[e-mail]

1
?????????????????????????

• ????
• ??????????
• kindo_at_kanto-gakuenac.jp

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• ??????????????????????????????????????????????????
  ????Manager??????????????????????????????????????
• ?????????????????????Manager??????????????????????
  ????????????????????????????P?????????????????????
  ?????????C????????????????????????????????????????
  ??????
• ??????????????????????????????????????????????????
  ??????????????????????????????????????????????????
  ????????????????????H.A. Simon????????????????????
  ???????????????????????????????????????????
• ?????????????????????????????????????????????????
  ??? ??????????????(??????????)???????????????????
  ??????????????????????(???????)????????????????
• ????????????????????????????????????????(???????)?
  ??????????????????????????????????????????????????
  ???????????????????????????????
• ?????????????????????????????????????????????Prolo
  g???????????????????????????????

3
????????????

• ???????????????Coase?Chamberlin?????????Chandler??
  ??????????????????????????????????????????????????
  ?????Arrow(1964)??????????????????????J.
  Marschak, H.A.Simon, L. Hurwicz, T. Marschak?R.
  Radner????K.Arrow?????????????????Organizations?
  Simon??????J.G. March?????????????????????????????
  ??????????????1
• ?????????????????????????????????????????????????
  ?????????????????????????????(DP)????????????Willi
  amson(1967)???????????????????????????????????????
  ??????????????????????????????????????????????????
  ??????
• ????????????(SpanOfControl)??????????????????????
  ??????????????(Loss Of Control)???????????????????
  ????????????????????????????????????????????(Beckm
  ann,1976 Calvo and Wellisz,1978 Keren and
  Levhari, 1979, 1989 Rosen, 1982)?
• Prat(1997)?????????????????????????DP??---????????
  ??????????Qian(1994)?????DP?????????????(???????)?
  ???????????????????????????????????Cremer
  (1981)??????(Marshak and Radner,1972)?????2???????
  ??????????????????????????BoltonDewatripont??????
  ????????????????(??)??????????????????Marshak and
  Reichellstein(1996)????????????????????????
• Geanakoplos and Milgrom(1991)?Cremer??????????mana
  ger???????????????????????????????????????????????
  ??????????????????????????????(Dow,
  1990)?????????????Arrow????????????????2???????
  ??????????????????(Aoki,1986)?????????????????????
  ???????

4
Radner???????

• ??????????????????????????????????????????????????
  ???????????????????????????????????????????????Rad
  ner????????????????????????????????????????()????
  ????????
• Radner(1992, 1993)?3??????????????????(1)?????????
  ?(2)?????????(3)???????(1)????????????????????????
  ??????(??????????)?(3)??????????????
• ??Radner?F.Knight?????????????????????????????????
  ??????????????????????????????????????????????????
  ????????????????????????????????????????????????
  ?????????????????????????????????
• ????????????????????????????????????????????????
  ??????????????????????????????????????????????????
  ??????Radner??????????????????????????????????????
  ??????????????????????????????????????????????????
  ????????????????????????????????????()??????Radne
  r?????????????????????????????????????????????????
  ?????????????????????????

5
Radner?????

• ????Radner??????????????????????????????????T?????
  ??????????????(?????)N??????(????)C???????????????
  ??????????P???????????????(Efficient
  Network)????????
• Radner(1993)??????????????????????????????????????
  ?????????????????????????(??????????????????????)?
  ????????????
• ????????????????p????????????????????????????????N
  ?T??????(P,C)????????????????????????????

