Équilibre de Nash
Équilibre stratégique.
In game theory, the Nash Equilibrium represents a conceptual 'truce' where every participant is making the best decision they can, given the decisions of others. It does not necessarily mean everyone is happy, but rather that no one can improve their own situation simply by changing their move while others stay put.
For crypto protocols, reaching a Nash Equilibrium where honest behavior is the most profitable strategy is the 'Holy Grail' of security design. If cheating is profitable (even briefly), the system is not in equilibrium and is vulnerable to attack.
graph LR
Center["Équilibre de Nash"]:::main
Pre_game_theory["game-theory"]:::pre --> Center
click Pre_game_theory "/terms/game-theory"
Rel_byzantine_fault_tolerance["byzantine-fault-tolerance"]:::related -.-> Center
click Rel_byzantine_fault_tolerance "/terms/byzantine-fault-tolerance"
Rel_game_theory["game-theory"]:::related -.-> Center
click Rel_game_theory "/terms/game-theory"
Rel_algorithmic_stablecoin["algorithmic-stablecoin"]:::related -.-> Center
click Rel_algorithmic_stablecoin "/terms/algorithmic-stablecoin"
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🧒 Explique-moi comme si j'avais 5 ans
🚗 Imagine two cars driving toward each other on a narrow road. If both swerve to their right, they pass safely. If one swerves and the other doesn't, they crash. The situation where *both* swerve right is a Nash Equilibrium—neither driver wants to change their move alone, because they would crash.
🤓 Expert Deep Dive
### The Mechanism of Stability
Formally, a set of strategy profiles $S = (s_1, s_2, ..., s_n)$ is a Nash Equilibrium if for every player $i$, $U_i(s_i, s_{-i}) \geq U_i(s'_i, s_{-i})$ for all possible deviations $s'_i$.
In blockchain mechanism design, we aim for Strong Nash Equilibria that are also Collusion-Resistant. Mere Nash stability is insufficient because it assumes players act independently. In reality, validators often collude off-chain. Thus, modern protocols (like Ethereum's Casper) must target Coalition-Proof Nash Equilibrium (CPNE).
Key Challenge: Many crypto games have multiple equilibria. The goal of economic coordination (e.g., via shelling points or difficulty adjustment) is to make the 'honest' equilibrium the Focal Point.