Mechanism Composition¶

Why It Matters¶

Designers often optimize individual mechanisms in isolation. But a collection of locally optimal mechanisms may perform poorly when composed. Participants strategize across mechanisms, gaming one to influence another. Understanding composition effects prevents unintended consequences and identifies beneficial combinations.

The Key Move¶

When combining mechanisms, trace the information and incentive flows between them. Does one mechanism's input depend on another's output? Can participants manipulate one mechanism to gain advantage in another? Ask: "If I game mechanism A, how does that affect my position in mechanism B?" Ideally, make mechanisms independent or align their incentives so gaming one mechanism doesn't undermine another.

Classic Application¶

School choice with assignment mechanism (deferred acceptance) and school improvement incentives (test-based accountability). Assignment mechanism aims for stable matching. Accountability mechanism incentivizes schools to improve. But composition creates gaming: schools can improve rankings by selective enrollment rather than genuine quality improvement. The mechanisms interact in ways neither designer anticipated.

Surprising Application¶

Open source contribution metrics. Platforms measure contributions (commits, issues, reviews) and display profiles (signaling mechanism) and use metrics for hiring (screening mechanism). Composition creates gaming: developers optimize for visible metrics rather than valuable contributions. Many commits with small changes, opening issues rather than fixing them, superficial reviews. Each mechanism works in isolation, but composition incentivizes metric gaming over value creation.

Failure Modes¶

Optimizing mechanisms independently without considering interactions. Ignoring that participants see the full system and strategize accordingly. Creating feedback loops where one mechanism's output amplifies another's failure. Not testing the composed system even if individual components are well-tested. Assuming composition is simply additive (the whole may be less than the sum of parts if incentives misalign).

Go Deeper¶

Segal and Whinston (2003), "Robust Predictions for Bilateral Contracting with Externalities." Wilson (1987), "Game-Theoretic Analyses of Trading Processes" - on multi-market interactions. Holmström and Milgrom (1991), "Multitask Principal-Agent Analyses" - shows how multiple incentive systems interact.