Preana: Game Theory Based Prediction with Reinforcement Learning

Transcription

1 Natural Scence, 2014, 6, Publshed Onlne August 2014 n ScRes. Preana: Game Theory Based Predcton wth Renforcement Learnng Zahra Eftekhar *, Shahram Rahm Computer Scence Department, Southern Illnos nversty Carbondale, Carbondale, SA Emal: * n.eftekhar@su.edu Receved 16 June 2014; revsed 20 July 2014; accepted 3 August 2014 Copyrght 2014 by authors and Scentfc Research Publshng Inc. Ths work s lcensed under the Creatve Commons Attrbuton Internatonal Lcense (CC BY). Abstract In ths artcle, we have developed a game theory based predcton tool, named Preana, based on a promsng model developed by Professor Bruce Beuno de Mesquta. The frst part of ths work s dedcated to exploraton of the specfcs of Mesquta s algorthm and reproducton of the factors and features that have not been revealed n lterature. In addton, we have developed a learnng mechansm to model the players reasonng ablty when t comes to takng rsks. Preana can predct the outcome of any ssue wth multple steak-holders who have conflctng nterests n economc, busness, and poltcal scences. We have utlzed game theory, expected utlty theory, Medan voter theory, probablty dstrbuton and renforcement learnng. We were able to reproduce Mesquta s reported results and have ncluded two case studes from hs publcatons and compared hs results to that of Preana. We have also appled Preana on Irans 2013 presdental electon to verfy the accuracy of the predcton made by Preana. Keywords Game Theory, Predctve Analytcs, Renforcement Learnng 1. Introducton Seeng the future has always been of great nterest for human knd. Predctng the future has mgrated from nsde the crystal balls or between the lnes of palms to very accurate scentfc models. That s because future s not as unpredctable as one mght thnk! A bg amount of the future s determned wth the optons people have and the choces they make. The optons they have very much depend on the support they fnd around them and the choces they make are nfluenced by ther experences and what they have learned from the past. Beng able to foretell the future n economc, educaton, healthcare and especally poltcs s essental not only to know what happens ahead of tme and prepare for t, but also to fnd the pressure ponts. That s beng able to * Correspondng author. How to cte ths paper: Eftekhar, Z. and Rahm, S. (2014) Preana: Game Theory Based Predcton wth Renforcement Learnng. Natural Scence, 6,

