# Economically Rational as a security proof

Is it possible to prove the security of a cryptocurrency payment protocol by saying that the actors will seek to maximize their profits. Would I need to set this up as a game and prove it that way or what can I do to get started?

The information I have is the state of the system and then I have just iterated each agents ability to change the system and just show that by following the protocol each agent maximizes their profit.

• One thing that your proof would need to take account of is coalitions; that is, could Alice take actions that would benefit Bob (more than it hurts Alice)? The other issue is that some people may have motives other than monetary profit within the cryptocurrency system; for example, if Alice can potentially damage the cryptocurrency of the Carol company, could Alice gain by shorting Carol's stock, and then proceeding with the damage? – poncho Oct 10 '18 at 17:31

## 1 Answer

The tricky part is what if the agents do not follow the protocol? It is often the case that by deviating from the protocol, an agent can gain a higher payoff than following the protocol. if this happens, then the agent may not follow the protocol. One party deviating from the protocol may cause other parties to change their strategy. Will they reach a stable state?

Therefore, to prove security, you would need to specify the following:

• All the parties (players);
• All actions can be performed by the parties (strategies);
• Is there any sequence or order of parties have to act, or they move simultaneously;
• What information do the parties have in the process? Do they know everything or only some information?
• The utility functions of each party -- taking into account not just money, but others types of payoffs.
• All assumptions

Putting those together, you can formally specify a game. Having the game formally specified, you will have all possible outcomes induced by all possible combination of parties' strategies, and payoffs for each party associated with the outcome. You can then analyse the game to see whether there exist an equilibrium (or more than one), which is a "solution" of the game. An equilibrium consists of a set of strategies for each party (and maybe probabilities). An equilibrium basically says if all parties choose the strategies in the equilibrium, they will not want to change their strategies because their utilities won't be better.

In the simplest case, if you have one equilibrium and it entails your security goal, then you can say you have proved security in the presence of rational parties. But the situation can be much more complicated.

• This is extremely helpful. I can specify all of the listed above. How 'secure' is the final statement? ["in presence of rational parties"] – channon Oct 10 '18 at 18:30
• And also do you have any reference for the format or model of how to specify the parties, actions, etc. that are common? – channon Oct 10 '18 at 18:32
• To start with, I recommend two textbooks: 1 Kevin Leyton-Brown and Yoav Shoham, Essentials of Game Theory: A Concise, Multidisciplinary Introduction, Morgan and Claypool Publishers 2 Michael Maschler, Eilon Solan, and Shmuel Zamir, Game Theory. Cambridge press – Changyu Dong Oct 10 '18 at 19:41
• How would this game identify a weakness in a supposed hard problem used in the protocol's key exchange (or whatever)? How do you reconcile behavioural theory with numeric cryptography such as differential analysis or flaws in a proof of work algorithm? – Paul Uszak Oct 10 '18 at 22:03
• This is not the kind of game used in cryptography, e.g. distinguish ability game. It won’t help identify weakness in hard problem. The rational assumption will give you a different security model (i.e. from semi-honest or purely malicious to something in the middle). The adversary will have economics constraints, In additional to computational constraints. The idea is the the adversary will not have motivation to attack if its payoff is worse. – Changyu Dong Oct 11 '18 at 10:14