved with effective self-policing mechanisms.
Axelrod came to his conclusion that cooperation based on reciprocity is collectively stable. In essence, it cannot be invaded by another strategy, such as defection. This stable state is achieved only if that shadow of the future looms large enough to impact each interaction and defection by players is punished.
Mutual cooperation between players in Bitcoin emerged with its inception. It was initially very low profile and relegated to cypherpunks and enthusiasts who were interested in its use case and decided to help facilitate the network. Further, the payoff for acting maliciously in its early stages was simply not worth the cost. While defection by a malicious actor in the short-term may have been successful, the vast majority of those involved in the early stages were invested in the longer term success of the concept purely out of interest or financial hopes.
Even if the majority of early miners were acting maliciously, yes their short-term gains would be solid and represent a non-iterated dilemma’s de facto equilibrium, however, as more time passed their payoff would decrease and their cost would increase, effectively making the strategy of defection within the network untenable.
Maintaining Mutual Cooperation in a Decentralized System
Axelrod’s experiments have some fascinating conclusions, but one of the most fascinating is the ability of a strategy predicated on mutual cooperation based on reciprocity to “invade” a strategy employed by the majority in a decentralized system with no central authority.
Specifically, a strategy based on mutual cooperation is the dominant strategy for stability and has an ability to permeate a group of other strategies due to the fact that it is more beneficial in terms of payoff to cooperate with other players in the long-term than it is to defect, so long as the situation is an iterated dilemma. As demonstrated, this is the case with a decentralized network utilizing PoW as its consensus model such as Bitcoin.
So, in the case of Bitcoin mining, a majority of the miners in the network could be acting maliciously (defecting), however, in the long run, this is simply not effective as the cost becomes too unbearable. The malicious miners would be better off cooperating with the rest of the network. Eventually, the smaller minority of miners coordinating with each other would achieve an overall higher payoff among each other, and that higher payoff would have subsequent effects on the malicious miners, thus eventually changing their strategy to one of cooperation.
Once cooperation based on reciprocity is established in a population, it can protect itself from invasion by uncooperative strategies. The payoff from cooperating in a system such as Bitcoin is higher than defecting, so the strategy of cooperation becomes collectively stable. For this to happen, little needs to be assumed about the individuals involved or the social setting. Players do not even need to communicate, and there is no need to assume trust between the players, the use of mutual cooperation as the dominant strategy can make defection unproductive and extremely costly.
The evolution of cooperation within the system allows the successful strategy to thrive even if the players do not know why or how.
The successfully implemented incentive structure and mechanics of Nakamoto Consensus in Bitcoin are an overall strategy that is designed to elicit cooperation in a decentralized system even from an egoist. The lack of a central authority ends up not being a problem at all because cooperation within the system is self-policing. The fundamental transparency of the Bitcoin blockchain, transaction verification, and network consensus are a requisite part of the players’ ability to further respond to other players’ previous choices.
In fact, when you really analyze historical or biological examples of the emergence of cooperation, it is not surprising at all that it has emerged in Bitcoin. Even bacteria are capable of forming direct interactions of mutual cooperation based on reciprocity. Humans have the ability of projection and can calculate the risks of short-term actions weighed against longer-term consequences.
With a collectively stable strategy of cooperation dominant in decentralized systems such as both Bitcoin and Ethereum now, even a 51% attack will only have a very limited scope of influence. In the short term, recent transactions may be manipulated, but a strategy of defection is not collectively stable with an impending future influencing the short-term decision making. Eventually, mutual cooperation between players in these systems will always prevail due to the incentive structure of their designs.
Whether that means inevitably needing to overcome a few attempts at a strategy of defection invading the collectively stable cooperation of the system is yet to be seen. It has not happened in Bitcoin yet, and the clock is ticking on the available resources to be able to do so.
The role of mutual cooperation and its coordinated effort to secure and validate decentralized systems while maintaining long-term system integrity is fundamental to the viability of cryptocurrencies.
In the case of Bitcoin and Ethereum, when you analyze them from this perspective, it is difficult to imagine that they will not be around for a very long time. Whether or not all of the permutations of game theory and its sustained importance on the continual success of Bitcoin were considered when Satoshi Nakamoto designed it is hard to grasp.
Regardless, Bitcoin represents a paradigm shift in trustless human interaction, and its seamless promotion of mutual cooperation in a decentralized value transfer system is quite an incredible accomplishment from any perspective, let alone a game theory one.