We consider the problem of detecting norm violations in open multi-agent systems (MAS). We show how, using ideas from scrip systems, we can design mechanisms where the agents comprising the MAS are incentivised to monitor the actions of other agents for norm violations. The cost of providing the incentives is not borne by the MAS and does not come from fines charged for norm violations (fines may be impossible to levy in a system where agents are free to leave and rejoin again under a different identity). Instead, monitoring incentives come from (scrip) fees for accessing the services provided by the MAS. In some cases, perfect monitoring (and hence enforcement) can be achieved: no norms will be violated in equilibrium. In other cases, we show that, while it is impossible to achieve perfect enforcement, we can get arbitrarily close; we can make the probability of a norm violation in equilibrium arbitrarily small. We show using simulations that our theoretical results hold for multi-agent systems with as few as 1000 agents---the system rapidly converges to the steady-state distribution of scrip tokens necessary to ensure monitoring and then remains close to the steady state.
Another strand of related work is on game-theoretic models of norm emergence. Axelrod Axelrod:86a showed by means of simulations how norms could emerge given simple game rules where players punish each other for violations (and punish players who don't punish violations), and a number of norm enforcement mechanisms with good incentive properties have been analysed @cite_13 @cite_12 . Axelrod's work has been extended by Mahmoud :12a to general scenarios and to incorporate learning. Da Pinninck :10a proposed a distributed norm enforcement mechanism that uses ostracism as punishment, and showed both analytically and experimentally that it provides an upper bound on the number of norm violations.
@cite_13 @cite_12
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The present paper extends the theory of self-enforcing agreements in a long-term relationship (the Folk Theorem in repeated games) to the situation where agents change their partners over time. Cooperation is sustained because defection against one agent causes sanction by others, and the paper shows how such a "social norm" is sustained by self-interested agents under various degrees of observability. Two main results are presented. The first one is an example where a community can sustain cooperation even when each agent knows nothing more than his personal experience. The second shows a Folk Theorem that the community can realize any mutually beneficial outcomes when each agent carries a label such as reputation, membership, or licence, which are revised in a systematic way. The paper considers the repeated prisoner's dilemma in a large-population random-matching setting where players are unable to recognize their opponents. Despite the informational restrictions cooperation is still a sequential equilibrium supported by "contagious" punishments. The equilibrium does not require excessive patience, and contrary to previous thought, need not be extraordinarily fragile. It is robust to the introduction of small amounts of noise and remains nearly efficient. Extensions are discussed to models with heterogeneous rates of time preference and without public randomizations.