6
???????(1???????)
??????????Reduction???????????????Skip-Level
Reporting???????????
7
????????
8
??????Manager???????
Prat(1997)??Radner????????????????????????????????
????????????DP???????????????????????????Prat???1?
2?????????????????????? ????????????????????????
?????????????R(L)??????????????????(???
k)?????????????w(k)?????????????????? ?
Prat????????????????????????????N?????????????
???????????????????3???????????????????? (1)??????
???????1???? (2)??????????????????????????????????
?????? (3)???(???1)??????2???????????1????????????
???
9
Prolog???????????
hierarchy0(a, -1,2,-5,1,
-6,2,3, 1 ). hierarchy0(c,
a,b,c,d, e,f,g ,
h ). Figure.
Prat?????????????????????????????????????????????P
rolog??????????? dpfirm0.pl ?????????????????????(
http//www.us.kanto-gakuen.ac.jp/indo/)?
??(?)???????????????????Prolog???????????????????
??(????) ????????????????????????????????????????
??????????????????????????????a??????A?????????B??
????C????????????????????????(????)????????????
?- compute_hierarchy_with_cost(A,B,C). A
-1, 2, -5, 1, -6, 2, 3, 1 B -31 (32
-6) (1 -52 -1) C 11
10
?????????
????????????(?????)?????????????????????????????
??????????????????????????????????????????????????
????????????? ???Prolog????????????5?????????????
?????????R?3????????(???)??????????(????)?????????
??????Prat???1????????????????????2????2??????????
???????????????????????????????????????? case
1-3 revenue(R,L)- R is 100-20L. case 1
wage_function(C,W)- W is 10
C. ----------------------------------------------
------------ ?- tell_and_solve(a,b,c,d,e,P). P
treea, b, c, d, e, items5, levels1,
revenue80, wages50, profit30 Yes case 2
wage_function(C,W)- W is 3 C
2. ----------------------------------------------
------------ ?- tell_and_solve(a,b,c,d,e,P). P
treea, b, c, d, e, items5, levels2,
revenue60, wages51, profit9 P treea,
b, d, c, e, items5, levels2, revenue60,
wages51, profit9 ------ltomittedgt------
case 3 wage_function(C,W)- W is 3 C
3. ----------------------------------------------
------------ ?- tell_and_solve(a,b,c,d,e,P). P
treea, b, c, d, e, items5,
levels3, revenue40, wages102, profit -62 P
treea, c, b, d, e, items5,
levels3, revenue40, wages102, profit -62
------ltomittedgt------
11
?????????Quian?????

• ????????Prat(1997)?????????????????????????DP?????
  ?(???????)????(???????)???????????????????????????
  ??????????????????????????????????????????????????
  ??????????????????????(SOC)?????????(??????)??????
  ?????????????????(Beckmann,1976 Calvo and
  Wellisz,1978 Keren and Levhari, 1979, 1989
  Rosen, 1982)?
• ??????????????(SpanOfControl)?????????????????????
  ?????????????????????????????????(Loss Of
  Control)??????????????????????????????????????????
  ?????????????????????????????????????????????????(
  ???????)??????????????????????????????
• Qian(1994)?????DP?????????????(???????)???????????
  ??Quian???????????????????0-1?????????????????????
  ?????????????????????????odesign.xls????????????(h
  ttp//www.us.kanto-gakuen/indo????????

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0-1????????????????(Quian,1994)

• Quian(1994)????????????????????????????Appendix
  A????????????????????????????????????
• Quian????????t????s(t)2??????x(t)2t????????????
  ????????
• ????????????????????????????????????????N?????????
  ?????????

13
???????????????????????

• Quian?????????(?????????)?????????????????????????
  ??????????????????????????????????????????????????
  ?????????????????????????????????????????(P1/S)?
• 0-1?????????1??????????????????0??????????????????
  ??????????????????????????????????????????????????
  ?????????????(???????????????????)

14
??????????????????

• Quian??????????DP??????????????????????????????(??
  ???odesign.xls)??? 0-1??????????Prat??????????????
  ?????????????????N100???????g????1????
• ???????SOC????????????????????????????????????????
  ??????????????????????????????????????????????????
  ?t???????????????????????????????????????????????

15
????????

• ????????????Frontline???MS????????????????????????
  ?????????????????????????????? (??????? ????????
  214115??????????????????http//www.solver.com/te
  chnology.htm??)
• ????????Lasdon ?Waren?????????(GRG2)??????????????
  ????????????????????(NLP)??????????
• ????????(MILP)????????????????????????????????????
  ?????????????????????????????????
• ????????????0-1??????20???????????????????????????
  ??????
• ??????????????????????????????????????????????????
  ??????????????????????????????????????????????????
  ?

16
???????????

