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"# $.6 $ J L* OqQ "G 1Ka 5 ,@ F := !F@.M J J1 )* !g> :Ek . ! 2 \ = W u1 @ 1 @& ! g > J 5 M m [ ! 1 ! . u * (6 . .*1 \= W 0 !+ !g> .6 "E; "a = . N1# & !1F8 .Z6 !L 1# J. !g> J1 "# ! !@1 ! g > 5 7! * K . Z 6 ! F @. M J ! g > J1 : = : 4.- ! (* y"# \# G.i J & (* J . \a @ "%@ !g> & .6 ! 6 !1F8 J F & !* K J * : = : - ! F @. M J J i F ( *0 ! L 1 # J . J s.*$.6 (L (* OCQ D # .6 x !E . J L* ! "# (b, x, i, j) 41W ! Z6 J 1 .1[ j & i Singleton Betting Integer Program Fractional Solution Objective Function Extra Information z x (b, x, i) 41W !E . J L* ! "# ! Z6 J ! "# $ J W [ "a = J ! . !@1 .6 .1* . i "# " X !LF $ # 5 \= W 1# J !L E# V G.i :V # : - !g> 5 "# Y J & 3. $ % # 41W 1# J !( # $.63 8* # !F !+ ! !@1 iF J G. "6 . !g> # \a @ !g> 5 7"# $1 \= W \= W ! .* $. "6 _6 5 !+ d ,-& "# 6& J1 "# +F "# 1[ $.6Fw 1# J !( < E* ! J o m T = k E 1 # L . *1 ! ! 2 & . Z 6 "# N1[ `6 9* l[ ! (6 1 # J ! L + & L K @ . Z 6 61 * & . Z 6 . # . Z 6 $ K \ = W "(@ 4 ' # !g> ` [ ! & J & 1# 6 1@& :a ! ! %G & & $.0 .& L "- 1 > h#1 $.6 3 8* ( 7 ` - $.0 , -& 5# (6& ! "E>* . Z 6 W [ A1 * ! L K @ . Z 6 ! # \ = W 1 # J ! ( ! g > & . > (* ! * 7 E# V n Va !g> J1 # : - ! . J $ @ & .6 & jl m* $.* ! ! Z6 W1 bf# .6 *.6 ( E# V Z Va & .. J * 1 (6 & OHQ ,@ (*0 1 $.0 "#! { * [ & $.6 om (* . L 3 8* +F ! [ ( * & & OCQ & OqQ J ! | !a # (L 7}+*& +a 1* (F 1Ka~ ( .F= Cq| 7)3* #.( [2] Y. Chen, L. Fortnow, E. Nikodova, D. Pennock. “Betting on Permutations”, Proceedings of the ACM Conference on Electronic Commerce, 2007. [3] M. Ghodsi, M. Mahini, V. Mirrokni, M. Zadimoghaddam. “Permutation Betting Markets: Singleton Betting with Extra Information”, Proceedings of the ACM Conference on Electronic Commerce, 2009. [4] D. Pennock, R. Sami. “Computational Aspects of Prediction Markets”, In Algorithmic Game Theory (N. Nissan, T. Roughgarden, E. Tardos, V. Vazirani, eds.), Cambridge University Press, 2007. [5] G. Tziralis, I. Tatsiopoulos. “Prediction Markets: An Extended Literature Review”, J. Prediction Markets, 1(1), 2006. OCQ
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