Smart contracts and reaction-function games

TL;DR

This paper introduces a formal framework for reaction-function games in blockchain smart contracts, demonstrating how they can support credible commitments and improve outcomes in strategic interactions.

Contribution

It formalizes reaction-function games with a fixed point solution concept, proves equilibrium existence, and applies the framework to investment games to show practical benefits.

Findings

Equilibrium existence is proven for reaction-function games.

Safe reaction functions can support Pareto improvements.

Blockchain commitments can overcome trust and free-riding issues.

Abstract

Blockchain-based smart contracts offer a new take on credible commitment, where players can commit to actions in reaction to actions of others. Such reaction-function games extend on strategic games with players choosing reaction functions instead of strategies. We formalize a solution concept in terms of fixed points for such games, akin to Nash equilibrium, and prove equilibrium existence. Reaction functions can mimic "trigger" strategies from folk theorems on infinitely repeated games -- but now in a one-shot setting -- for instance to support Pareto-improvements on Nash equilibrium outcomes. In some games, this can even be done through risk-free, safe reaction functions. We apply our theoretical framework to symmetric investment games, which includes two prominent classes of games, namely weakest-link and public-good games. In both cases, we highlight a particular safe and optimal reaction function. In this way, our findings highlight how blockchain-based commitment can help overcome trust and free-riding barriers.