• ?????????????????Hurwicz??????????????????????????
  ??????????????????????????????????????????????????
  ????????????(????)????????????????????????????????
  ?????????????????????????????????????????????
• ?????????????????????????????????????????????????R
  adner?????????????????????????????????????????????
  ????????????????????????????????????????(MIS)?????
  ?????????????????
• ???????????????????????Mount and
  Reiter(1990)??rd??????????????????????????????????
  ??????????????????????????????????????????????????
  ??Radner??????????????????????????????????????????
  ??????Marschak and Reichelstein(1996)?????????????
  ????????????????????????????????

17
???????

• ?????????????????????Hurwicz-Reiter???????????????
  ??????????
• E??????
• N??????????N1??n????
• ????????????ltS?g?hgt
• S??????????Si???S1Sn?
• fi??????i???????fiSEi?Si?
• g(g1??gn)??????
• gi(s?ei)fi(s?ei)-si?
• h????????????sifi(s?ei)???????
• ????(performance standard).
• ?????ltS?g?hgt?????FE?Z?????(realize)??????????e?E
  ???????2???????????
• µ(e)sg0?f
• h(s)s?µ(e)?F(e)?

18
???????????

• ???Marschak?Reichelstein??????????????????????????
  ?
• E??????
• N??????????N1??n????
• ????????????ltM?g?hgt
• M???????????????????????
• Mi??????i?????????
• M_i??????i?????????
• Pi(M)M??i???i????????
• Pi(m)???????i???????????
• gPi(M)Ei?Mi???????
• ????i?????gi(Pi(M)?ei)0?
• hPi(M)?Zi???????????????
• ????(performance standard).
• ???????????ltM?g?hgt?????FE?Z???????????????e?E????
  ???2??????????????
• µ(e)mg0?f
• h(s)m?µ(e)?F(e)?

19
?.???????????
??Q1

• ?. A Multiplant Firm(Marschak and
  Reichelstein,1995)
• 4???????????????A1?A2?A3?A4????
• ????????A1?A2?????Q1?Q2??????
• ????e1(Q1)?e2(Q2?I)??????????
• ????????A3?A2???????I?????e3(I)
• ??A4?????e4(Q1?Q2)?
• ??????????
• ????u1?u2?v gt ??? Q1?Q2?I?
• ????????????
• A4?A1???u1????A1?A4????? p1u1Q1-e1(Q1)
  ?????????Q1?????
• A4?A2???u2????A2?A4????? p2u2Q2-e2(Q2?I)
  ?????????Q1?????
• A2?A3???v????A3?A2????? p3vI-e3(I)
  ?????????I?????
• ?????????????????(2?4?2?4)?????6??????????????????
  ????????????????
• ??A3????????A1?A2??????????????????????????4??????
  ??8????????
• ?????????????????M???????????????????????????????s
  ender??????????????reciever???????????????

Agent 1 outputQ1 Coste1
Agent 4 Revenuee4
??U1
??U2
??Q2
Agent 2 OutputQ2 Coste2
Agent 3 OutputI Coste3
??V
??1
20
?????????Prolog???
??\?? \ 1 2 3 4 ------------------
1 - - - Q1 2 - - v Q2 3 - I -
- 4 u1 u2 - - ------------------ ?1.

• the individual agent and the network
• ---------------
• environment(e1,
• agents
• agents(1,2,3,4),
• agent(1), agent(2), agent(3), agent(4),
• output variables
• outputs(Q1,Q2,I),
• action and its responsibile agent
• output(1,Q1,agent(1)),
• output(2,Q2,agent(2)),
• output(3,I,agent(3)),
• local_environments
• valuations(E1,E2,E3,E4),
• valuation(agent(1),cost(E1),(1,Q1)),
• valuation(agent(2),cost(E2),(2,Q2),(3,I)),
• valuation(agent(3),cost(E3),(3,I)),
• valuation(agent(4),revenue(E4),(1,Q1),(2,Q2)),
  
