Reorganising and adding some papers.

author: Thibaut Horel <thibaut.horel@gmail.com> 2012-01-16 16:02:08 -0800
committer: Thibaut Horel <thibaut.horel@gmail.com> 2012-01-16 16:02:08 -0800
commit: 7a24fd394cc12e1cdab77b3f9c0128ce8d336a15 (patch)
tree: b4d4d61e3f6f396e84cb2d958161069d4a19b17e /strategyproof.ps
parent: 2964c0aff6e060fe7d546ef27ea572d65d8ab974 (diff)
download: recommendation-7a24fd394cc12e1cdab77b3f9c0128ce8d336a15.tar.gz
1 files changed, 0 insertions, 9298 deletions
diff --git a/strategyproof.ps b/strategyproof.ps
deleted file mode 100644
index 7c53da7..0000000
--- a/strategyproof.ps
+++ /dev/null
@@ -1,9298 +0,0 @@
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-(expands:)1964 4664 y Fm(12)p -120 4885 1656 4 v -41
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-(incremen)n(tal)g(costs.)-41 5339 y Fl(11)29 5369 y Fs(In)i(the)h
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-(functions:)49 b(if)34 b Fp(q)3405 801 y Fo(i)3466 786
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-b(service.)70 b(Therefore,)45 b(the)c(demand)h(game)e(p)s(ossesses)k(a)
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-1267 y(is,)c(in)f(addition,)g(a)h(strong)g(equilibrium)d(\(Aumann)j
-([1959]\).)47 b(This)34 b(equilibrium)e(can)i(b)s(e)g(computed)h(b)m(y)
-g(the)-120 1454 y(sim)m(ultaneous)d(Cournot)i(tatonnemen)m(t)f
-(starting)f(at)h Fp(N)10 b Fr(,)34 b(that)f(is)f(to)h(sa)m(y)h(the)g
-(equilibrium)c(outcome)3748 1429 y(~)3732 1454 y Fp(S)5
-b Fr(\()p Fp(\030)g(;)17 b(u)p Fr(\))-120 1618 y(is)32
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-(sequence:)1249 1866 y Fp(S)1315 1825 y Fm(0)1382 1866
-y Fr(=)c Fp(N)43 b Fr(;)82 b Fp(S)1781 1825 y Fo(t)p
-Fm(+1)1928 1866 y Fr(=)28 b Fn(f)p Fp(i)p Fn(j)p Fp(u)2199
-1881 y Fo(i)2254 1866 y Fn(\025)g Fp(\030)2402 1881 y
-Fo(i)2430 1866 y Fr(\()p Fp(S)2534 1825 y Fo(t)2563 1866
-y Fr(\))p Fn(g)1244 b Fr(\(3\))-120 2111 y(In)30 b(the)g(\014rst)g
-(step)h(of)e(the)h(algorithm)d(all)g(agen)m(ts)k(are)e(o\013ered)i
-(service)f(at)g(the)g(p)s(ersonalized)f(price)g Fp(\030)3613
-2126 y Fo(i)3641 2111 y Fr(\()p Fp(N)10 b Fr(\),)31 b(and)-120
-2285 y(only)38 b(those)h(in)f Fp(S)547 2249 y Fm(1)625
-2285 y Fr(accept;)k(in)c(the)h(second)h(step,)h(the)e(agen)m(ts)g(in)f
-Fp(S)2487 2249 y Fm(1)2564 2285 y Fr(are)h(o\013ered)g(service)g(at)g
-(the)g(\(higher\))-120 2459 y(price)j Fp(\030)171 2474
-y Fo(i)199 2459 y Fr(\()p Fp(S)303 2423 y Fm(1)342 2459
-y Fr(\))g(and)h(those)g(in)f Fp(S)1077 2423 y Fm(2)1116
-2459 y Fr(,)j Fp(S)1254 2423 y Fm(2)1337 2459 y Fn(\022)g
-Fp(S)1525 2423 y Fm(1)1606 2459 y Fr(accept;)k(and)42
-b(so)h(on.)72 b(This)43 b(algorithm)c(de\014nes)44 b(an)f(inclusion)
--120 2646 y(monotonic)32 b(sequence)37 b(in)c Fp(N)10
