## Final Report Summary - NINA (Norms in Action: Designing and Comparing Regulatory Mechanisms for Multi-Agent Systems)

My project, called NINA (an acronym standing for Norms IN Actions: Designing and Comparing Regulatory Mechanisms for Multi-Agent Systems), has studied computational procedures to resolve conflict in a system of “agents”. A system of agents, otherwise called a multi-agent system, is a set of co-existing computational entities, and can be used to encode the behaviour of software systems, robots, and anything that can reasonably be described as an entity endowed with beliefs and objectives, such as humans.

As agents are endowed with personal objectives, the actions available to one agent may promote or frustrate the realisation of another agents' objectives. This typical characteristic of multi-agent systems is referred to in the economic literature as “presence of externalities” and shows how such platforms are well-suited to make the study of conflict accurate and implementable. What this project has done is to model, on top of conflict, also the procedures needed to resolve it. Specifically, it has devised "programs" to handle externalities, i.e. by either letting agents do or intervening from outside, in order to achieve desirable systemic properties, such as efficiency. Conflict resolution procedures are what is intended with "norms".

Specifically the project objectives have been:

1) Devising a model of norms as endogenous contracts

2) Devising a model of norms as exogenous mechanisms

3 and 4) Carry out an algorithmic analysis of both models of norms

The project has achieved a number of results, from a modelling perspective and from a engineering perspective.

1) From a modelling perspective:

I have identified a model of multi-agent systems, that is both computationally well-behaved and well fit to model conflict, Boolean Games (Harrenstein et. al, 2001; Wooldridge et al. 2013). Briefly, in Boolean Games, each agent has control over a set of propositional formulas that he can set to true or false (e.g. turning a light switch on or off) and has a goal that he wants to achieve, that might depend on what the others decide to do with their propositional variables. So, an agent can help another agent realise his goal, but he can also prevent him from doing so. Unlike strategic games studied in game theory, Boolean Games are particularly well-suited to model goal-directed behaviour.

I have identified an established game-theoretic model of pre-play negotiation (Jackson and Wikie's Endogenous Games, 2005) that allows players, before a certain strategic game starts, to make binding commitments to sacrifice a part of the utility received by them at certain outcomes, in order to try and influence the other players' decision-making. After a simultaneous round of offers, players play the original strategic game updated with the transfers. Endogenous Games are an elegant model of contracts that players undertake in strategic interaction to obtain a more beneficial outcome in the end. Notice that Endogenous Games do not transform the starting non-cooperative game into a cooperative one, but allow utility-maximizer players to undergo a negotiation phase where they might end up improving upon their original payoff.

I have integrated the frameowork of Boolean Games with that of Endogenous Games, into the framework of “Endogenous Boolean Games” (Turrini 2013). Endgenous Boolean Games are a model of interaction among goal-directed agents where, before the interaction starts, agents are allow to undergo a negotiation phase. Endgenous Boolean Games allow to study the preconditions under which goal-directed agents can reach efficient outcomes {\em without external intervention}.

I have integrated the framework of Endogenous Boolean Games with taxation mechanisms, as originally applied to Boolean Games (Wooldridge et al 2013). These mechanisms have the effect of increasing the cost of actions taken by agents and therefore rule out some undesirable equilibria. I have constructed a procedure that, by making use of taxation mechanisms that can direct players towards rational contracts.

2) From an engineering perspective:

I have formulated the problem of resolving externalities in a boolean game as a computational problem. These can be distinguished in elimination/construction procedures and in taxation/negotiation mechanisms.

4.1) Elimination of undesirable equilibria through taxation mechanisms. I have studied the computational complexity of the following problem, under various notions of equilibrium: "Given a boolean game (N,S,p,G) and an equilibrium outcome s that has undesirable properties, check whether a taxation mechanism x exists such that the application of x to (N,S,p,G) removes the equilibrium. If it exists, construct the complete procedure".

4.2) Construction of desirable equilibria through taxation mechanism. I have studied the computational complexity of the following problem, under various notions of equilibrium: "Given a boolean game (N,S,p,G) and an outcome s that has desirable properties, check whether a taxation mechanism x exists such that the application of x to (N,S,p,G) adds outcome s as an equilibrium. If it exists, construct the complete procedure".

4.3) Elimination of undesirable equilibria through side-payments. I have studied the computational complexity of the following problem, under various notions of equilibrium: "Given a boolean game (N,S,p,G) and an equilibrium outcome s that has undesirable properties, check whether a profile of transfers t exists such that the application of t to (N,S,p,G) removes the equilibrium. If it exists construct the complete procedure".

4.4) Construction of desirable equilibria through side-payments. I have studied the computational complexity of the following problem, under various notions of equilibrium: "Given a boolean game (N,S,p,G) and an outcome s that has desirable properties, check whether a profile of transfers t exists such that the application of x to (N,S,p,G) adds outcome s as an the equilibrium. If it exists construct it".

What I have found is that all the problems are decidable, i.e. a yes/no answer will always be found after a finite number of time steps, and that the existence of an effective resolution procedure can always be proved constructively, i.e. we can come up with a formal recipe, a program. Without entering technical details, the complexity study has shown that the presence of side-payments or taxation mechanisms does not require significantly more time or space than the original problem of checking whether a certain outcome is or is not an equilibrium in a boolean game. Also, despite the fact that taxation mechanisms can simulate side-payments, this has been shown not to have substantial differences in terms of added complexity.

*Applicabilitity*

The model can be applied to describe those situations where interaction takes place between agents that are driven to the realisation of personal objectives, whose realisation heavily depends on what the other agents do, as well. The model provides solutions to how to regulate potential conflict in these systems, telling us what an exogenous form of solution can achieve (i.e. allowing an external authority to punish and reward agents) and whether I can, rather, resolve the conflict by allowing agents themselves to undergo a negotiation phase.

*Contact Details*

Paolo Turrini,

Research Fellow

Department of Computing Imperial College London

452 Huxley Building

180 Queen's Gate, London

http://www.doc.ic.ac.uk/~pturrini/