• end_of_model

mechanism(m1, message space for network
communication hear(fromagent(4),toagent(1),pri
ce_of(U1,output(1))), hear(fromagent(1),toagen
t(4),quantity_of(Q1,output(1))),
hear(fromagent(4),toagent(2),price_of(U2,output(
2))), hear(fromagent(2),toagent(4),quantity_of
(Q2,output(2))), hear(fromagent(3),toagent(2),
quantity_of(I,output(3))), hear(fromagent(2),to
agent(3),price_of(V,output(3))), agreement
rules agreement_rule(agent(1),local(cost(E1)),ma
x(arg(Q1),U1Q1-E1)), agreement_rule(agent(2),
local(cost(E2)),max(arg(Q2,I),U2Q2-E2-VI)),
agreement_rule(agent(3),local(cost(E3)),max(arg(I
),VI-E3)), agreement_rule(agent(4),local(reven
ue(E4)),max(arg(Q1,Q2),E4-U1Q1-U2Q2)),
end_of_model ).
21
?????????????????????????????

• ????????????????????
• m(Q1?Q2?I?u1?u2?v)????g1(P1(m)?e1)g1((Q1?u1)?
  e1)0????Q1?u1Q1-e1(Q1)?????????????????
• ???g4((Q1?Q2?u1?u2)?e1)0??????Q1?Q2???e4(Q1
  ?Q2)-u1Q1-u2Q2?????????????????????
• ??????????
• ????h????3??????(Q1?Q2?I)?????????????????????????
  ???4?Q1?Q2???????3?I???????????????????
• h4(P4(m))h4(Q1?Q2?u1?u2)(Q1?Q2)
• h3(P3(m))h4(I?v)I.
• ????
• M?M???????????????????????????ltM?g?hgt?????????(di
  mensionally minimal)?????????ltM'?g'?h'gt?????dim
  M' ? dim M ??????
• ?????????????ltM?g?hgt?(??????????????????)??????(un
  dominated)??????ltM'?g'?h'gt??????j?????dim
  Pj(M')gt dim Pj(M)????????i?????dim Pi(M') dim
  Pi(M)?????????
• ??????
• ??????????????n??????(l1??ln)??????????????????
  ???????????????????i?????li dim
  Pi(M)??????????????ltM?g?hgt????
• dim M gt ???(total effort)?
• dim Pi(M) gt ????(individual efforts)
• ????????????????????????????2?????????(dim
  MSdim Pi(M)2)?????????????????????????????????
  ???????????????????????????????????

22
????????Prolog?????

• Pi(M) hear or send by the agent i
• ------------------------------------------------
• ihears(M,I,PM)-
• part_of_message_that_i_hears(M,I,PM).
• part_of_message_that_i_hears(M,I,PM)-
• output_message_for_i(M,I,P1),
• mechanism(M,X),
• Qhear(fromJ,toI,_),
• findall(Q,
• (
• member(Q,X),
• J\I
• ),
• P2),
• union(P1,P2,PM).

no self-addressed messages -------------------
----------------------------- star_messages(M,MX)
- mechanism(M,X), Ohear(fromJ,toI,_),
findall(O, ( member(O,X), J \ I
), MX).
?????????????
?????????????
------------------------------------------------
dimensional complexities of message
space -------------------------------------------
----- dimension(M,ihears(I,PM),D)-
ihears(M,I,PM), length(PM,D). dimension(M,(from
J,toI,Msg),D)- mechanism(M,X),
Ohear(fromJ,toI,Msg), member(O,X),
length(Msg,D). dimension(M,star(MX),D)-
star_messages(M,MX), Ohear(from_J,to_I,MSG),
findall(MSG,member(O,MX),MY),
flatten(MY,MZ), length(MZ,D). dimension(M,ihear
s(I,star(PM)),D)- ihears(M,I,PM),
star_messages(M,MX), intersection(PM,MX,PMX),
length(PMX,D).
total effort ----------------------------------
-------------- total_effort(M,star(MX),D)-
dimension(M,star(MX),D). individual effort
vector (iefforts) -------------------------------
----------------- iefforts(M,Is,DV)-
individual_effort_vector(M,Is,DV). individual_eff
ort_vector(M,Is,DV)- mechanism(M,_X),
findall(agent(I),agent(I),Is), findall(D,
( member(agent(I),Is),
dimension(M,ihears(agent(I),star(_PM)),D) ),
DV).
???????
?????????
23
2???????????????????
------------------------------------------------
some claims about minimality and efficiency
------------------------------------------------
claim minimality implies both dominance and
efficiency -------------------------------------
----------- claim(no(1),2total_effort(D)sum_of_i
efforts(D1),Z)- total_effort(M,star(_MX),D),
iefforts(M,_Is,DV), sum(DV,D1), D0 is 2 D,
(D0 is D1-gtZtrueZfalse). claim(no(2),dimension
ally_minimal(D)-gtefficient_iefforts(DV),Z)-
dimensionally_minimal(M,_Class,D),
(efficient_iefforts(M,_Is,DV)-gtZtrueZfalse).
2?????? ??1???????????????????????? ??2????????
?????