2 Z. Eftekhar, S. Rahm tell what happens f certan factors are adusted or elmnated or certan steps are taken. Ths would make t possble for the nvolved partes to be able to make nformed decsons, prevent dsastrous outcomes and make desrable changes. Gven all the mportance, there has been relatvely small contrbuton from computer scence dscplne towards ntroducng an effectve model for poltcal predcton. The most sgnfcant model n lterature s the game theory based model ntroduced by poltcal scentst Professor Bruce Bueno De Mesquta [1], who has receved enormous attenton for hs model ncludng recevng the nckname The New Nostradamus n a televson documentary. The extreme predctve accuracy of the model seems to be more than a clam. Accordng to Dr. Stanley Feder of the CIA, reported on by the Salt Lake Cty Trbune [2], the Spatal Theory of Poltcs has been ganng ncreased acceptance at the agency and has resulted n accurate predctons n 90 percent of the stuatons n whch t has been utlzed. There s no exact specfcaton of the algorthm or the code of ths model n open lterature. However, over the last few years, some parts and peces of the man features of the algorthm and the math behnd them have been revealed n hs academc papers and books or by other researchers. One example of the research done n ths area s the one conducted n Department of Defense of Australa. They could fgure out some features of the algorthm but have not reported the outcome of the predcton. They have predcted the confrontatons of the players wthn a quadrant and clamed that the accuracy of ths algorthm wthn a quadrant s one hundred percent. They have also dscussed that they have assumed the probablty of status quo to be constant and equal to 1 and therefore could not reproduce any of Bruce Beuno de Mesquta s results other than the one ntroduced n the paper [3]. Another example s a research that appled the algorthm on Tawan s poltcal status and made a predcton. They have also gnored the calculaton of the probablty of the status quo(q) and consdered t to be constant and equal to 0.5 [4]. So far no one has been able to provde a complete pcture of ths model. In ths study, we have observed Bruce Bueno De Mesquta s publcatons closely and developed Preana, our poltcal predcton model, based on t. There were a lot of factors and features outstandng whch we duplcated usng expected utlty theory and probablty dstrbuton. Runnng Preana wth several data sets from Bruce Bueno De Mesquta s publcatons, we reproduced hs results wth over 90 percent accuracy n every example. Furthermore, knowng that preana was ratonal, we added a touch of machne learnng to model the bran of players regardng rsk-takng among one another. It mproved the results leadng to more logcal steps n each round of decson makng by players. Ths artcle proceeds as follows. In the second secton, the structure of the model s presented. In the thrd secton, the rsk component of the so-called Expected tlty Model by Bruce Bueno De Mesquta and the adusted Q-learnng method, whch models the bran of the players, are dscussed. Next, Secton four provdes and dscusses the results for three case studes: predcton for the ol prce, predcton for the delay of ntroducton of emsson standards for medum szed automobles and the predcton for the outcome of Iran s 2013 presdental electon. Fnally, Secton fve concludes the paper. 2. Structure of the Model In ths secton we provde descrpton of the overall desgn and structure of Preana. The model takes three arrays as the nput to start wth. These arrays are explaned n the followng subsecton. The Medan voter poston s then calculated usng the ntal nput. The medan voter poston s the poston of the player that, when compared wth every other player, s preferred by more votes. Medan voter poston defnton and calculaton wll be descrbed n a followng subsecton. At each teraton, the player whose deal poston s closest to the medan poston s most lkely to be the wnner for that teraton. Then the players start to negotate. They calculate the pay off (expected utltes) for themselves to challenge every other player and decde to whom they make challenge offers. After the offers are made, each player revews the offers t has receved and selects the one that maxmzes ts own pay off. Ths results n a change n the poston and power for some of the players and a possble shft n the poston of Medan Voter. Another round of negotaton starts wth the new postons and ths goes on untl the game reaches an equlbrum. That s when all players are satsfed wth ther poston, gven the poston of other players n the game, and no offer can possbly result to a postve pay off for any player. Ths s where the game ends and the Medan Voter poston n ths round s Preana s predcton to be the wnnng poston. Fgure 1 shows a general flowchart of the algorthm Model Input One of the strength ponts of the Expected tlty Model s that t only uses three smple arrays as ts nput. 1109

3 Z. Eftekhar, S. Rahm Fgure 1. Man steps n Preana algorthm. These arrays defne players ntal state. The most mportant array s the array of postons (x[]). Each player has an deal poston on a one-dmensonal left to rght contnuum.the more two gven players deal outcomes conflct, the more ther dstance s on ths scale. The unt of ths poston s specfed for each gven problem. Array of salence (s[]) determnes the prorty of the ssue and how much mportance t holds for each player. Array of capablty (c[]) determnes how much power or capablty a player has on the ssue. Table 1 represents an example of these three arrays from [5]. Ths s an example about What s the atttude of each stakeholder wth regard to the floor prce of ol n three months tme at whch Saud producton should decrease? 2.2. Medan Voter Poston The model focuses on the applcaton of Black s medan voter theorem [6] and Banks theorem on the monotoncty between certan expectatons and the escalaton of poltcal dsputes [7]. The medan voter theorem states that a maorty rule votng system wll select the outcome most preferred by the medan voter [8]. The medan voter poston s the poston of the player that, when compared wth every other player, s preferred by more votes. In each round of negotatons, the player whose poston s closest to the medan voter poston s the wnner. Ths mples that the wnner s the player who has more support from others. Accordng to Bruce Beuno de Mesquta [5], the votes for versus k, are: v k n k v = 1 = (1) The dfference between the dstance of player s poston from that of player and player k s calculated and normalzed. Ths, multpled by player s capablty and salence, shows player s support for player versus 1110

