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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,

  1. 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

  2. 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

  3. 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

  4. 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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