• responsibility(i.e., output function)
• activities for which the agent is responsible
• ------------------------------------------------
• is_responsible_for(agent(I),output(K,B))-
• agent(I),
• output(K,B,agent(I)).
• responsibility(agent(I),OUT)-
• agent(I),
• findall(output(K,B),
• (
• output(K,B,agent(I))
• ),
• OUT).

?????????????????
concern --------------------------------------
---------- has_concern_with(agent(I),output(K,B,J)
)- valuation(agent(I),_V,Con),
output(K,B,J), member((K,B),Con). concern(agent
(I),Y)- valuation(agent(I),_V,Con),
findall((K,B,J), ( member((K,B),Con),
output(K,B,J) ), Y0), sort(Y0,Y).
?????????
concerning_agents(X,Js)- Xoutput(K,B,agent(_
I)), X, findall((J), (
valuation(agent(J),_V,Con),
member((K,B),Con) ), Js0), sort(Js0,Js).
?????????????????
24
??????????Prolog?????
dominance -------------------------------------
----------- undominated(M,Class,Dx)-
var(Class), findall(M1,mechanism(M1,_),C0),
subtract(C0,pm(0),Class), iefforts(M,_Is,Dx),
M \ pm(0), Case1( dimension(M,ihears(ag
ent(I),star(PM)),D), dimension(M1,ihears(agen
t(I),star(PM1)),D1), D1 gt D ),
Case2forall(agent(I), (
dimension(M,ihears(agent(I),star(PM)),D),
dimension(M1,ihears(agent(I),star(PM1)),D1),
D1 D ) ), forall(
(member(M1,Class), M1 \ M ), ( Case1Case2
) ). undominated(M,Class,Dx)- \
var(Class), length(Class,_),
forall(member(A,Class),clause(mechanism(A,_),true)
), iefforts(M,_Is,Dx), member(M,Class),
Case1( dimension(M,ihears(agent(I),star(PM))
,D), dimension(M1,ihears(agent(I),star(PM1)),
D1), D1 gt D ), Case2forall(agent(I),
( dimension(M,ihears(agent(I),star(PM)),D)
, dimension(M1,ihears(agent(I),star(PM1)),D1
), D1 D ) ), forall( (
member(M1,Class), mechanism(M1,_), M1 \ M ),
( Case1Case2) ).

• ------------------------------------------------
• evaluation measures for network mechanisms
• minimality, dominance, and efficiency
• ------------------------------------------------
• minimality of mechanisms
• ------------------------------------------------
• dimensionally_minimal(M,Class,dim(star(D)))-
• var(Class),
• findall(M1,mechanism(M1,_),C0),
• subtract(C0,pm(0),Class),
• total_effort(M,star(MX),D),
• dimension(M,star(_MX),D),
• M \ pm(0),
• \ (
• member(M1,Class),
• dimension(M1,star(_MX1),D1),
• D1 lt D
• ).

efficiency ------------------------------------
------------ efficient_iefforts(M,Is,DV)-
undominated(M,_Class,_D), iefforts(M,Is,DV).
25
??????????
??Q1
??????????Prolog?????(network0.pl)???? ???????????
???????????????????????????
Agent 1 outputQ1 Coste1
Agent 4 Revenuee4
??U1
??U2
??U2
??Q2
??Q2
Agent 2 OutputQ2 Coste2
Agent 3 OutputI Coste3
??V