4 Z. Eftekhar, S. Rahm Table 1. Sample of the nput. Players Capablty Poston Salence HAWKS IRAN RSSIA IPEC GLF MILITARY KWAIT TRIBALS RELIGIOS LEADERS BSINESS SLTAN MAJLIS ABDLLAH FAHD SA NAZER ER/JPN k player k whch s v n the equaton. Ths support s calculated from all players. The sum of the support player gets versus player k and every other player s the total support t can get at the assocated round. The total support s calculated for all players and the one that has the maxmum total support s the medan voter poston at that round Expected tltes In each round, players make challenge offers to other players amng to make others shft ther postons towards ther deal poston. These offers are made based on the expected utltes calculated for each player versus the rest of the players. Players try to maxmze ther own pay off by makng offers to players whom they thnk they can convnce or force to make a coalton wth. At the same tme, players try to respond to the offer that leads to the maxmum pay off for them or at least requres them to move the least from ther deal poston. Fgure 2 llustrates the sequence of plays [1]. The expected utlty of player() for challengng player() from player() s pont of vew [9] can be calculated as: E = S P + 1 P + 1 S Q 1 Q T + 1 T (2) ( ) ( ) ( ) ( ) ( ) ( ) ( ) s f s sq b w Accordng to Fgure 2, S s the salence of the ssue for player, P s the probablty of success for player, s s the expected utlty of success for player, f s the expected utlty of losng for player, Q s the probablty of status quo, sq s the expected utlty from remanng n stalemate, T s the probablty that stuaton mproves for player when t does not challenge player, and b s the expected utlty n ths stuaton. w s the expected utlty n the stuaton that player does not challenge player, player s challenged by others and the results of these challenges worsens the stuaton for player. µ s the medan voter poston at each teraton. Equaton (2) s estmated from four perspectves [5]; (1) s expected utlty for challengng from s pont of vew (2) s expected utlty for challengng from s pont of vew (3) s expected utlty for challengng from s pont of vew (4) s expected utlty for challengng from s pont of vew The calculaton of b, w, s, f and q are explaned n detals n [3], but here are the equatons: 1111

5 Z. Eftekhar, S. Rahm Fgure 2. Game tree n expected utlty model. b w s f x x = xmax xmn x x = xmax xmn = = r r ( x µ x x ) x max x mn ( x µ x x ) x max ( ) = sq The above equatons are used to calculate the expected utlty of player for challengng player from s pont of vew. x s the poston of player, x s the poston of player, x max s the hghest poston n the game and x mn s the lowest poston n the game. r s the rsk component for player versus player. When player wants to make an offer to player, t calculates ts own expected utlty from ths challenge and compares t to what t perceves of Player s expected utlty versus hmself. We have concluded that: b w s f r x mn x x = xmax xmn x x = xmax xmn = = r r ( x µ x x ) x max x mn ( x µ x x ) x max ( ) = sq r x mn r r r r 1112

6 Z. Eftekhar, S. Rahm And usng b, of vew, s ( ) E : w, s, f and ( ) ( ) q Player s expected utlty versus player, from player s pont ( 1 ) ( 1 ) ( 1 ) ( 1 ) ( ) E = S P + P + S Q Q T + T (3) 2.4. Probablty of Success (P) s f s sq b w The probablty of success for player n competton wth player s also calculated by the support of thrd-party players for player s polces versus player s polces. Smlar to fndng the medan voter poston, t s not only about whch player s polces the partes prefer, but also the thrd-partes salence on the ssue and ther capablty or power are consdered. Equaton (4) shows the probablty of success for player n competton wth player accordng to Expected tlty Model [3]. P = ( ) ( ) c s x x x x kfarg > 0 k k k k n c 1 ksk x k k x xk x = where x, x and x k are the postons for player, player and player k respectvely. c k s the power of player k and s k s the salence and mportance of the ssue for player k. The numerator calculates the expected level of support for. The denomnator calculates the sum of the support for and for so that the expresson shows the probablty of success for, and t obvously falls n the range of 0 and Probablty of Status Quo (Q) The calculaton of the probablty of status quo (Q) has never been talked about n any of Bruce Beuno de Mesquta s publcatons. He consders Q constant n some publcatons such as [9] n whch he consders Q to be 1. Ths means that when decdes not to challenge, and reman n stalemate wth each other and the change n ther postons n respondng to other players offers does not affect ther stuaton aganst each other. In dfferent publcatons [10] and [11], he consders Q to be 0.5 whch means whether the change n the poston affects players stuatons versus one another or not, s completely random. In ths work, we have been able to calculate ths probablty for each par of players. Accordng to Fgure 2, when A does not challenge B, B s challenged by other players and may lose and be forced to move. If B moves, ts poston changes and ts dstance to A ether decreases (wth probablty T) or ncreases (wth probablty 1-T). Therefore, the probablty of status quo n ths stuaton s the probablty that B does not move at all. Ths s the probablty that B wns the challenge wth every other player except A n that round. Ths probablty s calculted as follows: ( ( )) Q P S = 1 kk, k, k + k The probablty that player() wns every challenge aganst another player(k), s the sum of two probabltes. frst, the probablty that player() challenges player(k) and player k does not challenge t back and surrenders whch s ( 1 Sk ). Second, the probablty that player() challenges player(k) and player(k) does respond to ts challenge and agan player() wns ths confrontaton whch s P. The probablty that player() wns aganst every other player except player(), s the multplcaton of ths sum for all players except player() Probablty of Postve Change (T) Accordng to Fgure 2, when A decdes not to challenge B, but B moves due to other challenges, ts move ether mproves or worsens the stuaton for A. B move would be towards the medan voter poston, so the postons of A, B and the medan voter ( µ ) versus one another determnes whether B moves closer to A or further away from t. If B moves closer to A, t mproves the stuaton for A, so T = 1. If B moves further away from A, t worsens the stuaton for A, so T = 0 [3] Offer Selecton Accordng to Bruce Beuno de Mesquta [5], the probablty wth whch confrontaton, compromse or captu- (4) 1113

