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Z )drs/shapexml.xmlPK-!NIhddrs/downrev.xmlPKl KR :2___PPT9  n*   ?<  c $ ? 3380___PPT10. 9@ PK![Content_Types].xmlN0EH-J@%ǎǢ|ș$زULTB l,3;rØJB+$G]7O٭Vj'Ub;j&$ݕU{/UܹtKGrtЉKKqщ&۬KaO S~vDqF5^SثejCü*C嚓q zQ H )Z+ `Gߵd2!rhDz"bЈM.P}T1At"mm/ea in).˭N*-Le7ʝ_3UzG@ G# rBEJM-^_A9KCScS4AzRA%}kk%Y2+ +65pYJ!M5)ˀ?̠Q7߼2[{mݝMfPʯæ?1fz6JY eڿ\jmŪiT ^k GE.V41K@@4Nv&eM[Njb}1cks{֜\HclmN45xxФǘVw%>Y)h=& -G3uOPK! ѐ'theme/theme/_rels/themeManager.xml.relsM 0wooӺ&݈Э5 6?$Q ,.aic21h:qm@RN;d`o7gK(M&$R(.1r'JЊT8V"AȻHu}|$b{P8g/]QAsم(#L[PK-![Content_Types].xmlPK-!֧6 0_rels/.relsPK-!kytheme/theme/themeManager.xmlPK-!Z]4theme/theme/theme1.xmlPK-! ѐ'g theme/theme/_rels/themeManager.xml.relsPK]b : P WO 7(     x670e0e?Rectangle 2>  W From risk analysis to adversarial risk analysis Part V. Noncooperative games for RA *X 2($ X Z  F@67?Text Box 3 7E  David Ros david.rios@icmat.es Skype: david.rios.insua AXA-ICMAT Chair in ARA and Royal Academy of Sciences ,  2CNCF5        JI\  h67?81 Marcador de pie de pgina^   m DRI. USST (     33___PPT10i.P+D=' = @B +"A H@0((     rP670e0e?Ttulo 1 `}   1So far     670e0e?0Marcador de contenido 2#'gF  Conceptual framework in RA IDs as problem structuring tool Probabilities for modeling uncertainty Utilities for modeling preferences Expected utilities for optimal alternatives Computational framework for risk analysis This deck Basic concepts for game theory (towards RA) X , (,   h067?8Marcador de pie de pgina 3^   r DRI. USST (    /  x67?HMarcador de nmero de diapositiva 4^ `  v* (   33___PPT10i. o+D=' = @B +" @r(     r670e0e?1 Ttulo `}   7 Risk Analysis    670e0e?02 Marcador de contenido" PK![Content_Types].xmlJ0*miG]`Hm6 Xwt?. g#Wi3E).+7 >ON ޑ1ˋz "+R RhB.} /<^ITխ%rHK4uK~I0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!~?fQzdrs/shapexml.xml]o6}!ubD.`xQgc@KtY"5v<쎔"݂`mSʹ<(y;Eݔ[Kcs~3R:^|ϙuBeJ&FZv7'V VvX%|\5l/t%͵)[sݫR9Ee"W|M,ay)Q+aRi2RTyy XK[wJˏ<gD[$7uq]c(jPK!f"drs/downrev.xmlDK0p_Ku!Tu&^6IjoAr4,4rJay"YEpɜr澌HrBhbr)Cհ0u7ST7ʲiHPǏ W`&bsݯW=xy~B___PPT9  ~What would be the impact over system performance of identified threats? Based on data and prior info& Make forecasts of threat occurrence Make forecasts of threat impacts To make risk management decisions Sometimes, other agents in scene: security, cybersecurity, competitive marketing, social robotics, auctions,& 8gG??    hp77?81 Marcador de pie de pgina^   m DRI. USST (     33___PPT10i.if+D=' = @B +" "P (   B   rP670e0e?1 Ttulo `}   |. Best security resource allocation in a city? /- / b   670e0e?02 Marcador de contenido `  x City as a map with cells Each cell has a value (multiattribute) For each cell, a predictive model of delictive acts (COMPSTAT, PREDPOL,& ) Allocate security resources (given constraints) For each cell predict impact of resource allocation Optimal resource allocation .      