3. Multi-agent systems (MAS) 3.1 Formal Definitions and Properties Multi-agent systems (MAS) are used to describe We can now refine our agent definition: several agents that interact with each other Definition : Agent in a MAS (positively, but also negatively). An agent Ag in a MAS is an agent, i.e. Ag = ( Sit , Act , Dat ), Positive interaction is usually known as cooperation, with the following structural extensions: collaboration is used as a more elaborated word for Act = Act Own ∪ Act Co interaction, and competitive settings describe usually systems where negative interaction takes place. Act Own : the agent’s own actions Act Co : communication and cooperation actions An element s of Sit has an environment part Env(s) and a partner part Part(s) Multi-Agent Systems Jörg Denzinger Multi-Agent Systems Jörg Denzinger Agent in a MAS (cont.) Putting agents together Dat consists of Definition : Multi-Agent System An multi-agent system Mult is a 5-tuple Dat Own : the set of individual (own) data areas (resp. their values) of Ag Mult = (Sit,Ag,Mact, α ,MultL) Dat KS : the set of sure data about other agents Sit is a set of situations (Sure Knowledge) Ag a set of agents (in a MAS) Dat KA : the set of assumptions about other agents Mact is the set of elemental actions possible in Mult (Assumption Knowledge) (Mact ⊆ A ∈ Ag Act (A)) α :Mact → Ag assigns to each action of Mact the just introduction of additional terms, all old terms agent that performs it. (definitions) still valid MultL is the action language of Mult Multi-Agent Systems Jörg Denzinger Multi-Agent Systems Jörg Denzinger Remarks (I) Remarks (II) Each action of a MAS has to be assigned to an agent An agent of Ag can itself be a multi-agent system hierarchies can be introduced this way Simultaneous actions of agents have to be If A ∈ Ag is a MAS, then it can be useful to eliminate sequentialized for MultL the internal communication and cooperation actions Combined actions have to be expressed as out of MultL(A). Then we have simultaneous actions Mact ⊂ A ∈ Ag Act (A)) Agents can have other actions as the ones they Sometimes it is useful to combine a sequence in contribute to Mact. But since they are never MultL into one new action performed, they can be eliminated (for simplicities better understandability of system sake). Then we have allows for introduction of combined actions, again Mact = A ∈ Ag Act (A)) Multi-Agent Systems Jörg Denzinger Multi-Agent Systems Jörg Denzinger 1
3.1.1 Formal Properties and a little Remarks (III) Theory This definition of a MAS is rather specific and is A MAS Mult can, from the outside, be seen as just aimed at allowing to prove the following properties one agent ( Sit = Sit, Act = Mact, Dat = (Ag, α ,MultL), f Ag as needed to produce MultL). Therefore all the A more general definition that covers better the large formal properties of 2.1 can also be properties of a variety of MAS would simply be: Mult = ( � , � n � ) multi-agent system. with � set of agents and � n � set of environment Basic questions are states What properties must agents in Mult fulfill, so that Mult has a certain property? But, for the moment, let’s stick with the specific definition! If Mult has a certain property, what does this tell us about this property regarding an element of Ag? Multi-Agent Systems Jörg Denzinger Multi-Agent Systems Jörg Denzinger Additional formal properties (I) Example Definition : Behavior of an agent in a MAS Let Act (A) = {b,c} and s = bddbecb ∈ MultL. Let Mult = (Sit,Ag,Mact, α ,MultL) be a MAS and A ∈ Ag Then we have an agent. Then the behavior L A of A in Mult is defined h A (s) = bbcb as L A = h A (MultL) with h A (t) = t, if t ∈ Act (A) h A (t) = ε , else ( ε :empty word). We project the whole action sequences of Mult down to the actions performed by A Multi-Agent Systems Jörg Denzinger Multi-Agent Systems Jörg Denzinger Additional formal properties (II) Example: Definition : Interaction of agents in a MAS Let Ag = {A,B} with Act (A) = {a 1 ,a 2 ,a 3 } and Let Mult = (Sit,Ag,Mact, α ,MultL) be a MAS. The Act (B) = {b 1 ,b 2 }. interaction L Ags of the agents in Mult is defined as the Let further MultL = {a 1 a 2 b 1 a 1 a 2 , a 1 a 2 b 2 a 3 }. formal language Then L Ags = α (MultL). L Ags = {AABAA, AABA}. Analysis of the interaction of the agents allows to detect: If only a subset of the agents is involved in the actions If there are specific work chains Multi-Agent Systems Jörg Denzinger Multi-Agent Systems Jörg Denzinger 2
Some good results A bad result Theorem : Theorem: Let Mult = (Sit,Ag,Mact, α ,MultL) be a MAS. Let Mult = (Sit,Ag,Mact, α ,MultL) be a MAS. (1) If MultL is deadlock free, then so is L Ags . But it is If all agents A ∈ Ag are fair (with respect to Act (A)), possible that for all A ∈ Ag L A is not deadlock free. then MultL does not have to be fair. (2) If MultL is fair, then it is possible that L Ags and L A for all A ∈ Ag are not fair. For all proofs: see Burkhard (1992) making sure that all agents have a certain property a MAS can have a property even without its agents does not ensure that the MAS has it. having it (some form of synergy) Multi-Agent Systems Jörg Denzinger Multi-Agent Systems Jörg Denzinger Dimensions for describing MAS (I) Dimensions for describing MAS (II) System model Similar to the situation with single agents there are a lot of properties of MAS that cannot be defined formally. individual … team … society In contrast to the single agent case all these properties Granularity together allow for a rather good first classification fine grained … coarse grained (and comparison) of a MAS, provided that the vague Number of agents values for some of these properties are interpreted in small … medium … big a uniform manner. Ability to adapt of agents and the whole MAS The following property dimensions are an extension of fixed … programmable … able to learn … the dimensions reported in Sridharan (1986). autodidactic Multi-Agent Systems Jörg Denzinger Multi-Agent Systems Jörg Denzinger Example: project teams Dimensions for describing MAS (III) (teamwork method) (I) Control distribution See also 2.2.5, Denzinger (1995) being controlled … dependent … independent Experts, referees, a supervisor Resources Working cycle: limited … rich … unlimited Experts work, then their work is judged by referees and Interaction scheme judgements and selected results are communicated to simple … complex supervisor. Supervisor generates out of all results of Solution strategy the best expert and the selected results of the others a synthesis … analytical new start state for all experts and selects the experts for the next cycle. Degree of cooperation between agents cooperative and selfless … competitive and hostile Multi-Agent Systems Jörg Denzinger Multi-Agent Systems Jörg Denzinger 3
Example: project teams (teamwork method) (II) System model: team Granularity: coarse grained Number of agents: small (to medium) Ability to adapt: able to learn Control distribution: being controlled Resources: weekly limited Interaction scheme: more on the complex side Solution strategy: synthesis Degree of cooperation: competitive and cooperative (more on the selfless side) Multi-Agent Systems Jörg Denzinger 4
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