• mechanismm1
• hear(fromagent(4), toagent(1),
  price_of(_G292, output(1)))
• hear(fromagent(1), toagent(4),
  quantity_of(_G314, output(1)))
• hear(fromagent(4), toagent(2),
  price_of(_G336, output(2)))
• hear(fromagent(2), toagent(4),
  quantity_of(_G358, output(2)))
• hear(fromagent(3), toagent(2),
  quantity_of(_G380, output(3)))
• hear(fromagent(2), toagent(3),
  price_of(_G402, output(3)))
• agreement_rule(agent(1), local(cost(_G418)),
  max(arg(_G314), _G292_G314-_G418))
• agreement_rule(agent(2), local(cost(_G445)),
  max(arg(_G358, _G380), _G336_G358-_G445-_G402_
  G380))
• agreement_rule(agent(3), local(cost(_G481)),
  max(arg(_G380), _G402_G380-_G481))
• agreement_rule(agent(4), local(revenue(_G508)),
  max(arg(_G314, _G358), _G508-_G292_G314-_G336_
  G358))
• end_of_model
• diagnosis for the mechanism
• mechanism m1
• the total effort 6
• the individual efforts 2, 4, 2, 4
• the mechanism is dimensionally minimal.
• the mechanism is efficient.

??1
mechanismm2 hear(fromagent(4), toagent(1),
price_of(_G292, output(1))) hear(fromagent(1),
toagent(4), quantity_of(_G314, output(1)))
hear(fromagent(4), toagent(2), price_of(_G336,
output(2))) hear(fromagent(2), toagent(4),
quantity_of(_G358, output(2)))
hear(fromagent(3), toagent(2),
quantity_of(_G380, output(3)))
hear(fromagent(2), toagent(3), price_of(_G402,
output(3))) hear(fromagent(3), toagent(1),
quantity_of(_G424, output(3)))
hear(fromagent(1), toagent(3), price_of(_G446,
output(3))) agreement_rule(agent(1),
local(cost(_G462)), max(arg(_G314, _G424),
_G292_G314-_G462-_G446_G485))
agreement_rule(agent(2), local(cost(_G498)),
max(arg(_G358, _G380), _G336_G358-_G498-_G402_
G485)) agreement_rule(agent(3),
local(cost(_G534)), max(arg(_G424, _G380),
(_G446_G402) (_G424_G380)-_G534))
agreement_rule(agent(4), local(revenue(_G570)),
max(arg(_G314, _G358), _G570-_G292_G314-_G336_
G358)) end_of_model diagnosis for the
mechanism mechanism m2 the total effort 8
the individual efforts 4, 4, 4, 4 the
mechanism is NOT dimensionally minimal. the
mechanism is NOT efficient.
26
????????????

• Marschak and Reichelstein?????????????????????????
  ????
• Z(A)-?????????Z(A)????????????????Z(A)????????????
  ?????????????????
• Z(A)-?????????????????????????????????????????????
  ??????????????????????????
• ?????????AI?????????????????????????????????(??2
  )??????dimPI(M)2abs(AI)
• ???????????????????

27
??????????????????
a meta model price mechanism with
z(a)-coordinator --------------------------------
---------------- metamodel(mechanism(pm(N),
------------message space for network
communication ------------ (
hear(fromagent(J),toagent(I),price_of(_U,X))-
coordinator(pm(N),J,C),
Ccoordinator(agent(J),X,concerning_agents(Ta)),
member(I,Ta), I \ J ), (
hear(fromagent(I),toagent(J),quantity_of(_Q,X))
- coordinator(pm(N),J,C),
Ccoordinator(agent(J),X,concerning_agents(Ta)),
member(I,Ta), I \ J ),
------------agreement rules------------ (
agreement_rule(agent(J),local(VAL),max(arg(ARG),Z
sum(R)-sum(C)))- agent(J),
valuation(agent(J),VAL,_Concerns),
member((VAL,Z),(cost(E),-VAL),(revenue(E),VAL)),
findall(A, (
hear(fromagent(J),toagent(I),A) ),
ARG), findall((p(U)q(Q),to(I),X), (
hear(fromagent(J),toagent(I),quantity_of(
Q,X)), hear(fromagent(I),toagent(J),pric
e_of(U,X)) ), C),
findall((p(U)q(Q),to(I),X), (
hear(fromagent(I),toagent(J),quantity_of(Q,X)),
hear(fromagent(J),toagent(I),price_of(U,
X)) ), R) ), end_of_model )).

