Reverse Stackelberg Calculator

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Mathias Hall-Andersen, Nikolaj I. Schwartzbach

This is supplementary material to our paper (Hall-Andersen and Schwartzbach, 2021).

This small widget computes reverse Stackelberg equilibria in finite games with perfect information. This corresponds to two players able to deploy smart contracts to constrain their moves. The leader (player 1) deploys a smart contract and announces it, after which the follower (player 2) deploys their contract, and then the game is played. The leader's contract is allowed to reason about the contract deployed by the follower. When there is not perfect information the problem can be shown to be Σ₂^P-complete. As of present, it only supports two players.

Instructions

The game tree is inputted as raw JS code and parsed using eval(...).

Tree structure

• To make a leaf, use the syntax ["leaf",u1,u2] where ui is the payoff of player i.
• To make a branch, use the syntax ["node",i,c1,c2,...,cn] where i is the index of the player to whom the node belongs, and cj is the j^th child.

Choose preset... Mutual benefit (default) Nuclear threat Escrow contract Ultimatum game Centipede game Prisoner's dilemma Battle of the sexes ["node",1, ["leaf",3,3], ["node",2, ["leaf",5,5], ["leaf",0,10] ] ]

Compute equilibria

Solutions

⮃ Switch contracts 💣 Add nuke

References

• Mathias Hall-Andersen and Nikolaj I. Schwartzbach. Game theory on the blockchain: a model for games with smart contracts. In 14th International Symposium on Algorithmic Game Theory, 2021.

Department of Computer Science. Aarhus University.