7 Z. Eftekhar, S. Rahm laton occur can be easly dsplayed n a polar coordnate space. Ths space s dvded nto sx sectons and the boundary between each two s consdered to be a turnng pont n the probablty functons. Fgure 3 shows ths polar coordnate space, along wth assocated labels for each of the sx sectons. In Bruce Beuno de Mesquta publcatons, there s no exact defnton of how these sectors are defned or separated from one another or how the players decde to whom they make a challenge offer and to whose offer they respond. However, he does explan how offers are made based on the expected utltes of a player versus another, combned wth what the proposer perceves of the expected utlty of the other player versus tself. In Preana, f the two players both assume they have the bgger utlty compared to the opponent and that ther utlty s bg enough to make the other player move to ther poston, they both make challenge offers to one another and they both stck to ther offer and they confront. Clearly ths has hgh cost for both players. If a player thnks t has bgger utlty, but not bg enough to make the other player completely move to ts own poston, he offers a compromse. If the other player responds to ths offer, they both move towards each other. Accordng to Bruce beuno de Mesquta, they move by weghted average of s and s expectatons [5]. If a player receves an offer and knows that the proposer s too strong for t to challenge, t gves n and completely moves to the proposer s poston. If both players thnk there s no postve utlty n challengng each another, they make no offer and stay n the stalemate zone. The medan voter poston s calculated at the begnnng of the frst round of negotaton and s selected to be the wnner poston of the game wth the ntal postons, capabltes and salence. At the end of each round of negotaton, every player has a set of offers that has to choose from and then responds to the one that consders s the best choce to maxmze ts pay off. If such an offer does not exst, t chooses the offer that requres t to move the least from ts deal poston [5]. After all players have selected the offer they want to respond to, they move to the poston assocated wth the offer and the array of poston and capablty are updated. In the followng round, the medan voter poston, the probabltes of success and status quo, the expected utltes and the rsk factor are all calculated wth the updated poston array, and then new offers are made. The game contnues untl t reaches an equlbrum and that s when no player has an offer to make to the other players gven every other players poston. In ths stuaton, all payers prefer to stay at ther current poston. The medan voter at ths fnal round would be the wnnng poston. The player whose deal poston n the ntal array of nputs s nearest to ths medan voter, s most lkely to be able to enforce t s deal outcome. 3. Rsk In ths secton, we brefly defne the Expected tlty Model s rsk takng component. Ths functon calculates a rsk or securty value for each player n confrontaton wth all other players. In Preana, we add learnng module Fgure 3. Scenaros n expected utlty model. 1114

