A Smart Contract Development Stack, Part II: Game Theoretical Aspects

Game theory is “the study of mathematical models of conflict and cooperation between intelligent rational decision-makers” [Wikipedia]. In particular, it looks at how rules in cooperative processes (“games”) impact the outcome, and also how the parties taking part in the game can cheat, i.e., exploit the rules for their own benefit.

In my previous post I sketched some ideas of how smart contracts can be expressed declaratively to avoid low-level mistakes, and also emphasised that techniques from functional safety, such as model checking, can be used to ensure properties of (state-based) contracts. However, as Björn Engelmann pointed out to me, many (smart) contracts are, by definition, cooperative processes, which is why they are susceptible to “game-theoretical” exploits. In this post I will mention a few, and show some ideas how they can be remedied.

A First Example: Sybil Attacks

sybil attack is one where a reputation-based system is subverted by one (real-world) party creating loads of fake (logical) identities who then behave in accordance with the real world party’s goals. For example, consider a decision that is based on majority vote. An attacker could create lots of additional parties and thereby taking over the majority, leading to a decision in the interest of the attacker. This attack only works, of course, if it is at all possible to include additional parties in the set of decision makers, but this kind of dynamic group is certainly not rare. So what can be done to prevent it?

Vote in

One thing that can be done is to require that new parties cannot just join, but have to be voted in by the existing members. It would then be there task to ensure, through means outside the contract, that a join request is valid in the sense that is does not original from a malicious real-world entity. The last example in my previous post showed this process. However, ensuring this validity can be a lot of effort, risking that it isn’t done consistently. It can also be exploited by the existing decision makers to keep unwanted additional parties out, reducing the openness of the overall process (if that openness is required in the first place).

Rate Limitations

Another approach to reducing the risk from Sybil attacks is to limit the rate at which new parties can request to join the process. To implement this declaratively, I have implemented a facility by which the rate of commands that come into an interactor (read: the events that come into a state machine) can be limited. The following code expresses that while the machine is in state requesting, only three commands per second are allowed (obviously a value that is useful only for testing). If more requests come in, they are rejected.

The Interceptor Framework

The rate keyword shown above is an example of an interceptor. Interceptors are associated with a state (or with a parent state in a hierarchical state machine). Every trigger or variable access that enters the machine is first passed to all applicable interceptors (they are collected by walking up the state hierarchy). The interceptor can observe the command or variable access and decide what to do about it:

·       It can let the request through unchanged,

·       It can make arbitrary changes to the request,

·       Or it can block the request completely.

In the example above, the request is completely blocked if the frequency of requests exceeds the one specified in the rate interceptor. Note that interceptors are different from guard conditions because they apply, hierarchically, to all transitions in a state, and they can also maintain their own state . The rate interceptor maintains a counter of the number of requests in the given timespan to decide about rejection.

Interceptors are a bit similar to Solidity’s Function Modifiers, although interceptors are associated with states and not single functions.

I have implemented several other interceptors that can all be used to help with the game theoretical nature of smart contracts. More examples follow below, after we have introduced context arguments.

Context Arguments

A command entering an interactor (e.g., a triggering event entering a statemachine) can have arguments. For example, when triggering a buyevent, that event may carry the price the client may want to pay for whatever they buy. Guard conditions can take the arguments into account.

In addition, I have extended interactors to support context arguments. They are essentially a second list of arguments that are different from the regular arguments in the following way:

·       They are optional in the sense that an interceptor decides whether they are required or not for a given command

·       For the client, special syntax exists to supply values for the arguments without explicitly mentioning it for each command.

For (Ethereum-style) smart contracts, an obvious context argument is the sender of a message; this allows the contract to make decisions about the validity of a command and also to ensure that the sender’s account pays the transaction fees.

We are now ready to look at the next interceptor.

The SenderIs interceptor

It is rather obvious that, for contracts to be valid, one often has to check that commands come from a limited set of parties. To continue with the example above, only the set of already-voted-in decision makers can take part in a vote. The following code enforces this by using the senderIs interceptor:

This interceptor takes as an argument a collection of parties, and for every command or variable read that comes in, it checks that the sender is in the list of parties (players in the example above). If it isn’t, the request fails. It also fails if no sender context argument is supplied by the client at all.

Note how within a state that (transitively) has a senderIs interceptor, a variable sender is available that refers to whoever sent this command; interceptors that enforce (by otherwise failing) that a given context argument is specified can also make available special variables with which that context argument can be accessed to make further decisions in the implementation. In the example above, the sender variable is passed into a multi-party boolean decision (as explained in the previous post) that handles the actual decision of whether the requesting sender should be allowed in.

Obviously, one could perform the validation of the sender manually in every guard condition of every transition; but as you can tell from the words “manually” and “every”, this is tedious and error prone, and should thus be avoided.

Turn-by-Turn Games

Many “games” require a fair allocation of opportunities to participating parties. One way of achieving this is to run a game turn-by-turn, where each party can make one “move” in every “round”. In my example, I have a bidding process:

Note how the bidding state uses a takeTurns interceptor. Again, it takes as an argument a list of parties which have to take turns. You can configure how strict the turn-by-turn policy should be enforced. Unordered means that in each round, everybody has to make a move, but the order is not relevant. Ordered means that the order given my the list of parties passed to the interceptor is strictly enforced. A violation leads to a failure of the command. The interceptor also provides access to the list of allowed next movers; this could potentially be used to notify parties that it’s their turn.

Now, there is a risk of a denial of service attack: assume ordered mode, and the next party P just doesn’t make its move: the whole process is stuck. Nobody else can make a move because it’s P’s turn. But P just doesn’t do anything. This is why a turn-by-turn game should always include a timeout:

In the refined example above, we specify a timeout of 500. If the next party does not make their move within 500 time units after the previous one, that party is removed from the game. It then becomes the another party’s turn. It’s also possible to just skip the “sleeping” party and give the turn to the next one in line. Further policies can be imagined, such as skip three times and then remove, or whatever.


When I chatted with Björn about safety of smart contracts and mentioned model checking, he said that he doesn’t know how to do model checking for game-theoretical properties. Obviously I don’t know either. But instead of checking, another way to reduce the risks is to support correctness-by-construction, i.e., make it very simple to define contracts that do not have a particular class of risks, for example by providing declarative means for things like authorisation, rate limiting or turn-by-turn games. This is what I have shown in this post.

It should also become more and more obvious why higher-level abstractions (compared to a “normal” programming language) are needed to efficiently express safe smart contracts. Trying to implement all of these things “with normal code” or just with libraries will lead to many low-level mistakes. DSLs are really very useful here.