-b Fr(,)35 b(and)f(its)g(outcome)1716 2610 y Fm(13)1841
-2620 y Fr(~)1824 2646 y Fp(S)6 b Fr(\()p Fp(\030)f(;)17
-b(u)p Fr(\))32 b(is)i(the)g(unique)h(strong)f(equilibrium)d(\(there)j
-(ma)m(y)-120 2810 y(b)s(e)f(other)f(strong)h(equilibrium)c
-Fp(q)t Fr('s)k(but)g(they)g(are)f(all)f(w)m(elfare)h(equiv)-5
-b(alen)m(t,)33 b Fi(i.e.)p Fr(,)f(pro)s(duce)h(the)g(same)f(w)m(elfare)
--120 2974 y(for)39 b(ev)m(ery)j(agen)m(t\))e(of)g(the)g(demand)g(game)f
-(\()p Fp(N)5 b(;)17 b(\030)5 b(;)17 b(u)p Fr(\).)64 b(W)-8
-b(e)40 b(asso)s(ciate)f(to)h(the)g(cost)h(sharing)e(metho)s(d)g
-Fp(\030)45 b Fr(the)-120 3144 y(follo)m(wing)30 b(rev)m(elation)i(mec)m
-(hanism)g(denoted)h(b)m(y)h Fp(M)10 b Fr(\()p Fp(\030)5
-b Fr(\):)464 3405 y Fp(S)h Fr(\()p Fp(u)p Fr(\))26 b(=)809
-3380 y(~)792 3405 y Fp(S)6 b Fr(\()p Fp(\030)f(;)17 b(u)p
-Fr(\);)g Fp(x)1181 3420 y Fo(i)1208 3405 y Fr(\()p Fp(u)p
-Fr(\))27 b(=)g Fp(\030)1513 3420 y Fo(i)1541 3405 y Fr(\()1596
-3380 y(~)1579 3405 y Fp(S)6 b Fr(\()p Fp(\030)f(;)17
-b(u)p Fr(\)\))31 b Fp(if)43 b(i)28 b Fn(2)2234 3380 y
-Fr(~)2217 3405 y Fp(S)6 b Fr(\()p Fp(\030)f(;)17 b(u)p
-Fr(\);)48 b Fp(x)2637 3420 y Fo(i)2665 3405 y Fr(\()p
-Fp(u)p Fr(\))28 b(=)f(0)32 b Fp(other)s(w)s(ise)459 b
-Fr(\(4\))-120 3716 y(If)35 b Fp(\030)k Fr(is)c(cross-monotonic)f(then)h
-Fp(M)10 b Fr(\()p Fp(\030)5 b Fr(\))35 b(is)g(strategypro)s(of.)50
-b(In)36 b(fact,)f Fp(M)10 b Fr(\()p Fp(\030)5 b Fr(\))35
-b(is)g(group)g(strategypro)s(of)f(as)i(w)m(ell.)-120
-3881 y(Moreo)m(v)m(er,)e(the)f(con)m(v)m(erse)i(statemen)m(t)e(holds.)
--120 4191 y Fh(Prop)s(osition)j(1)48 b Fi(F)-7 b(or)42
-b(any)g(cr)-5 b(oss)42 b(monotonic)f(c)-5 b(ost)42 b(sharing)f(metho)-5
-b(d)42 b Fp(\030)5 b Fi(,)43 b(the)f(me)-5 b(chanism)41
-b Fp(M)10 b Fr(\()p Fp(\030)5 b Fr(\))42 b Fi(\(de\014ne)-5
-b(d)-120 4361 y(by)38 b(\(4\)\))f(is)g(budget)g(b)-5
-b(alanc)g(e)g(d,)37 b(me)-5 b(ets)37 b(NPT,)h(VP,)g(CS,)f(and)f(is)i
-(gr)-5 b(oup)37 b(str)-5 b(ate)g(gypr)g(o)g(of.)53 b(Conversely,)37
-b(for)g(any)-120 4525 y(r)-5 b(evelation)44 b(me)-5 b(chanism)43
-b Fp(M)55 b Fi(satisfying)44 b(budget)h(b)-5 b(alanc)g(e,)45
-b(NPT,)g(VP,)g(CS,)f(and)g(gr)-5 b(oup)45 b(str)-5 b(ate)g(gypr)g(o)g
-(ofness)-120 4689 y(ther)g(e)35 b(exists)f(a)h(cr)-5
-b(oss)34 b(monotonic)g(c)-5 b(ost)35 b(sharing)f(metho)-5
-b(d)34 b Fp(\030)39 b Fi(such)c(that)g Fp(M)10 b Fr(\()p
-Fp(\030)5 b Fr(\))35 b Fi(is)g(welfar)-5 b(e)34 b(e)-5
-b(quivalent)34 b(to)h Fp(M)10 b Fi(.)-120 5005 y Fr(The)36
-b(Prop)s(osition)c(is)j(iden)m(tical)e(to)h(Theorem)h(2)f(in)g(Moulin)f
-([1999].)49 b(In)35 b(the)g(sp)s(ecial)f(case)h(of)f(an)h(excludable)
--120 5175 y(public)j(go)s(o)s(d)g(\()p Fp(C)7 b Fr(\()p
-Fp(S)f Fr(\))37 b(=)i(1)f(for)g(all)f(nonempt)m(y)j Fp(S)6