8 Z. Eftekhar, S. Rahm to ths functon to model the bran of each player. The players learn from the offers they make n each round. When player() makes an offer to player(), and does not result n a postve pay off, he concludes that t had underestmated player() s abltes whch means that next tme t s more careful n confrontng player(). And on the other hand, when t can enforce an offer, has more confdence n confrontaton wth player() n the future Expected tlty Model s Rsk-Takng Component Expected tlty Model s rsk takng component s explaned n detals n Bruce Beuno de Mesquta and Stokman [12]. The rsk-takng component s a trade off between poltcal satsfacton and polcy satsfacton [13]. Poltcal satsfacton or securty s beng seen as a member of wnnng coalton whle polcy satsfacton s supportng the polcy that s most close to that of the player tself even f that polcy does not wn. The rate at whch players make ths trade-off s dfferent from one another. The securty of a player ncreases and the rsk decreases by takng a poston close to the medan voter poston. Therefore, the players who take postons close to the medan voter poston, who s the wnner at the assocated round, are feelng more vulnerable and tend to be more rsk averse [5]. What enters the calculaton of rsk n the Expected tlty Model, s the actual expected utlty, the maxmum feasble expected utlty and the mnmum feasble expected utlty. Algebracally, the rsk-takng component s calculated as follows [9]: R n n n 2 E 1 E 1 E = = max = 1 mn = n n E 1 E = max = 1 mn and R 1 r 3 = (6) R 1+ 3 As seen n Equaton (3), the rsk factor s used n the calculaton of expected utltes, and accordng to Equaton (5), rsk s calculated usng the expected utltes. It can be nterpreted from Bruce Beuno de Mesquta s statements that frst the expected utltes are calculated wthout consderng the rsk (r = 1) and then these utltes are used to calculate the rsk for each player [3] Preana s Rsk-Takng Component Accordng to Bruce Beuno de Mesquta [9] the purpose of Equaton (6) s that r[] ranges between 0.5 and 2. However, accordng to ths equaton, the greater R[], the smaller r[]. So r[] s actually the level of securty rather than rsk of player. That explans why expected utltes are exponentally ncreasng by r whch s a postve number between 0.5 and 2. Ths securty level s calculated n each round takng nto account the support each player gets from other players, the expected utltes, and the dstance from the medan voter poston. What seems to be left out n the Expected tlty Model s that players cannot look ahead n rounds or even look back and learn from ther mstakes or achevements. There are several rounds of negotatons before players reach an equlbrum and the game comes to an end. It s possble that player() underestmates player() s capabltes and ts supporters and makes a challenge offer and consecutvely loses some utlty. In realty, ths should change player s assumptons about player, and therefore, next tme when wants to make an offer to, does t more conservatvely. To montor the offers and to learn from the outcomes, we have modeled the bran of each player. Bruce Beuno de Mesquta calculates r[] for each player usng the securty for player() n confrontaton wth any other player. In contrast, we have extended the securty to be a twodmensonal array. R[][] s the rsk of player n confrontaton wth player. The array s ntalzed wth the rsk calculated from the Expected tlty Model n each round and then adusted n each round. We have taken the dea of ncludng a learnng matrx and a learnng rate from the Q-learnng method ntroduced by Watkns n 1989 [14]. Here s how we form the learnng matrx: Make a two-dmensonal matrx named learn and ntate t to all 0, At the end of each round, each player montors the offers t has made, (5) 1115

