Conventions under Heterogeneous Behavioural Rules

GAICIL Insights

Nobody voted to drive on the right, to adopt a particular file format or to make a given protocol the standard.¹ Conventions emerge. Conventions under Heterogeneous Behavioural Rules, by Jonathan Newton, examines how they emerge when the agents choosing strategies follow different behavioral rules. Strategies are updated according to agents' behavioral rules, where each agent is a player or a coalition of players.

Classic results on the stochastic stability of conventions rely on an asymmetry property of the strategy updating process. The paper shows asymmetry can be defined at the level of the behavioral rule, and that asymmetric rules can be mixed and matched while keeping the aggregate process asymmetric. Asymmetry is robust to heterogeneity within an agent, when Alice follows different rules at different times; between agents, when Alice and Bob follow different rules; and in the timing of updating. These results greatly expand and convexify the domain of behavioral rules for which stochastic stability results are known.

Translated: predictions about which conventions win in the long run do not require everyone to behave alike. Real populations are messy. People use different rules of thumb, switch rules over time and update at different moments. As long as individual rules satisfy asymmetry, the aggregate process does too, and the classic results apply. Theory survives contact with diversity.

That robustness matters more every year, because the population forming conventions now includes machines. AI agents update strategies frequently and according to programmed rules; humans update occasionally, by habit or imitation. The paper suggests conventions can still be analyzed with established tools in such mixed populations, provided each type of agent's rules meet the asymmetry condition. The arrival of algorithmic agents need not break the theory of social order.

Conventions are the plumbing of the AI economy. Technical standards for data formats, interoperability protocols and safety practices are conventions. Their emergence determines whether AI systems can work together and whether markets coalesce around efficient standards. Understanding how heterogeneous agents, firms, developers and automated systems converge on conventions helps predict which standards will prevail and whether intervention is needed at all.

Coalitions get a seat in the model, which fits the real world nicely. In AI markets, groups of firms coordinate on standards through consortia. The framework accommodates such coalitions alongside individual agents, allowing analysis of how coordinated groups and lone actors jointly shape conventions.

Policy gets reassurance and guidance. Reassurance: stable conventions emerge robustly from heterogeneity, so markets can converge on standards without uniform behavior or central decree. Guidance: stability conditions depend on the properties of behavioral rules. Policymakers seeking efficient conventions can focus on how agents update strategies, for example by improving information about the adoption of alternatives, which shapes the rules agents follow. Publishing who has adopted which standard may be a strong tool in its own right.

The paper candidly notes that its results do not exhaust the subject, proposing more behavioral rules and different payoff specifications as avenues for research. Behavioral rules embedded in AI systems are an obvious candidate. As AI agents increasingly take part in coordination problems, analyzing their rules within this framework would clarify how they affect the conventions that emerge.

Stepping back, social order can emerge robustly from diverse behavior. Conventions arise even when agents follow different rules at different times. In an economy where AI agents and humans interact, that supports confidence in decentralized coordination. Markets and communities can converge on conventions without central direction, and theory like this identifies when that convergence is reliable. Policies that keep standard-setting open and decentralized let those conditions do their work.

A closing challenge: before writing a mandatory standard for AI interoperability, ask whether the convention is already forming on its own. Theory suggests it often will, even in a crowd of very different minds.