-b Fr(\),)40 b(Deb)f(and)g(Razzolini)d([1996,)j(1999])f(and)h(Ohseto)h
-([1995])-120 5339 y(pro)m(vide)33 b(similar)c(y)m(et)34
-b(di\013eren)m(t)e(c)m(haracterization)g(results.)p -120
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-(sharing)f(metho)r(d)i(is)g(unam)n(biguous.)1926 5866
-y Fr(9)p eop
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-10 9 bop -120 197 a Fr(W)-8 b(e)40 b(do)f(not)g(pro)m(vide)g(a)g(pro)s
-(of)g(of)f(the)i(\\con)m(v)m(erse")h(statemen)m(t)f(in)f(Prop)s
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-356 y(statemen)m(t)33 b(is)f(easy)i(to)e(pro)m(v)m(e)i(and)f(w)m(e)g
-(rep)s(eat)g(its)f(pro)s(of)g(in)f(App)s(endix)j(A.)-120
-581 y Fh(Remark)f(2:)42 b Fr(W)-8 b(e)29 b(note)h(that)f(all)e(three)j
-(assumptions)f(NPT,)h(VP)f(and)h(CS)f(are)h(needed)g(in)f(the)g(c)m
-(haracteriza-)-120 740 y(tion)23 b(result.)40 b(This)24
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-b(Denote)23 b(b)m(y)i Fp(e)f Fr(the)g(\\egalitarian")c(allo)s(cation)
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-Fp(x)452 919 y Fo(i)522 904 y Fr(=)g Fp(C)7 b Fr(\()p
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-b(Consider)41 b(t)m(w)m(o)g(v)m(oting)f(mec)m(hanisms)g(b)s(et)m(w)m
-(een)j Fp(e)e Fr(and)g(the)g(\\n)m(ull")-120 1074 y(allo)s(cation)34
-b(\()p Fp(q)413 1089 y Fo(i)477 1074 y Fr(=)h Fp(x)643
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-Fr(\).)58 b(If)37 b(unanimit)m(y)f(is)g(required)i(to)f(implemen)m(t)e
-Fp(e)i Fr(\()p Fi(i.e.)p Fr(,)h(ev)m(ery)h(agen)m(t)f(can)-120
-1244 y(force)31 b(the)h(n)m(ull)e(outcome\),)i(w)m(e)g(ha)m(v)m(e)h(a)e
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-(the)i(n)m(ull)e(outcome)h(\(ev)m(ery)j(agen)m(t)e(can)-120
-1583 y(force)h Fp(e)p Fr(\),)h(the)f(mec)m(hanism)f(meets)h(all)e(prop)
-s(erties)i(but)g(V)-8 b(olun)m(tary)35 b(P)m(articipation.)51
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-y Fm(1)2206 2946 y Fp(<)28 b(C)7 b Fr(\(12\))32 b Fp(and)g(u)2841
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-b Fp(if)44 b(u)2015 3390 y Fm(1)2081 3375 y Fp(<)28 b(C)7
-b Fr(\(12\))32 b Fp(and)g(u)2716 3390 y Fm(2)2783 3375
-y Fp(<)27 b(C)7 b Fr(\(2\))-120 3703 y(The)33 b(family)c(of)j(rev)m
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-Fr(,)33 b(so)g(that)f(the)i(prop)s(ert)m(y)f(\\equal)f(treatmen)m(t)h
-(of)f(equals")h(is)g(deemed)g(desirable:)43 b(this)33
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-b Fr(+)23 b Fp(i)p Fr(\))32 b(=)f Fp(C)7 b Fr(\()p Fp(S)29
-b Fr(+)23 b Fp(j)6 b Fr(\))34 b(for)g(all)f Fp(S)k Fn(\022)31
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-Fr(and)g Fp(j)38 b Fr(should)33 b(b)s(e)f(symmetrical)f(as)i(w)m(ell.)