9 Z. Eftekhar, S. Rahm If a proposal has been made by and not responded to by, decrement learn [] [] by 1, If a proposal has been made by that leads to confrontaton n whch has to move towards, decrement learn [] [] by 3, If a proposal has been made by that leads to compromse n whch has to move more than, decrement learn [] [] by 2, If a proposal has been made by that leads to havng to captulate and move towards, decrement learn [] [] by 3, If a proposal has been made by that leads to confrontaton n whch has to move towards, ncrement learn [] [] by 1, If a proposal has been made by that leads to compromse n whch has to move more than, ncrement learn [] [] by 2, If a proposal has been made by that leads to havng to captulate and move to, ncrement learn [] [] by 3. As specfed above, the learn matrx s updated after each round by consderng each offer and ts outcome for the proposer. If the outcome s postve, t ncreases the securty player feels to challenge player next tme. However, f the outcome s negatve, player learns that t had underestmated player s expected utlty versus ts own and ts securty level versus player decreases. The more the number of the loss or gans s, the more effectve s matrx learn. Here s how we adust the rsk: r[] [] elements are ntated wth r[] of the Expected tlty Model. Then n each teraton: learn[ ][ ] r = r + β S (7) The securty level s updated after each round and kept n the memory of each player for future rounds. Equaton (7) ndcates that the more mportance or salence an ssue has for a player, the less rsk that player can afford on the ssue. If a player s rather ndfferent on the ssue, the experence of a loss or an unseen opportunty wll not be so heavy on t. The possblty of ths player makng the same mstake agan s more than a player to whom the ssue s of great prorty and mportance. That s why we do not consder the learnng rate to be constant for each player as t s n Q-learnng. The learnng rate s a multplcaton of salence and a constant β. In ths artcle and the followng case studes, we have consdered β to be set to We have selected 0.01 expermentally gven the fact that ths value should be very small but not too small, so that t can make a dfference. It should be small because the rsk factor s n the range of 0.5 and 2 and f β s too large, t wll change the rsk factor rratonally and mght even push t out of range. Furthermore, f β s too small, t does not make any dfference n the outcome of the equatons when added to the ntal rsk factor. Expermentng wth dfferent values of β for the dfferent problems n hand, we realzed that dfferent problems have dfferent tolerance for the level of ncrease n β before startng to respond rratonally. Fndng the rght way to calculate β for a gven problem doman would be a target for the future work. 4. Results To evaluate the performance of Preana, we have ncluded two case studes from Bruce Beuno de Mesquta s publcatons. We have compared the results of Preana s predcton to that of the Expected tlty Model and the real outcomes of the ssue f avalable. There are hundreds of pages of output for each example that can be nterpreted whch nclude useful nformaton such as the offers that are made n each round, the ones that can be enforced, the outcome of each confrontaton n each round, formed coaltons or separatons, and the flow of the whole system towards the fnal outcome. Here, for each case study, we only show the change n the poston of each player and the medan voter poston over tme (rounds) Case Study 1: Predctng the Floor Prce of Ol n Three Months Tme As our frst case study, we consder the same example that ts nput data s shown n Table 1. Fgures 4-7 show the players postons and the wnner poston n subsequent rounds. As we see n Fgures 4-6, all of the players n ths game change ther postons over rounds untl they all reach a poston very close to the wnnng poston whch s Fgure 7 shows the Medan voter or the wnnng poston n dfferent rounds of negotatons whch ends up to be equal to n the last round where equllbrum s reached. Preana s predcted prce, as shown n Fgure 6 and Table 2 s whch s closest to the deal prce for 1116

10 Z. Eftekhar, S. Rahm Fgure 4. Poston of frst group of players over dfferent rounds n case study 1. Fgure 5. Poston of second group of players over dfferent rounds n case study 1. Fgure 6. Poston of thrd group of players over dfferent rounds n case study 1. SA and FAHD whch s Bruce Beuno de Mesquta [5] states that the outcome of the Expected tlty Model for ths case study s whch s very close to what s reported by Preana Case Study 2: The Years of Introducton of Emsson Standards for Medum Szed Automobles Ths s another case study from Bruce Beuno de Mesquta [12]. The ssue s to predct the number of years that would need to pass before the ntroducton of emsson standards for medum szed automobles. The players and ther ntal capabltes, postons and salence are llustrated n Table 3. Fgures 8-10 show the players postons and the wnner poston n subsequent rounds. 1117

11 Z. Eftekhar, S. Rahm Fgure 7. The medan voter poston n each round n case study 1. Fgure 8. Poston of frst group of players over dfferent rounds n case study 2. Fgure 9. Poston of second group of players over dfferent rounds n case study 2. Fgure 10. The Medan voter poston n each round n case study

12 Z. Eftekhar, S. Rahm Table 2. Output for case study 1. Players Intal poston Round 1 Round 2 Round 3 Round 6 Round 16 HAWKS IRAN RSSIA IPEC GLF MILITARY KWAIT TRIBALS RELIGIOS LEADERS BSINESS SLTAN MAJLIS ABDLLAH FAHD SA NAZER ER/JPN Medan Voter Table 3. Input for case study 2. Players Capablty Poston Salence Netherlands Belgum Luxembourg Germany France Italy K Ireland Denmark Greece Accordng to Bruce Beuno de Mesquta [12], the outcome of the Expected tlty Model for ths case study s 8.35 and the actual delay has been 8.83 years. As shown n Fgure 9, Preana predcts the outcome to be 8.15 years Case Study 3: The Wnner of Iran s 2013 Electon The last case study s the predcton of the recent 2013 presdental electon n Iran. The nput for Preana s taken from the web-poles before the electon and ntervew wth experts about the ntal stuaton of each canddate before the electon. The canddates postons are determned on a one-dmensonal scale, the most reformst beng on the poston 10 and the most fundamentalst beng on the poston 1. The canddates and ther ntal capabltes, postons and salence month perod before the electon are shown n Table 4. Fgures show the players postons and the wnner poston n subsequent rounds. Preana shows the wnner of the electon to be poston 9.2 whch s n the mddle of the deal poston for the two reformst canddates Aref and Ruhan. What happened n realty was exactly lke what s shown n Fgure 12. Reformsts got stronger and stronger durng the debates and rght before the electon, Ruhan and Aref made a coalton together and Aref left the competton n favor of Ruhan. Eventually Ruhan won the electon [15]. Ths s more clearly llustrated n Fgure