h77?81 Marcador de pie de pgina^   m DRI. USST (     33___PPT10i.if+D=' = @B +" `$~(  $B $  rP670e0e?1 Ttulo `}   |. Best security resource allocation in a city? /- /  $  670e0e?02 Marcador de contenido `   City as a map with cells Each cell has a value (multiattribute) For each cell, a predictive model of delictive acts (COMPSTAT, PREDPOL,& ) Allocate security resources (given constraints) For each cell predict impact of resource allocation Optimal resource allocation NB: The bad guys also operate intelligent and organisedly!!! .JJK  $ h`67?81 Marcador de pie de pgina^   m DRI. USST (     33___PPT10i.if+D=' = @B +" p((  ( (  r670e0e?1 Ttulo `}   7 Risk Analysis x ( PA??Picture 2_ Dx ( PA??Picture 3D < x ( PA??Picture 4S  ( h67?81 Marcador de pie de pgina^   m DRI. USST (     33___PPT10i.iDf+D=' = @B +"r yq,Y(  , ,  r670e0e?1 Ttulo `}   7 Risk Analysis  ,  A?5%?Picture 2    , hp67?81 Marcador de pie de pgina^   m DRI. USST (     33___PPT10i.iDf+D=' = @B +": A90!(  0 0  r670e0e?1 Ttulo `}   1Problem  0  670e0e?02 Marcador de contenido `  "Need to deal with decision situations with several decision makers. Noncooperative games Nasheq, refinements and variations Decision Analysis/Bayesian approach ->ARA Level-k & . Cooperative games Bargaining Group Decision Making Voting & .. From competition to cooperationZZ, ER !   0 h 67?81 Marcador de pie de pgina^   m DRI. USST (     33___PPT10i.i kf+D=' = @B +" 4q(  4  4  xp 770e0e?Rectangle 2 `}   @Games. Basic concepts   4  x770e0e?Rectangle 3M `  ; Several decision makers My utility depends not only on what I do, but also on what others do Conflict and cooperation Players, Payoff function Game: Set of known rules determining what may be done, their consequences and the associated payoffs Z  4 h` 77?81 Marcador de pie de pgina^   m DRI. USST (     33___PPT10i.i0f+D=' = @B +" 8q(  8 8  x770e0e?Rectangle 2 `}   9Many variations  8  x(770e0e?Rectangle 3 `  BNumber of players: 2, 3, & , n, infinite Number of strategies. Finite, Infinite (Discrete, Continuous) Payoff function: Zero sum games, Constant sum games, non constant games Deterministic, stochastic Situation prior to game. Cooperative, Noncooperative Representation Normal form. Tables. Simultaneous Extensive form. Trees. Sequential MAIDs Differential games :]]l  8 h77?81 Marcador de pie de pgina^   m DRI. USST (     33___PPT10i.i@f+D=' = @B +" <(  <R <  xP770e0e?Rectangle 2 `}   @Basic game concepts through simple examples. Critical assessmentAAA  <  x770e0e?Rectangle 3'gb >6___PPT9 ~ Two players, two alternatives , " ! > < ^@'77??Text Box 4@S%f   Fixed strategies Common knowledge Simultaneous selection No previous discussion Raiffa, Metcalfe, Richardson (2002) Heargreaves-Heap, Varoufakis (2006) Banks, Rios, DRI (2015) Rothkopf (2007), Lippman, McCardle (2012), D. Wolpert (2012) Kadane, Larkey (1982), Raiffa (1982)H]  !  < h 77?81 Marcador de pie de pgina^   m DRI. 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])cFd, *l龢b6 |o"O^ ug,3Y+&SjFȝ/4ZPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!n*drs/downrev.xmlPK e~  1Small gains for Intelesa; large gains for Levante2 22    X c $s77"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!*drs/downrev.xmlDN@I|͘x[1%PY?6tg ŧwÅ^9;ӈ#9_[Vp;H@V\*}c> kl,3yϮzS̴=Pa*6no+vxpaB--+*o#KW> |wxhup"Pn+/g ι} wDh r PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!*drs/downrev.xmlPK   C  %Hide infor or lead in wrong direction& &&   X c $@^77"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!:Mcdrs/downrev.xmlDn0EHk*uN `PՇZ>ģ&Dv!}-tyՙ-:ӈ9_[Vp;H@V\*nc> kl,yX̯z3̴=Pa*6ng+vxpaB-=TT׿FGz|>~9)M~ "P{\3U+&SjBȝ/4ZPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!:Mcdrs/downrev.xmlPK  eC  0Small gains for Levate; large gains for Intelesa1 11   X c $@77"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Ygdrs/downrev.xmlDn0EH5+NS%)>Ԫ<$S_EY޹suftbO>*$ VNV~Vc,)8R|+ LtPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!Ygdrs/downrev.xmlPK e C  vNone gains. 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USST (     33___PPT10i.i@f+D=' = @B +"     (  "   x"'0e0e?Rectangle 2 `}   V Formal concepts     xP#'0e0e?Rectangle 3    G     d'??Text Box 4  ^ C  2    ~'0e0e?Rectangle 5d  rj___PPT9LD 8There are n agents: Alternative set for each agent: Si , i {1,& , n} Alternatives for each agent: si Si Evaluation for each agent Let (s1,& , si ,& , sn) combination of strategies : ui (s1,& , si ,& , sn) the utility that i-th agent perceives. Game in normal form: Specifies the set of strategies S1, ... ,Sn and the utility functions u1, . . . ,un. Denote the game through G = {S1, ... ,Sn; u1,& ,un}. l "    C n                   "                                                   P@  h)'?81 Marcador de pie de pgina^   m DRI. USST (     33___PPT10i.i`f+D=' = @B +"     0 (  ;   x'0e0e?Rectangle 2 `}   o' Formal concepts. Nondominated strategy( ( (    xP'0e0e?Rectangle 3    G     d '??Text Box 4  ^ C     ~'0e0e?Rectangle 5wq  LNondominated solution: Game in normal form, si and si  strategies for i-th agent. si is dominated by strategy si  if for every combination (s1, ... ,si -1, si +1, ... ,sn) : ui (s1, ... ,si -1, si , si +1, ... ,sn) < ui (s1, ... ,si -1, si  , si +1, ... ,sn) Rational players do not use dominated strategies.   " 3 -                             3C P  hp'?81 Marcador de pie de pgina^   m DRI. USST (     33___PPT10i.i7f+D=' = @B +"  @(  *   x'0e0e?Rectangle 2 `}   ^ Formal concepts. Nasheq     x'0e0e?Rectangle 3    G     d$'??Text Box 4  ^ C      ~'0e0e?Rectangle 5zLx~ ZR___PPT94, 0 Nasheq: s1*, & , sn* form a Nasheq if si* is i-th best response to the other n - 1 agents (s1*, ... ,si*-1, si*+1, ... ,sn*): ui (s1*, ... ,si*-1, si*, si*+1, ... ,sn*) e" ui (s1*, ... ,si*-1, si, si*+1, ... ,sn*) for each si Si ; i.e solution of max ui (s1*, ... ,si*-1, si, si*+1, ... ,sn*) s.t. si Si No agent has incentives to abandon it unilaterally Nasheq as crossing of best responses\  "                                "                               ]   h'?81 Marcador de pie de pgina^   m DRI. USST (     33___PPT10i.i^f+D=' = @B +" } P (  4   xC30e0e?Rectangle 2   h" Formal concepts. 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J pure strategies in S1, K pure strategies in S2 S1= { s11, ... ,s1J}, S2 = { s21, ... ,s2K}. Agent 1 believes agent 2 will use (s21, ... ,s2K) with probs p2 = (p21, ... ,p2K), expected utility of agent 1 if he uses p1 = (p11, ... ,p1J) is Same with agent 2. (p1* ,p2*) is Nasheq if 6      Z          '      )         FF     P@  d('??Text Box 4  ^ C    bA???Picture 5"@'' 9   \A???Picture 6"@E' =   \A???Picture 6"@ 4   \A ???Picture 7"@ j   hp'?81 Marcador de pie de pgina] }   m DRI. USST (     33___PPT10i.if+D=' = @B +# *"` (  -   x0'0e0e?Rectangle 2 `}   a Formal concepts. 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G game whose strategy sets are open intervals with payoff functions twice differentiable If a profile (s1*, & , sn*) satisfies, for each agent i, and then it is a Nasheq.  [       AY                  $$((,,00               HA K??1 Objetoc ] -  K  HA L??2 Objeto : J L  h0*'?81 Marcador de pie de pgina^   m DRI. 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But some criticisms Common knowledge assumption Multiple equilibria, with difficulties to distinguish among them Social dilemmas, with many practical implications Not always useful for decision support to a party Sometimes useful to communicate before game starts. Sometimes not, to avoid threats. Sometimes move first. Sometimes wait. & .. Useful, to forecast the game result& if we know the participants preferences Behavioral GT. Stahl, Wilson (1995), Camerer (2003), Gintis (2009)| "   C B    *  C P@  h`%'?81 Marcador de pie de pgina^   m DRI. USST (     33___PPT10i.if+D=' = @B +" : A9!(     x&'0e0e?Rectangle 2 `}   R Wrapping up     i  FW2?Text Box 6'A  Games for conflict situations Questions david.rios@icmat.es Skype: david.rios.insua If you have time, please watch Adversaries https://www.youtube.com/watch?v=pcyaa2oRz_g B 2,b,  H +    S,?T  hW2?81 Marcador de pie de pgina^   r DRI. 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Oh+'0 px    (Слайд 1 FonaryevDavid130Microsoft Office PowerPoint@v$7@7jG@@@ tGg  pp  pA