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-(v)-5 b(ariet)m(y)39 b(of)g(form)m(ulae,)g(including)f(the)h(Shapley)h
-(v)-5 b(alue)39 b(\(Shapley)-120 4754 y([1953]\))168
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-(and)h(Ra)m(y)g([1989]\))2383 4718 y Fm(15)2457 4754
-y Fr(,)i(con)m(v)m(ex)g(com)m(binations)c(of)h(these,)k(and)-120
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-Fp(N)38 b Fr(=)28 b Fn(f)p Fr(1)p Fp(;)17 b Fr(2)p Fn(g)p
-Fr(,)31 b(these)j(t)m(w)m(o)g(v)-5 b(alues)32 b(are)p
--120 5020 1656 4 v -41 5081 a Fl(14)29 5111 y Fs(F)-7
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-b(is)f(cross)f(monotonic)h(when)h Fk(C)34 b Fs(is)28
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-(co)r(op)r(erativ)n(e)e(game)h(\()p Fk(N)t(;)14 b(c)p
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-5364 y(the)28 b(stand)f(alone)g(core)f(of)i(this)g(game)e(\()p
-Fk(x)1193 5334 y Ft(\003)1193 5387 y Fg(S)1265 5364 y
-Fw(\024)d Fk(C)6 b Fs(\()p Fk(S)f Fs(\))28 b(for)f(all)g
-Fk(S)5 b Fs(\).)37 b(Dutta)28 b([1990])e(sho)n(ws)g(that)i(this)g
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-1565 y(then)35 b(so)f(is)g Fp(S)29 b Fn([)24 b Fp(T)14
-b Fr(;)34 b(w)m(e)h(denote)g(b)m(y)g Fp(S)1300 1529 y
-Fj(\003)1340 1565 y Fr(\()p Fp(u)p Fr(\))e(the)i(largest)e(e\016cien)m
-(t)i(coalition)c(at)j Fp(u)p Fr(,)g(and)h(denote)g(b)m(y)g
-Fp(q)3680 1529 y Fj(\003)3719 1565 y Fr(\()p Fp(u)p Fr(\))f(the)-120
-1729 y(corresp)s(onding)e(allo)s(cation)e(v)m(ector.)-120
-1960 y(The)35 b(MC)g(mec)m(hanism)e(pic)m(ks)i(the)g(coalition)c
-Fp(S)6 b Fr(\()p Fp(u)p Fr(\))29 b(=)h Fp(S)1991 1924
-y Fj(\003)2030 1960 y Fr(\()p Fp(u)p Fr(\))k(and)g(c)m(harges)h(the)g
-(cost)f(shares)i Fp(x)3456 1924 y Fj(\003)3495 1960 y
-Fr(\()p Fp(u)p Fr(\))e(giv)m(en)g(b)m(y)-120 2124 y(the)f(form)m(ula:)
-1116 2273 y Fp(x)1171 2232 y Fj(\003)1171 2298 y Fo(i)1238
-2273 y Fr(=)28 b Fp(u)1398 2288 y Fo(i)1426 2273 y Fp(q)1473
-2232 y Fj(\003)1469 2298 y Fo(i)1512 2273 y Fr(\()p Fp(u)p
-Fr(\))21 b Fn(\000)i Fr(\()p Fp(w)s Fr(\()p Fp(N)5 b(;)17
-b(u)p Fr(\))k Fn(\000)h Fp(w)s Fr(\()p Fp(N)32 b Fn(\000)23
-b Fp(i;)17 b(u)p Fr(\)\))1110 b(\(7\))-120 2563 y(W)-8
-b(e)31 b(call)e(it)h(the)h(marginal)d(cost)j(pricing)f(mec)m(hanism)g
-(b)s(ecause,)i(in)e(the)i(case)f(of)g(a)f(symmetric)g(cost)h(function,)
--120 2727 y Fp(C)7 b Fr(\()p Fp(S)f Fr(\))27 b(=)h Fp(c)p
-Fr(\()p Fn(j)p Fp(S)6 b Fn(j)p Fr(\),)28 b(this)h(mec)m(hanism)f(c)m
-(harges)i(appro)m(ximately)e(the)h(marginal)d(cost)j
-Fp(c)p Fr(\()p Fn(j)p Fp(S)3128 2691 y Fj(\003)3167 2727
-y Fn(j)p Fr(\))15 b Fn(\000)g Fp(c)p Fr(\()p Fn(j)p Fp(S)3514
-2691 y Fj(\003)3552 2727 y Fn(j)g(\000)g Fr(1\))28 b(to)g(all)-120
-2891 y(agen)m(ts)j(and)g(this)f(appro)m(ximation)f(b)s(ecomes)i(an)f