13 Z. Eftekhar, S. Rahm Table 4. Input for case study 3. Players Capablty Poston Salence Jall Haddad Gharaz Rezay Ghalbaf Velayat Ruhan Aref Fgure 11. Poston of frst group of players over dfferent rounds n case study 3. Fgure 12. Poston of second group of players over dfferent rounds n case study 3. Fgure 13. The medan voter poston n each round n case study

14 Z. Eftekhar, S. Rahm Fgure 14. Aref and Ruhan s coalton n case study Concluson Ths work was ntated wth two maor obectves n mnd. The frst obectve was to uncover the hdden elements of today s most promsng game theory based predctve analyss tool developed by Bruce Bueno De Mesquta. On ths front, we developed a methodology whch produces comparable results to what Buenos model generates. The second obectve was to mprove what game theory can offer by applyng machne learnng to game theory. The authors beleve both of these obectves are reached. Three case studes were presented and evaluated for the proof of concept. These case studes compared the results of the present work wth the pror one. The thrd case study llustrated the power of ths work n predctng real word poltcal phenomena such as recent presdental electon n Iran. We beleve ntegraton of game theory and machne learnng s not only promsng but even necessary to move towards more dynamc and realstc approaches. Ths work s ust a steppng stone towards such ntegraton. References [1] de Mesquta, B.B. (2011) A New Model for Predctng Polcy Choces: Prelmnary Tests. Conflct Management and Peace Scence, 28, [2] Feder, S.A. (1995) FACTIONS and Polcon: New Ways to Analyze Poltcs. In: Westerfeld, H.B. (Ed.), Insde CIA s Prvate World: Declassfed Artcles from the Agency s Internal Journal, Yale nversty Press, Yale, CT, [3] Scholz, J.B., Calbert, G.J. and Smth, G.A. (2011) nravellng Bueno De Mesquta s Group Decson Model. Journal of Theoretcal Poltcs, 23, [4] eng, B. (2012) Applyng Bruce Bueno de Mesquta s Group Decson Model to Tawan s Poltcal Status: A Smplfed Model. The Vsble Hand: A Cornell Economcs Socety Publcaton, Ithaca, NY. [5] de Mesquta, B.B. (1997) A Decson Makng Model: Its Structure and Form. Internatonal Interactons: Emprcal and Theoretcal Research n Internatonal Relatons, 23, [6] Black, D. (1948) On the Ratonale of Group Decson-Makng. Journal of Poltcal Economy, 56, [7] Banks, J.S. (1990) Equlbrum Behavor n Crss Barganng Games. Amercan Journal of Poltcal Scence, 34, [8] Holcombe, R.G. (2006) Publc Sector Economcs. Pearson Prentce Hall, pper Saddle Rver, 155. [9] De Mesquta, B.B. (1985) The War Trap Revsted: A Revsed Expected tlty Model. Amercan Poltcal Scence Revew, 79, [10] De Mesquta, B.B. and Lalman, D. (1986) Reason and War. Amercan Poltcal Scence Revew, 80, [11] De Mesquta, B.B. (2009) A New Model for Predctng Polcy Choces: Prelmnary Tests. 50th Meetng of the Internatonal Studes Assocaton, New York, February 2009, 36p. [12] De Mesquta, B.B. (1994) Poltcal Forecastng: An Expected tlty Method. In: Stockman, F., Ed., European Communty Decson Makng, Yale nversty Press, Yale, Chapter 4, [13] Lamborn, A. (1991) The Prce of Power. nwn Hyman, Boston. [14] Watkns, C.J.C.H. (1989) Learnng from Delayed Rewards. PhD Thess, nversty of Cambrdge, England. [15] Hassan Rouhan Wns Iran Presdental Electon BBC News, 15 June

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