Game theory is a part of mathematics that helps us understand how people make choices in situations where the outcomes depend not only on their own decisions, but also on those of others. In the world of cryptocurrencies, such as Bitcoin, this theory is crucial to ensuring the security and reliability of the network.
Game theory is not something new. It began to be formally studied in the 1920s, but it was in 1944 that John Von Neumann and Oskar Morgenstern published their major work, "Theory of Games and Economic Behavior". This study laid the foundations for using mathematics to analyse situations where several players interact with each other.
In the context of cryptocurrencies, game theory is used to design systems where each participant has an interest in behaving honestly.
Let's take bitcoin as an example.
In bitcoin, people called "miners" use powerful computers to solve complex mathematical problems in order to validate transactions and create new blocks on the blockchain. In exchange for this work, they receive bitcoins as a reward. Game theory dictates that it is more profitable for them to follow the rules and validate transactions correctly than to cheat. If they cheated, not only would they lose their reward, but it would also be very expensive in terms of energy and equipment.
Game theory also helps to protect the network against attacks. For example, to successfully fool the system (as in a 51% attack), a group of miners would have to control more than half of the network's computing power, which is extremely expensive and difficult to achieve. Game theory principles show that the costs and risks associated with such an attack deter miners from engaging in it.
The consensus mechanism, such as the Proof of Work used by bitcoin, is also based on game theory. It ensures that all network participants are working towards a common goal, which is to secure the network and validate legitimate transactions.
Game theory is one of the pillars of blockchain security. The ability to assess and model the behaviour of players on the network means that their actions can be anticipated and steered, thanks in particular to economic incentives. Coupled with a high level of cryptography at a very high cost, game theory enables the bitcoin network to be one of the most secure in the world today.
It should be noted that game theory works all the better when the network has a large number of participants. Indeed, if we assume that all the players in a network act rationally, i.e. to obtain rewards by securing the network, it will be all the more difficult for a malicious actor to take control of the blockchain if there are a large number of validators.
For more information
https://www.vwl.uni-mannheim.de/media/Lehrstuehle/vwl/von_Thadden/TheoriedesJeux.pdf
https://www.youtube.com/watch?v=G9ER5bLxQEU