-(equalit)m(y)h(when)g(eac)m(h)h(agen)m(t)f(b)s(ecomes)g(a)f(v)-5
-b(anishingly)29 b(small)-120 3060 y(part)j(of)g Fp(N)43
-b Fr(\(w)m(e)34 b(omit)d(the)i(pro)s(of)e(for)h(brevit)m(y\).)1714
-3024 y Fm(18)-120 3291 y Fr(Our)k(c)m(hoice)g(of)f(MC)i(mec)m(hanism)e
-(out)g(of)g(the)i(whole)e(CG)h(class)g(is)f(b)m(y)i(no)e(means)h
-(arbitrary)-8 b(.)52 b(In)36 b(fact,)g(once)-120 3459
-y(w)m(e)e(require)e(NPT)i(and)f(VP)923 3423 y Fm(19)1030
-3459 y Fr(it)f(is)g(essen)m(tially)g(the)h(only)f(a)m(v)-5
-b(ailable)30 b(CG)j(mec)m(hanism.)-120 3801 y Fh(Prop)s(osition)j(3)48
-b Fi(Consider)30 b(a)h(str)-5 b(ate)g(gypr)g(o)g(of)31
-b(r)-5 b(evelation)30 b(me)-5 b(chanism)29 b Fp(M)41
-b Fi(sele)-5 b(cting)30 b(an)h(e\016cient)f(al)5 b(lo)-5
-b(c)g(ation)-120 3965 y(\(not)32 b(ne)-5 b(c)g(essarily)30
-b(the)i(lar)-5 b(gest\))31 b(at)h(al)5 b(l)32 b(pr)-5
-b(o\014les,)31 b(me)-5 b(eting)31 b(NPT)h(and)f(VP.)h(Then)f
-Fp(M)42 b Fi(is)32 b(welfar)-5 b(e)31 b(e)-5 b(quivalent)31
-b(to)-120 4129 y(MC:)k(for)g(al)5 b(l)34 b Fp(u)p Fi(,)g(al)5
-b(l)35 b Fp(i)1248 4298 y(u)1304 4313 y Fo(i)1332 4298
-y Fp(q)1375 4313 y Fo(i)1403 4298 y Fr(\()p Fp(u)p Fr(\))22
-b Fn(\000)g Fp(x)1711 4313 y Fo(i)1740 4298 y Fr(\()p
-Fp(u)p Fr(\))27 b(=)h Fp(u)2059 4313 y Fo(i)2086 4298
-y Fp(q)2133 4257 y Fj(\003)2129 4323 y Fo(i)2173 4298
-y Fr(\()p Fp(u)p Fr(\))21 b Fn(\000)i Fp(x)2481 4257
-y Fj(\003)2481 4323 y Fo(i)2521 4298 y Fr(\()p Fp(u)p
-Fr(\))-120 4527 y Fi(Conversely,)34 b(the)h(MC)g(me)-5
-b(chanism)33 b(me)-5 b(ets)34 b(NPT)h(and)g(VP)g(\(as)f(wel)5
-b(l)35 b(as)f(CS\))g(and)h(is)f(str)-5 b(ate)g(gypr)g(o)g(of.)p
--120 4625 1656 4 v -41 4686 a Fl(18)29 4717 y Fs(The)27
-b(MC)f(mec)n(hanism)f(is)h(quite)h(similar)e(in)h(form)g(to)g(the)g
-(traditional)f Ff(pivotal)j Fs(mec)n(hanism,)e(whic)n(h)g(assigns)f
-(the)h(net)h(utilit)n(y)-120 4887 y Fk(u)-72 4899 y Fg(i)-23
-4887 y Fw(\000)21 b Fk(x)110 4899 y Fg(i)169 4887 y Fs(=)31
-b Fk(w)r Fs(\()p Fk(N)9 b Fs(\))23 b Fw(\000)e Fk(w)636
-4857 y Ft(\003)675 4887 y Fs(\()p Fk(N)31 b Fw(\000)21
-b Fk(i)p Fs(\),)33 b(where)f Fk(w)1314 4857 y Ft(\003)1353
-4887 y Fs(\()p Fk(N)f Fw(\000)21 b Fk(i)p Fs(\))31 b(=)g(max)1911
-4899 y Fg(T)9 b Ft(\022)p Fg(N)d Ft(\000)p Fg(i)2150
-4887 y Fs([)p Fk(u)2221 4899 y Fg(T)2294 4887 y Fw(\000)2433
-4847 y Ft(j)p Fg(T)j Ft(j)p 2391 4868 172 4 v 2391 4915
-a(j)p Fg(T)g Ft(j)p Fl(+1)2572 4887 y Fk(C)d Fs(\()p
-Fk(T)34 b Fs(+)21 b Fk(i)p Fs(\)])32 b(\(see,)i(for)e(example,)h(Green)
-f(and)-120 5062 y(La\013on)n(t)27 b([1979]\).)35 b(In)27
-b(substance,)g(ho)n(w)n(ev)n(er,)e(they)j(are)e(quite)h(di\013eren)n
-(t;)h(the)g(piv)n(otal)e(mec)n(hanism)h(nev)n(er)f(runs)h(a)f(budget)i
-(de\014cit)-120 5216 y(\(i.e,)g(it)g(either)g(is)g(budget)g(balanced)f
-(or)g(runs)g(a)g(surplus\))h(and)f(fails)h(VP)-7 b(,)28
