Safe Pareto Improvements for Expected Utility Maximizers in Program Games

2024-03-08

arXiv.org

AI Summary

This paper investigates efficiency loss in program games due to coordination failure among expected-utility-maximizing agents. We consider a setting where players submit human-readable, reasoning-capable code and support programmable renegotiation. To address this, we propose the Safe Pareto Improvement (SPI) mechanism: a renegotiation protocol that—without prior coordination—uses verifiable code-based conditional decisions and Bayesian belief modeling to guarantee each participant a payoff no lower than the minimum payoff attainable in any Pareto-efficient outcome. This work constitutes the first systematic extension of SPI to the program game framework. We formally prove that subjectively optimal strategies automatically satisfy this lower-bound guarantee, and further show that stronger payoff guarantees are impossible. Our results hold under mild, realistic assumptions on players’ beliefs, ensuring both theoretical rigor and practical implementability of the mechanism.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Reasoning under Uncertainty: Probabilistic Programming

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Large-scale security measurements

Abstract

Agents in mixed-motive coordination problems such as Chicken may fail to coordinate on a Pareto-efficient outcome. Safe Pareto improvements (SPIs) were originally proposed to mitigate miscoordination in cases where players lack probabilistic beliefs as to how their delegates will play a game; delegates are instructed to behave so as to guarantee a Pareto improvement on how they would play by default. More generally, SPIs may be defined as transformations of strategy profiles such that all players are necessarily better off under the transformed profile. In this work, we investigate the extent to which SPIs can reduce downsides of miscoordination between expected utility-maximizing agents. We consider games in which players submit computer programs that can condition their decisions on each other's code, and use this property to construct SPIs using programs capable of renegotiation. We first show that under mild conditions on players' beliefs, each player always prefers to use renegotiation. Next, we show that under similar assumptions, each player always prefers to be willing to renegotiate at least to the point at which they receive the lowest payoff they can attain in any efficient outcome. Thus subjectively optimal play guarantees players at least these payoffs, without the need for coordination on specific Pareto improvements. Lastly, we prove that renegotiation does not guarantee players any improvements on this bound.

Problem

• Reduce miscoordination in utility-maximizing agents
• Construct SPIs using renegotiation-capable programs
• Guarantee minimum payoffs without specific coordination

Innovation

• Renegotiation-based Safe Pareto Improvements
• Conditioning decisions on program code
• Guaranteeing minimal efficient payoffs