• ?????????????????????????????
• ???????network0.pl????????????????????????????????
  ??????????????????????????

28
Prolog???????????????????

• ???network0.pl????Marschak and Reichelstein???????
  ??????????????????

mechanismpm(2) hear(fromagent(3),
toagent(2), price_of(_G294, output(3)))
hear(fromagent(2), toagent(4), price_of(_G316,
output(2))) hear(fromagent(1), toagent(4),
price_of(_G338, output(1))) hear(fromagent(2),
toagent(3), quantity_of(_G360, output(3)))
hear(fromagent(4), toagent(2),
quantity_of(_G382, output(2)))
hear(fromagent(4), toagent(1),
quantity_of(_G404, output(1)))
agreement_rule(agent(1), local(cost(_G420)),
max(arg(price_of(_G430, output(1))),
-cost(_G420)sum( (p(_G456)q(_G458), to(4),
output(1)))-sum())) agreement_rule(agent(2),
local(cost(_G480)), max(arg(price_of(_G490,
output(2)), quantity_of(_G498, output(3))),
-cost(_G480)sum( (p(_G524)q(_G526), to(4),
output(2)))-sum( (p(_G546)q(_G548), to(3),
output(3))))) agreement_rule(agent(3),
local(cost(_G568)), max(arg(price_of(_G578,
output(3))), -cost(_G568)sum(
(p(_G604)q(_G606), to(2), output(3)))-sum()))
agreement_rule(agent(4), local(revenue(_G628)),
max(arg(quantity_of(_G638, output(2)),
quantity_of(_G646, output(1))),
revenue(_G628)sum()-sum( (p(_G672)q(_G674),
to(2), output(2)), (p(_G692)q(_G694), to(1),
output(1))))) coordinators(mechanism(pm(2)))3,
2, 1 coordinator(agent(3), output(3),
concerning_agents(2, 3)) coordinator(agent(2),
output(2), concerning_agents(2, 4))
coordinator(agent(1), output(1),
concerning_agents(1, 4)) diagnosis for the
mechanism mechanism pm(2) the total effort
6 the individual efforts 2, 4, 2, 4 the
mechanism is dimensionally minimal. the
mechanism is efficient.
mechanismpm(1) hear(fromagent(2),
toagent(3), price_of(_G294, output(3)))
hear(fromagent(2), toagent(4), price_of(_G316,
output(2))) hear(fromagent(1), toagent(4),
price_of(_G338, output(1))) hear(fromagent(3),
toagent(2), quantity_of(_G360, output(3)))
hear(fromagent(4), toagent(2),
quantity_of(_G382, output(2)))
hear(fromagent(4), toagent(1),
quantity_of(_G404, output(1)))
agreement_rule(agent(1), local(cost(_G420)),
max(arg(price_of(_G430, output(1))),
-cost(_G420)sum( (p(_G456)q(_G458), to(4),
output(1)))-sum())) agreement_rule(agent(2),
local(cost(_G480)), max(arg(price_of(_G490,
output(3)), price_of(_G498, output(2))),
-cost(_G480)sum( (p(_G524)q(_G526), to(3),
output(3)), (p(_G544)q(_G546), to(4),
output(2)))-sum())) agreement_rule(agent(3),
local(cost(_G568)), max(arg(quantity_of(_G578,
output(3))), -cost(_G568)sum()-sum(
(p(_G606)q(_G608), to(2), output(3)))))
agreement_rule(agent(4), local(revenue(_G628)),
max(arg(quantity_of(_G638, output(2)),
quantity_of(_G646, output(1))),
revenue(_G628)sum()-sum( (p(_G672)q(_G674),
to(2), output(2)), (p(_G692)q(_G694), to(1),
output(1))))) coordinators(mechanism(pm(1)))2,
2, 1 coordinator(agent(2), output(3),
concerning_agents(2, 3)) coordinator(agent(2),
output(2), concerning_agents(2, 4))
coordinator(agent(1), output(1),
concerning_agents(1, 4)) diagnosis for the
mechanism mechanism pm(1) the total effort
6 the individual efforts 2, 4, 2, 4 the
mechanism is dimensionally minimal. the
mechanism is efficient.
29
??

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