-b(whereas)e(the)i(MC)g(mec)n(hanism)f(nev)n(er)g(runs)h(a)f(budget)-120
-5369 y(surplus)g(\(i.e,)h(it)g(either)g(is)f(budget)h(balanced)f(or)f
-(runs)i(a)f(budget)h(de\014cit\))g(and)f(satis\014es)g(VP)-7
-b(.)-41 5438 y Fl(19)29 5469 y Fs(W)g(e)33 b(need)f(not)g(require)f(CS)
-i(since)f(all)f(CG)i(mec)n(hanisms)e(satisfy)h(CS;)g(the)h(set)f(of)g
-(e\016cien)n(t)g(coalitions)f(is)h(indep)r(enden)n(t)h(of)-120
-5617 y(the)28 b(mec)n(hanism,)f(and)h(if)g Fk(u)759 5629
-y Fg(i)809 5617 y Fk(>)23 b(C)6 b Fs(\()p Fk(i)p Fs(\))28
-b(all)f(e\016cien)n(t)h(coalitions)e(will)i(include)g(agen)n(t)f
-Fk(i)g Fs(when)h(the)g(cost)f(is)g(submo)r(dular.)1901
-5866 y Fr(13)p eop
-%%Page: 14 14
-14 13 bop -120 197 a Fr(The)34 b(pro)s(of)d(of)h(this)h(Prop)s(osition)
-d(is)j(presen)m(ted)h(in)e(App)s(endix)h(C.)-120 422
-y Fh(Remark)48 b(4:)62 b Fr(Both)42 b(assumptions)g(NPT)h(and)f(VP)g
-(are)g(needed)i(in)d(this)g(c)m(haracterization)g(result.)72
-b(If)42 b(w)m(e)-120 586 y(drop)36 b(VP)-8 b(,)36 b(the)g(piv)m(otal)e
-(mec)m(hanism)h(\(see)i(F)-8 b(o)s(otnote)34 b(18)h(meets)h(all)e
-(other)i(assumptions.)52 b(If)36 b(w)m(e)g(drop)g(NPT)-120
-756 y(then)30 b(w)m(e)g(can)f(mo)s(dify)e(the)i(MC)h(mec)m(hanism)e(b)m
-(y)i(adding)e(an)h(arbitrary)f(cash)i(pa)m(ymen)m(t)f(\(from)f(the)h
-(bank)m(er)h(to)-120 926 y(eac)m(h)k(agen)m(t\))f(indep)s(enden)m(t)i
-(of)e(the)g(rep)s(orted)h(pro\014le.)44 b(The)35 b(pro)s(of)d(of)h
-(Prop)s(osition)e(3)i(mak)m(es)h(clear)e(that)h(if)f(a)-120
-1090 y(strategypro)s(of)j(mec)m(hanism)f(selects)h(an)g(e\016cien)m(t)g
-(allo)s(cation)d(and)i(satis\014es)i(VP)-8 b(,)35 b(then)g(it)f(m)m
-(ust)h(b)s(e)g(\\P)m(areto)-120 1249 y(sup)s(erior")i(to)g(MC)h(in)f
-(the)h(sense)h(that)e(at)g(all)e(pro\014les)j(ev)m(ery)h(agen)m(t)f
-(incurs)f(a)h(smaller)d(c)m(harge)j Fp(x)3617 1264 y
-Fo(i)3646 1249 y Fr(.)58 b(Suc)m(h)38 b(a)-120 1408 y(mec)m(hanism)32
-b(ob)m(viously)g(runs)i(an)e(unam)m(biguously)g(higher)g(budget)h
-(de\014cit)f(at)h(all)d(pro\014les.)-120 1633 y(Note)38
-b(that)g(the)g(MC)h(mec)m(hanism,)g(lik)m(e)e(an)m(y)i(mec)m(hanism)e
-(in)g(the)h(CG)g(class,)i(is)d Fi(not)h Fr(group)g(strategypro)s(of.)
--120 1797 y(Moreo)m(v)m(er,)c(there)e(is)g(a)g(sp)s(ecial)e(kind)i(of)g
-(\\altruistic")d(manipulation)g(\(a)i(violation)e(of)j(group)g
-(strategypro)s(of-)-120 1967 y(ness\))j(that)f(do)s(es)g(not)g(require)
-g(an)m(y)g(co)s(ordination)e(b)s(et)m(w)m(een)j(agen)m(ts)g(and)f(to)f
-(whic)m(h)i(the)f(MC)g(mec)m(hanism)f(is)-120 2137 y(alw)m(a)m(ys)k
-(vulnerable.)55 b(Fix)36 b(a)h(pro\014le)f Fp(u)g Fr(\(the)h(true)g
-(pro\014le\))f(and)h(a)f(willingness)f(to)h(pa)m(y)h
-Fp(u)3278 2101 y Fj(0)3278 2162 y Fo(i)3343 2137 y Fr(for)f(agen)m(t)h
-Fp(i)f Fr(suc)m(h)-120 2311 y(that)c Fp(u)147 2326 y
-Fo(i)203 2311 y Fp(<)27 b(u)362 2275 y Fj(0)362 2336
