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59 1[] (Gibbons, 1992) (1) (2) (3) (1) 32113344((,),(,)) (2) (,)TR(,)BL34115544((,),(0,,)) (3) (,)DR 2[] (Gibbons, 1992) (1) (2) (1) ABCABBCabab (2) (,)Ab(,)Ca32115522((,,0),(,,0)) 3[] (Francesco Squintani, 2006) i1/4iw[0,]iicw∈12ycc=+yi12(,)iiiuccywc=+− 1212(,)iiiuccccwc=++−121102cc−=+3212()04cc−−+*1221()4ccc=− L R T 2,1 0,2 B 1,2 3,0 L C RT 0,4 5,6 8,7B 2,9 6,5 5,1 L C RU 1,‐2 ‐2,1 0,0M ‐2,1 1,‐2 0,0D 0,0 0,0 1,1 a b cA 0,3 8,5 4,2B 2,6 6,3 4,5C 4,4 0,3 0,360 *2111()4ccc=−0iicw≤≤ *****1211211(,):0,44ccccc⎧⎫≤≤+=⎨⎬⎩⎭ 4[] (Jimmy Chan 2008) i(1,2i=)[,]xxixiixc−0x0.5()xc− (1) 0.5c=x=−∞100x= (2) 0.5c=100x=−x=∞ (3) 0.5c=100x=−100x= (4) 0c=100x=−100x= (1) 0x00x≤1x−(,100]x∈−∞ (2) 100−100−99−0x≤0xx1x+0x (3) (2)0x≤1000x100990x3x=2211{1,2} (4) 0x000x00x≥ 5[] (Jimmy Chan, 2008) (1) (2) (3) (1) (,)AA(,)BB21123333((,),(,))2233{(2,1),(1,2),(,)} (2) ,,,xyzw 2xy≥2wz≥2xz≥2wy≥ min{,}max{/2,2}xwyz≥ A B A 2,1 0,0 B 0,0 1,2 A B A x y B z w 61 CE payoff (2/3, 2/3) (1, 2) (2, 1) {}1212(,):2,2,min{,}max{/2,2},1,,,,uuuxwuxwxwyzxyzwxyzw+=+=+≥+++=∈ (3) 6[] (William Sandholm, 2006) 121p 2p12,[0,1]pp∈i(,)(1)iijijipppppπ=+−ji≠ (1) (i)1(ii)12(iii)1211 (2) iipi(,)120iijjiidppppdpπ=+−=*1()2jijppp+=ijjpp≥jp*()ijpp*()iijppp *()ijppjp*()iijppp**()(1())(1)ijjijijipppppppp+−+−*()iijpppjjpp≥*()()()ijjjijjppppppp−−**()(1())(1)ijjijijipppppppp+−+−*((),)(,)ijjijpppppππ (1) 0jp≥(i)*12(0)iipp≥=(iii)12112p≥(ii)1*312224()pp≥=(i)1*371148()pp≥= (2) 00x=11122tittix−==∑1,2,t=…ijtpx≥ti*11122()iitttppxxx+≥=+=itpx≥ttx1121pp==121pp== 7[] (Debraj Ray, 2006) Ni{1,2,,}K…ix11ninixx==∑23x1(23x) 62 2K≥2233(1)KKKK−−−(0){1,2,,}iiRSK==…0m≥{}(1)():(),iiiiiiiRmsRmsRmss−−−+=∈∃∈i0()iimRRm∞==∩K23x23KKiK1K−1K1/nKK(1){1,2,,1}iRK=−…(1){1}iRK−=1 8[] (Bingyong Zheng 2008) 1c1x2tx1a(0)a≥21b−(0)b≥10ab−−≥12 (1) a1b−11(1)13abpctab−⎛⎞=+−−+⎜⎟⎝⎠22(1)13bapctab−⎛⎞=+−−+⎜⎟⎝⎠ (2) (3) (1) (4) (1) x2212()((1))ptxaptxb+−=+−−,2112(1)2ppbaxtab−−+=+−−x1x212112(,)Dpp212(,)Dpp 211121(,)2(1)2ppbaDppxtab−−+==+−− 122121(,)12(1)2ppabDppxbtab−−−=−=++−− 11p1112()(,)pcDpp−122212[(1)]()2pctbapp++−−=222121[(1)]()2pctabpp++−−=*1(,)(1)13abpabctab−⎛⎞=+−−+⎜⎟⎝⎠*2(,)(1)13bapabctab−⎛⎞=+−−+⎜⎟⎝⎠ 63 (2) (1)112(,)Dpp212(,)Dpp (3) i ***12(,)[(,)](,,(,),(,))iiiabpabcDabpabpabπ=− 1a1(,)abπ1110ppaπ∂∂=∂∂a1π*11122()idDDppcdaapaπ⎛⎞∂∂∂=−+⎜⎟∂∂∂⎝⎠(1)1356(1)Dabaab∂−−=∂−−12223(1)Dpapaab∂∂−+=∂∂−−10ab−−≥*0ipc−10ddaπ110a=211b−= (4) 1220()((1))xxtsadstsbds−+−−∫∫x(1)14a=314b−= 