Now that the dust has settled around our airdrop announcement, we wanted to take a closer look at the game theory underpinning the 5th airdrop and how it could signal a huge reward for a select group of RPM token holders. If you aren’t interested in some game theory basics, how it plays into crypto-economic design and it’s role in the 5th airdrop, all you really need to know is this:
The fewer people that hold through to end, the larger the reward becomes for those that do. To simplify this even further, if only one person held their initial balance, they would receive the entire 800 million bonus tokens up for distribution.
Do we have your attention yet? If so, read on for an exploration of traditional game theory, behavioral/economic incentives and how we are attempting to reward holders with an interest in the long-term success of the RepMe Network.
Let’s start with a bit of the basics.
What is Game Theory?
To put it simply, game theory is the study of decision making within a pre-determined set of parameters (games, scenarios, etc). Devised by John Van Neumann and Osker Morgenstern in 1944, it was considered a breakthrough in the study of oligopoly markets. Using mathematical models, it can be used to analyze economics, psychology, logic, computer science and yes, distributed systems like blockchains.
Another way to look at game theory is a microcosm of human behavior wherein under a set of conditions, specific incentive structures can lead to predictable behaviors by honest and rational players.
In a typical game theory model, there are 3 primary components.
- Players
- Strategies
- Outcomes
Players are the users that make decisions. Strategies are the maneuvers that players make while simultaneously taking into account potential strategies of other players. Outcomes are the result of the players’ moves within the system, and with the right incentive mechanisms, can be driven to a certain direction or played out repeatedly with similar outcomes.
Still with us? Wonderful! Time to press on with an actual example.
The Prisoners Dilemma
To make the above clearer, lets explore a well-known game theory scenario known as the Prisoner’s Dilemma.
In this scenario, there are two prisoners being interrogated separately for a crime that they are both equally guilt of. Let’s call them Alice and Bob. Both Alice and Bob are offered an opportunity to confess and receive a reduced sentence. The outcome of this scenario can play out in 4 ways, with both Alice and Bob having to make one of two possible decisions, either confess or don’t confess. This results in the 4 possible outcomes laid out in the table below.
As you can see, the overall solution with the least jail time for both prisoners is for both prisoners to remain silent and not confess. However, this outcome is considered unstable as it makes an assumption that both prisoners will knowingly leave a better deal on the table where they could potentially receive 0 years and be set free if they confess and the other prisoner does not. Game theory model outcomes and behavioral psychology tell us that this outcome is highly unlikely, as rational players will inherently betray the other due to self-interests.
In game theory, the solution to a game where each player chooses their optimal strategy given the strategy was chosen by the other and they have nothing to gain by shifting their strategy is known as Nash Equilibrium. This is a stable state and is represented in the top left corner of the chart. In this outcome, Alice and Bob are both making the best decisions that they can while taking into account the other player’s decision.
The example of the Prisoner’s Dilemma can be used in a variety of real-world situations to demonstrate cooperative behavior between players. In distributed systems, this concept is critical to maintaining trustless consensus models and has important ramifications when applied to cryptocurrencies in the context of crypto-economics.[1]
Game Theory and Crypto-Economics
Crypto-economics can be defined as the combination of cryptography, economics, and game theory incentive models incorporated into distributed blockchain protocols in order to create a secure, stable, and sustainable system. While a complete discussion of crypto-economic game theory is well outside the scope of this article, let’s cover a quick and dirty example.
Proof of Work and Game Theory
The easiest way to understand how game theory can influence distributed networks is through everyone’s favorite blockchain network: Bitcoin.
In order for Bitcoin to remain secure, it needs to reach consensus about the state of the blockchain without needing to trust the other nodes in the network. This problem is solved through Proof of Work (POW) and was the primary innovation that the Bitcoin network offered.
POW consensus has miners solve complex puzzles by utilizing a real world asset in the form of electricity. This usage of electricity creates a financial incentive for the miners to remain honest and at the same time makes the network difficult and costly to attack. Coupled with the block rewards offered by mining, a positive feedback loop is created that reinforces the security of the network. Incentive structures predicated on game theory mechanisms come into play in order to encourage the players (users and miners) in the system to act honestly.
The above example only scratches the surface of the complexity of crypto-economic game theory. If you are interested in this topic, we suggest this wonderful paper authored by Rajani Singh, Ashutosh Dhar Dwivedi, and Gautam Srivastava for a deeper dive.
RepMe’s 5th Airdrop and Fair Cake-Cutting
To bring this all back around the the RepMe Network, the 5th airdrop most closely resembles a game theory fair division problem known as “Fair Cake-Cutting.”
The problem involves a heterogeneous resource, such as a cake with different toppings, that is assumed to be divisible — it is possible to cut arbitrarily small pieces of it without destroying their value. The resource has to be divided among several partners who have different preferences over different parts of the cake, i.e., some people prefer the chocolate toppings, some prefer the cherries, some just want as large a piece as possible. The division should be subjectively fair, in that each person should receive a piece that he or she believes to be a fair share.
The “cake” is only a metaphor; procedures for fair cake-cutting can be used to divide various kinds of resources, such as land estates, advertisement space or broadcast time. [2]
This piece of game theory explores how players form subjective opinions about their “fair share” and the strategies they develop to reduce any sort of dissonance. In the case of the airdrop, this theory pits holders (community) against sellers (speculators) in a battle to determine who can accrue the most value while aligning with their longer term intentions and beliefs.
How this ends up playing out will certainly be exciting to watch from the sidelines and we will be sure to author a detailed follow-up posts with the results. Have fun!
[1] https://blockonomi.com/game-theory/ — Credit to blockonomi for their writings on game theory.
