🎭 MEV and Credible Commitment Devices 🗳️
Xinyuan Sun
Research, Flashbots ⚡🤖
This is Kim
Tips for nerds: this box is a commitment device, since it is common knowledge that this commitment is credible, we say it is credible commitment device
This is Kim
Kim has a box.
This box allows him to delegate arbitrary actions, and it is common knowledge that this box executes things faithfully.
Now Kim wants to use this box to improve the efficiency of the games that he is playing with his frienemy Don.
Tips for nerds: this box is a commitment device, since it is common knowledge that this commitment is credible, we say it is credible commitment device
This is Kim
Kim has a box.
This box allows him to delegate arbitrary actions, and it is common knowledge that this box executes things faithfully.
Now Kim wants to use this box to improve the efficiency of the games that he is playing with his frienemy Don.
Tips for nerds: this box is a commitment device, since it is common knowledge that this commitment is credible, we say it is credible commitment device
Prisoner’s Dilemma
Kim would want to delegate the box prior to game begins.
Prisoner’s Dilemma
Now box makes the game work, great!
Tips for nerds: Folk theorem for commitment device states that any payoff within the convex hull of individually rational payoff sets are achievable (for single-shot games even)
Problem with Prisoner’s Dilemma
But Kim wouldn’t be so “benevolent” surely, he would be rational…
Tips for nerds: this is the classic Stackelberg competition scenario, where the leader or the mechanism designer gets an asymmetric payoff
Problem with Prisoner’s Dilemma
Now the only payoff possible is (3,1), where Don is indifferent between using the device and not.
Problem with Prisoner’s Dilemma
Suppose both Kim and Don can use the box, now (3,1) (1,3) are the set of implementable payoffs. Not sure if desirable.
Cooperative Games
Let’s abstract away the “person with box,” call her C, and we call Kim&Don A&B.
We have the box, which is a credible commitment device, so it feels natural to model this as cooperative games. Specifically, suppose ABC use the box to form coalitions.
v(A) = v(B) = 1, v(C) = 0
v(AB) = 2, v(AC) = v(BC) = 3
v(ABC) = 4
Core of this game (no sub-coalition could deviate profitably) is (A: 1, B: 1, C: 2)
Harsanyi dividend is d(A) = 1, d(B) = 1, d(C) = 0, d(AB) = 0, d(AC)=d(BC)=2, d(ABC)=-2
Shapley value (4/3, 4/3, 4/3), not in core, no fair payoff.
Cooperative Games
Let’s abstract away the “person with box,” call her C, and we call Kim&Don A&B.
We have the box, which is a credible commitment device, so it feels natural to model this as cooperative games. Specifically, suppose ABC use the box to form coalitions.
v(A) = v(B) = 1, v(C) = 0
v(AB) = 2, v(AC) = v(BC) = 3
v(ABC) = 4
Core of this game (stable, no sub-coalition could deviate profitably) is (A: 1, B: 1, C: 2)
Harsanyi dividend is d(A) = 1, d(B) = 1, d(C) = 0, d(AB) = 0, d(AC)=d(BC)=2, d(ABC)=-2
Shapley value (4/3, 4/3, 4/3), not in core, no fair payoff.
Core
The core manifests itself, e.g., Kim and Don can both use the box and bid in first price auction.
Core
There is no point in using the box anymore. The box is useless.
Generalization of Cooperative Games: Externality
The box we have at hand is a permissionless credible commitment device called crypto (-economic mechanisms).
We want to use it for coordination, for playing cooperative games.
Tip for nerds: it is possible to reduce the externality by use of special bidding languages (quine preferences), but it is hard to define a fixpoint semantics for it in reality
Generalization of Cooperative Games: Externality
The box we have at hand is a permissionless credible commitment device called crypto (-economic mechanisms).
We want to use it for coordination, for playing cooperative games.
But there are some externalities when we use the box to form coalitions, unlike traditional cooperative game theory setting where coalition formation has no externality.
Externality comes from all agents saying: “if the other agents do not cooperate with me to achieve maximum social welfare state and transfer me all of the surplus value, I will commit to making their lives most miserable (e.g., leaving of coalition, etc,.)”
Tip for nerds: it is possible to reduce the externality by use of special bidding languages (quine preferences), but it is hard to define a fixpoint semantics for it in reality
Generalization of Cooperative Games: Extortion
The externality is extortion (collusion).
We model extortion as a function: k(a,b) for profit that coalition a can extort from coalition b when they use the box as a coalition formation device.
You extort: best state of mega-coalition - worst state of extortee (coalition b) - your original profit (coalition a) + externality of coalition b’s formation.
Currently we assume there is no innate coalition formation cost.
Generalization of Cooperative Games: Extortion
The externality is extortion (collusion).
We model extortion as a function: k(a,b) for profit that coalition a can extort from coalition b when they use the box as a coalition formation device.
You extort: best state of mega-coalition - worst state of extortee (coalition b) - your original profit (coalition a) + externality of coalition b’s formation.
Currently we assume there is no innate coalition formation cost.
Generalization of Cooperative Games: MEV
So we know the extortion equation.
We discover that in this case, MEV is the maximum possible extortion profit by any sub-coalitions considering their externality of formation (using the box), i.e.,
One could verify that assuming no innate coalition formation cost, we have MEV equals max surplus welfare that is possible to be gained from coordination.
Generalization of Cooperative Games: MEV
So we know the extortion equation.
We discover that in this case, MEV is the maximum possible extortion profit by any sub-coalitions considering their externality of formation (using the box), i.e.,
One could verify that assuming no innate coalition formation cost, we have MEV equals max surplus welfare that is possible to be gained from coordination.
Generalization of Cooperative Games: MEV
So we know the extortion equation.
We discover that in this case, MEV is the maximum possible extortion profit by any sub-coalitions considering their externality of formation (using the box), i.e.,
One could verify that assuming no innate coalition formation cost, we have MEV equals max surplus welfare that is possible to be gained from coordination.
This is Kim
Kim has a box.
With MEV, the box is useless.
Kim is sad.
Tips for nerds: this box is a commitment device, since it is common knowledge that this commitment is credible, we say it is credible commitment device
This is Kim
Kim has a box.
With MEV, the box is useless.
Kim is sad.
Tips for nerds: this box is a commitment device, since it is common knowledge that this commitment is credible, we say it is credible commitment device
This is Kim
Kim has a box.
With MEV, the box is useless.
Kim is sad.
Tips for nerds: this box is a commitment device, since it is common knowledge that this commitment is credible, we say it is credible commitment device
This is Kim
Kim has a box.
With MEV, the box is useless.
Kim is sad.
We are all Kim
Tips for nerds: this box is a commitment device, since it is common knowledge that this commitment is credible, we say it is credible commitment device
🎭 MEV and Credible Commitment Devices 🗳️
Xinyuan Sun
Research, Flashbots ⚡🤖