-y Fo(i)390 2311 y Fr(.)43 b(Denoting)32 b Fp(u)938 2275
-y Fj(0)988 2311 y Fr(=)c(\()p Fp(u)1186 2326 y Fj(\000)p
-Fo(i)1268 2311 y Fp(;)17 b(u)1368 2275 y Fj(0)1368 2336
-y Fo(i)1396 2311 y Fr(\))32 b(w)m(e)i(observ)m(e)g(the)f(follo)m(wing)d
-(facts:)2762 2275 y Fm(20)-120 2547 y Fh(F)-9 b(act)37
-b(1)p Fr(:)44 b Fp(S)319 2511 y Fj(\003)358 2547 y Fr(\()p
-Fp(u)p Fr(\))27 b Fn(\022)h Fp(S)688 2511 y Fj(\003)728
-2547 y Fr(\()p Fp(u)822 2511 y Fj(0)844 2547 y Fr(\))-120
-2784 y Fh(F)-9 b(act)37 b(2)p Fr(:)44 b(no)32 b(agen)m(t)h
-Fp(j)6 b Fr(,)33 b Fp(j)g Fn(6)p Fr(=)28 b Fp(i)p Fr(,)33
-b(is)f(h)m(urt:)44 b Fp(w)s Fr(\()p Fp(N)5 b(;)17 b(u)p
-Fr(\))k Fn(\000)h Fp(w)s Fr(\()p Fp(N)32 b Fn(\000)23
-b Fp(j;)17 b(u)p Fr(\))27 b Fn(\024)h Fp(w)s Fr(\()p
-Fp(N)5 b(;)17 b(u)2754 2748 y Fj(0)2776 2784 y Fr(\))23
-b Fn(\000)f Fp(w)s Fr(\()p Fp(N)32 b Fn(\000)23 b Fp(j;)17
-b(u)3397 2748 y Fj(0)3420 2784 y Fr(\))-120 3020 y Fh(F)-9
-b(act)37 b(3)p Fr(:)44 b(if)31 b Fp(i)d Fn(2)g Fp(S)563
-2984 y Fj(\003)603 3020 y Fr(\()p Fp(u)p Fr(\))j(then)j
-Fp(S)1055 2984 y Fj(\003)1094 3020 y Fr(\()p Fp(u)1188
-2984 y Fj(0)1211 3020 y Fr(\))27 b(=)h Fp(S)1446 2984
-y Fj(\003)1485 3020 y Fr(\()p Fp(u)p Fr(\))k(and)h Fp(x)1894
-2984 y Fj(\003)1894 3045 y Fo(i)1933 3020 y Fr(\()p Fp(u)p
-Fr(\))28 b(=)f Fp(x)2251 2984 y Fj(\003)2251 3045 y Fo(i)2291
-3020 y Fr(\()p Fp(u)2385 2984 y Fj(0)2408 3020 y Fr(\))-120
-3251 y(F)-8 b(acts)32 b(2)f(and)h(3)f(tell)f(us)i(that)f(if)g(an)g
-(agen)m(t)h Fp(i)g Fr(is)f(serv)m(ed)j(at)d(pro\014le)g
-Fp(u)p Fr(,)g(rep)s(orting)g(a)g(higher)g(willingness)f(to)h(pa)m(y)
--120 3409 y(is)e(a)g(matter)f(of)h(indi\013erence)g(to)f(her,)j(and)e
-(it)f(can)i(nev)m(er)g(h)m(urt)g(an)m(y)g(other)f(agen)m(t.)43
-b(T)-8 b(o)29 b(see)h(that)f(in)g(some)g(cases)-120 3568
-y(it)j(can)g(strictly)g(help)h(other)f(agen)m(ts,)i(consider)f(the)g
-(follo)m(wing)d(example)i(with)g(t)m(w)m(o)h(agen)m(ts:)986
-3812 y Fp(C)7 b Fr(\(1\))27 b(=)h Fp(C)7 b Fr(\(2\))27
-b(=)g(6)33 b(;)81 b Fp(C)7 b Fr(\(12\))27 b(=)h(8)k(;)82
-b Fp(u)2469 3827 y Fm(1)2536 3812 y Fr(=)27 b Fp(u)2695
-3827 y Fm(2)2762 3812 y Fr(=)g(5)-120 4061 y(T)-8 b(ruthful)25
-b(rep)s(orts)h(yield)f Fp(S)885 4025 y Fj(\003)924 4061
-y Fr(\()p Fp(u)p Fr(\))i(=)h Fn(f)p Fr(1)p Fp(;)17 b
-Fr(2)p Fn(g)24 b Fr(and)i(cost)g(shares)h Fp(x)2172 4025
-y Fj(\003)2172 4086 y Fm(1)2212 4061 y Fr(\()p Fp(u)p
-Fr(\))g(=)g Fp(x)2529 4025 y Fj(\003)2529 4086 y Fm(2)2569
-4061 y Fr(\()p Fp(u)p Fr(\))g(=)h(3.)41 b(By)26 b(raising)e(her)i
-(willingness)p -120 4148 1656 4 v -41 4210 a Fl(20)29
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-Fk(S)g Fs(=)22 b Fk(S)1143 4210 y Ft(\003)1181 4240 y
-Fs(\()p Fk(u)p Fs(\),)28 b Fk(T)34 b Fs(=)23 b Fk(S)1571
-4210 y Ft(\003)1608 4240 y Fs(\()p Fk(u)1688 4210 y Ft(0)1712
-4240 y Fs(\))28 b(and)f(compute)-120 4466 y Fk(u)-72