x(xֵֽƽΥ罽ƽֽƭֽƭέֽ֥ƭƭ֭ޔ筭ޭޭֵέƵƥƭƽ{{{{ν{{s{{k{kss{眔ﵭsssνcksƽ֌{Όνεks{ޔΜscZƵ֭έƜƽssνƜΔ{{Υƽƽ{ƽέƥƵs{{ﭽƽƭƭƥέƭﭭƽޥƽƽޭޭޭޭޭޭޭޭ΄֔ޭޭޭޭޭޭޭޭ絽ޭ΄֔ޜƄΌޜ֜ޭ֜ޭ֥֥֜֜ޥ֜޵ޭ޵Δsޭ֔ޭޥνssskέΥ{{ƭﵭ{Ƶ޵ޜ֔Ό֭΄ޭ֥֜޵֌΄΄ޭޭ֥޽ޭΔΌΌ֔ƽZ֜k΄sƽcksƌƭƽs{Ƶޭ޵֥֜νέﵭƜƭ便ssksskƽƽν{{ﭥcck{ckk{{{ƽν{{{{{ƽƵ{{{{{{{{{RZc{{{{{{ޔ{{{{{{{{{{{{{{ƽs{{{{{{{{ֽcZZRJBֵccckkkkkk{cs{J91ޔ{RZcޜ{cccέZZc֜ZZZƭRZZZRRkkkRZcﭽΔ{{ck{ZRJksckkﭽΜ{JRRcck{εֽJRR֜JJRsƽZZRƵJRRRJJcZZJJR99BssssssZRJֵckkޭ{Δ{ckkƵs{ƽ{cckƽccZ{kZcc{kkkޜ111cckƽccc焄cks{ckskkkޭZcs{{{sskccc{{{{Zckcckνֵ1BB{{{kssk{kccƽ{scccƵ9BBBBJƽk{skcZck{kcZZJJJccZkcZZRJ9BBckss猄sRJRZccZZRcZZJB9kcZZZZ{{ckkνs{cckBRZZcckscck9BBs{Rcsck{֜{kkcƄ{s{{cks{cksƵZckJRR{Zckƽ{cckZZcskcZRJccZ{skcZBJJJRR{s{ZRZJJJRZZkcZZZcckkc{ƵkcZRZZJRZkkskccﵽƽRJJRcsJRkRck{{scks֌s9BJZRRBJRƭ{kcZ9BBƽs{νZJ9BBBJJRRcsZks{skks{sRcsJZkRJ9{kcsƭRcscsνs{ƵBBBcksRZcJZkRB9RcsJZkk{JBB!B9)kks9BBkkk)19Ƶs{νބskΜ{99BcZZRcssBB9JZkJZkBJRΜ֌{sks{{scZksƵRJBBJZν{BRZs{Ƶck{νJBBcZRcckRcsBJRΜ֌sƄƌs{νスƄƽ֌{ks{ƵZRJΌ焄祭ބƽZksքƵ޵ތƽ֌ν猌ޭJ919BRJRZ991B99kZJ999JBBZRJsk{ν{kZ119ֽ!JRc9BJ))1ޥ!BBB19Bsks99999BRJBs199k{99B{scZcs{scRJBJZc{!!BJRBB9999RJJքRZkƵ!)1Ƶk{νk{ν9BJ!JRkB11BJRRB9Zk{BBBkZJBBBBBBބ119Ƶk{999Zcs{s19JBRcBJRJRZƽ111B99Δ{JJRkkkB99BBB焌999ƵBBB99BBBB{k{Ƶ֜{JRZ1)!BBB猔19B{skcZckƵsƵkscs{{skBJZRZk!!sss{{{9BJB99JZc119cRB111JBB991k{BBJ{k֭!)1JRc9BJ֭1)!BBBRck΄ƵkcZ999111BBB9BJ{νs{{k{kcRJJJ1))))1111111ν9BJνs{νk{νֵ)19JRk9))JRRkkk{kcckssskc9BRkccRZcZRJ{{{199)9{ssBBBJJJ9BBksksccZB99RRckkcss{RJB{skc{{ZJBBBBJB9kZRkcZs{{kcRBBBJJJBBJ!!!ƽZRR{{RRJBBJBJRƵBJJ9BJ{{Ƶcs{{kkckss{s)99sskƽJJRBBJεZRR999sZRJk{ƜcZZB99RZkJ91k{νBBB999ޥƜ{JRk119JJJJJJRRRccccZZccc֭ks ՜.+,D՜.+,    A Presentacin en pantalla (4:3)+3' .ArialTahoma WingdingsSymbolDiseo predeterminado1_Diseo predeterminado EquationX From risk analysis to adversarial risk analysis Part V. Noncooperative games for RA So far Risk Analysis/ Best security resource allocation in a city? / Best security resource allocation in a city? Risk AnalysisRisk AnalysisProblemGames. Basic concepts Many variationsABasic game concepts through simple examples. Critical assessment Game matrix Consider this game Dominance+ The doom of rationality Social dilemmas ' Prisoners dilemma (years in prison)"A social dilemma in cybersecurity The negotiators dilemma  Consider this game Iterated dominance Iterated dominance Consider this game  Nash equilibria  Nash equilibria. Which one? Nash equilibria. Best response Nash equilibria. Best response Nash equilibria. Computation Nash equilibria. Computation Nash equilibria. Existence Nash equilibria. Existence Nash equilibria. Existence Consider this game Formal concepts( Formal concepts. Nondominated strategy Formal concepts. Nasheq# Formal concepts. Mixed strategies Formal concepts. Results Assessment Wrapping up Fuentes usadasTemaServidores OLE incrustadosTtulos de diapositiva' 8@ _PID_HLINKSA$mailto:david.rios@icmat.esmailto:david.rios@icmat.esmailto:david.rios@icmat.es,https://www.youtube.com/watch?v=pcyaa2oRz_gmailto:david.rios@icmat.es,https://www.youtube.com/watch?v=pcyaa2oRz_g_ DavidDavid  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Root EntrydO)PicturesCCurrent UserSummaryInformation(PowerPoint Document(0 DocumentSummaryInformation8