9[] (Debraj Ray, 2006) 1[0,1]ic∈0.5 1,2i=i[0,1]iA=i()ji≠ 1122(,)1iijiiijiijaaauaaaaaaaa⎧−⎪=−=⎨⎪−⎩ i[0,1]()iFviF{}[0,1]:()()0,iivFvFvεεε∈+−−∀0()lim()iiFvFvεε↓−viF**12(,)FF*iS*iF(1,2)i= (i) **12SS=(,)vw*iF(,)vw*jF(,)vw0i(,)vw(,)vw**12(,)FF (ii) v*iFv*jF0ε*(,)jSvvε−=∅∩v*iF0ε(,]vvε−jj*jF(,]vvε−vδ+(1v)0(1v=)δ0 (iii) 0vv*iF1,2i=(ii) 64 (iv) 0M∃*[0,]iSM=1,2i=*ivS∉{}**inf:,i=∈≥*wv≥(i)**jwS∈(iii)*w*iFj*wv*wv=(ii)00M (v) 1,2i=*[0,1]iS=*()iFvv=[0,1]v∀∈(ii)(iii)00*iFjv*()iFvv−ji≠i[0,]M*(0)0iF=*()jFvv=1M=j[0,]M*()iFvv= [0,1] 10[] (William Sandholm, 2006) {1,2,3,}N=…()In()OutvNM(i) 0(ii) 11−(Borel‐Cantelli) Borel‐Cantelli{}1iiA∞=iA*AiA(a) 1Pr()iiA∞=∞∑*Pr()0A=(b) {}1iiA∞=1Pr()iiA∞==∞∑*Pr()1A= Borel‐Cantelli11 1[] (Bingyong Zheng, 2008) (1) (2) (1, 3) E F DC BA 2 2 1 (4, 2) (3, 4) (2, 1) 65 (1) (,)CBE(,)CBF(,)CBF (2) (,,)BECJH(,,)BFCJH(,,)AFDJG,(,,)AFDJH(,,)BFCJH(,,)AFDJH 2[] (William Sandholm, 2006) (1) 1AB1B2CD2D1EFG111111111111231212((),(),(),(),(),())(,,0,0,,)AEAFAGBEBFBGσσσσσσσ== 11211111111133244(((),()),((),(),()))((,),(,,))bbAbBbEbFbG==1 (2) AE AF BEBFC 2, 1 2, 1 3, 43, 4D 2, 1 2, 1 4, 21 ,3 IG IH JG JHAE 2,1,6 2,1,6 2,1,6 2,1,6 AF 5,3,1 5,3,1 5,3,1 5,3,1 BE 3,1,6 3,1,6 4,4,0 4,4,0 BF 3,1,6 3,1,6 4,4,0 4,4,0 IGIHJG JHAE4,6,04,6,0 2,0,8 2,0,8 AF4,6,04,6,0 2,0,8 2,0,8 BE6,2,22,5,3 6,2,2 2,5,3 BF6,2,22,5,3 6,2,2 2,5,3 A BC D C D(4,6,0) (2,0,8) (3,1,6) (4,4,0) (6,2,2) (2,5,3) (5,3,1) (2,1,6) 2 3 3 1 1 E F I J I J GHPlayer 1 Player 2 Player 1 Player 3 Player 1 Player 3 Player 2 chooses C Player 2 chooses D 66 (1) 51111111116622(((),()),((),(),()))((,),(0,,))bbAbBbEbFbG==1σ1111()()()3AEAFAGσσσ++=11()3BEσ=111()()6BFBGσσ== (2) 111111122((),(),(),())(,0,0,)ACADBCBDσσσσ= 3[] (Gibbons, 1992) (1,2,3)i=()PQAQ=−0A123Qqqq=++iqi0c0(i) 110q≥(ii) 231q2q3q 11q23231 11q23 212320max()qAqqqcq≥−−−− 312330max()qAqqqcq≥−−−− 231322Acqqq−−−=1232Acqqq−−−=123NAcqq−−=133NAcqq−−=231112310max()NNqAqqqcq≥−−−−112Acq−=23236Acqq−== 4[] (Gibbons, 1992) (1) A()CIA()PIACIPIB()CUIB+()()PCVIBkIB−++0k0A≥()CIA()PIA0CA0PAUV()()CPIAIA+ (2) CIPICISCIS−SB12()()CUISUSB−++C D D C 1 1 A B 67 12()[()()]PCVIBkUISUSB−+−++1U2UV (1) A(())(())PCVIABkIAB−++'1()()()PBAIAVk−=+()BA(()())CUIABA+'''()[()()]0CCPUIBIAIA++=''()()0CPIAIA+= (2) S12()[()()]PCVIBkUISUSB−+−++''2()()PVIBkUSB−=+''2''''210kUdBdSkUV−=−−()BS12()()CUISUSB−++'1'2()011()CUISdBUSBdS−=++S1()CUIS−()0dBSdS+BS+2()USB+2()USB+1()CUIS−''12()()0CUISUSB−++S 5[] (Francesco