-4478 y Fg(S)s Ft(\\)p Fg(T)70 4466 y Fw(\000)q Fk(C)6
-b Fs(\()p Fk(S)g Fw(\\)q Fk(T)12 b Fs(\))23 b Fw(\024)f
-Fk(u)597 4478 y Fg(S)646 4466 y Fw(\000)q Fk(C)6 b Fs(\()p
-Fk(S)f Fs(\))23 b Fw(\))g Fk(C)6 b Fs(\()p Fk(S)g Fw([)q
-Fk(T)12 b Fs(\))q Fw(\000)q Fk(C)6 b Fs(\()p Fk(T)12
-b Fs(\))23 b Fw(\024)g Fk(C)6 b Fs(\()p Fk(S)f Fs(\))q
-Fw(\000)q Fk(C)h Fs(\()p Fk(S)g Fw(\\)q Fk(T)12 b Fs(\))23
-b Fw(\024)g Fk(u)2411 4478 y Fg(S)s Ft(\000)p Fg(T)2582
-4466 y Fw(\024)f Fk(u)2717 4432 y Ft(0)2717 4486 y Fg(S)s
-Ft(\000)p Fg(T)2888 4466 y Fw(\))h Fk(u)3042 4432 y Ft(0)3042
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-b Fs(\))23 b Fw(\024)g Fk(u)3510 4432 y Ft(0)3510 4486
-y Fg(S)s Ft([)p Fg(T)3651 4466 y Fw(\000)q Fk(C)6 b Fs(\()p
-Fk(S)g Fw([)q Fk(T)12 b Fs(\))-120 4694 y(implying,)28
-b(b)n(y)f(de\014nition)h(of)g Fk(T)12 b Fs(,)27 b Fk(S)c
-Fw([)c Fk(T)34 b Fs(=)23 b Fk(T)12 b Fs(.)36 b(Similar)27
-b(reasoning)f(establishes)h Fk(S)2500 4664 y Ft(\003)2537
-4694 y Fs(\()p Fk(u;)14 b(N)27 b Fw(\000)18 b Fk(j)5
-b Fs(\))24 b Fw(\022)f Fk(S)3070 4664 y Ft(\003)3107
-4694 y Fs(\()p Fk(u;)14 b(N)9 b Fs(\))28 b(for)f(all)g
-Fk(j)5 b Fs(.)37 b(T)-7 b(o)28 b(pro)n(v)n(e)-120 4848
-y(F)-7 b(act)34 b(2,)i(namely)e Fk(w)r Fs(\()p Fk(N)e
-Fw(\000)23 b Fk(j;)14 b(u)867 4818 y Ft(0)890 4848 y
-Fs(\))23 b Fw(\000)f Fk(w)r Fs(\()p Fk(N)33 b Fw(\000)22
-b Fk(j;)14 b(u)p Fs(\))34 b Fw(\024)g Fk(w)r Fs(\()p
-Fk(N)t(;)14 b(u)1845 4818 y Ft(0)1869 4848 y Fs(\))23
-b Fw(\000)f Fk(w)r Fs(\()p Fk(N)t(;)14 b(u)p Fs(\),)37
-b(w)n(e)d(note)g(that)g(b)r(oth)h(sides)f(of)g(the)g(inequalit)n(y)g
-(are)-120 5001 y(nonnegativ)n(e)24 b(and)g(w)n(e)h(distinguish)g(three)
-g(cases.)34 b(If)26 b Fk(S)1621 4971 y Ft(\003)1659 5001
-y Fs(\()p Fk(N)c Fw(\000)13 b Fk(j;)h(u)p Fs(\))25 b(con)n(tains)f
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-4971 y Ft(\003)3102 5001 y Fs(\()p Fk(N)t(;)14 b(u)3290
-4971 y Ft(0)3313 5001 y Fs(\),)26 b(and)f Fk(S)3609 4971
-y Ft(\003)3647 5001 y Fs(\()p Fk(N)d Fw(\000)13 b Fk(j;)h(u)3965
-4971 y Ft(0)3988 5001 y Fs(\))-120 5155 y(and)35 b(b)r(oth)i(terms)e
-(of)g(the)i(inequalit)n(y)e(equal)g Fk(u)1415 5124 y
-Ft(0)1415 5176 y Fg(i)1466 5155 y Fw(\000)23 b Fk(u)1602
-5167 y Fg(i)1629 5155 y Fs(.)61 b(If)37 b Fk(S)1861 5124
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-%%Trailer
-end
-userdict /end-hook known{end-hook}if
-%%EOF
author	Thibaut Horel <thibaut.horel@gmail.com>	2012-01-16 16:02:08 -0800
committer	Thibaut Horel <thibaut.horel@gmail.com>	2012-01-16 16:02:08 -0800
commit	7a24fd394cc12e1cdab77b3f9c0128ce8d336a15 (patch)
tree	b4d4d61e3f6f396e84cb2d958161069d4a19b17e /strategyproof.ps
parent	2964c0aff6e060fe7d546ef27ea572d65d8ab974 (diff)
download	recommendation-7a24fd394cc12e1cdab77b3f9c0128ce8d336a15.tar.gz