Dynamic Difficulty Adjustment in a Whac-A-Mole like Game

Transcription

1 Dynamic Difficuly Adjusmen in a Whac-A-Mole like Game Bruno E. R. Garcia and Marcio K. Crocomo Deparmen of Informaics IFSP - PRC Piracicaba, SP, Brazil brunoely.gc@gmail.com, marciokc@ifsp.edu.br Kleber O. Andrade Deparmen of Informaics FATEC - AM Americana, SP, Brazil kleber.andrade@faec.sp.gov.br Absrac Based on he Evoluionary Algorihm (EA) proposed by [1], his paper presens a new EA version wih dynamic difficuly adjusmen for a Whac-a-Mole like game used in moor rehabiliaion of hand. This new version considers user performance as inpu and generaes he posiion and ime ha he arge will say on screen. In order o simulae differen users needs, a variey of player profiles were creaed wih diverse horizonal movemen speed (ulnar deviaion/radial deviaion of he hand) and verical movemen speed (supinaion/pronaion of hand), as well as disincive player aenion deficis (response ime o he appariion of he arges). The resuls show ha he developed EA can adjus he difficuly facors of he game according o he skill se of each profile. Keywords-Human-Compuer Ineracive; Serious Games for Rehabiliaion; Arificial Inelligence; Evoluionary Algorihm; Dynamic Difficuly Adjusmen. I. INTRODUCTION In he pas years, he game indusry has been profiing more han he movie indusry [], [3]. To keep his posiion, hey are reinvening heir ideas and echniques [4]. Nowadays, researchers are invesing effors in improving he performance, movemens, and sraegies of he games [5]. The game indusry is using a lo of AI echniques like: Fuzzy [6], Decision Trees [7], Arificial Neural Neworks [8], [9], Q-Learning [10] and ohers. All of hese echniques have been used o improve he qualiy of he games and he resuls of hese applicaions are posiives in general [5]. One of he challenges of he game indusry is o keep players ineresed while playing [1], [11]. For his purpose, he difficuly adapaion in a game is very imporan. In order o keep he player ineresed, we can le him ge neiher frusraed or bored during gameplay. So, i is imporan o keep he player in balance beween he difficuly of he game and his skill. One way of represening his balance is hrough he Flow Channel [1], [13]. Flow channel is defined as he sae of he mind ha keeps a person focused on an aciviy [1]. The adapaion of he game challenge based on he player skill level can keep he player in he flow channel. The imporance of he Dynamic Difficuly Adjusmen (DDA) increases in rehabiliaion games because we don jus have o adjus he difficuly o keep he player ineresed in he game while playing, we also have o adjus i o keep he player in his limis since exploring he limis of he player is he bes way o his rehabiliaion [14], [15]. So, if he game is aracive and explores he player s skill, he player rehabiliaion ends o be very posiive. I is imporan o noe ha a number of facors may inerfere wih a game s difficuly, such as he game s response ime, or he player s required moor skill. In games aimed a rehabiliaion, i becomes imporan o consider hese facors separaely. As an example, a player who has a moor limiaion may be frusraed if he game requires a high moor coordinaion capaciy bu allows a long response ime. On he oher hand, if he game requires a quick response ime, bu low moor coordinaion, he same player may become frusraed. In his paper, we represen hese difficuly facors of a game as chromosomes parameers, o be dynamically adjused by an Evoluionary Algorihm (EA). In doing so, we are able o adap he game difficuly for differen kind of simulaed players. The objecive of his research is no only o verify if our EA can adap he difficuly level of he game according o simulaed players skill level, bu, more specifically, o verify if he difficuly facors of he adaped game correcly corresponds o he se of skills of he simulaed player profiles used in our experimens. The res of he paper is srucured as follows. In Secion II we discuss relaed work in games wih dynamic difficuly adjusmen. In secion III we presen he seleced game and he creaed virual players used in he experimens. In Secion IV we explain he EA approach used o dynamically adjus he game difficuly. Secion V presens he resuls. Finally, Secion VI presens he conclusion and ideas for fuure work. II. RELATED WORKS Alhough players migh enjoy unpredicabiliy or novely during gameplay experiences, he DDA will only be effecive if i does no disrup or degrade he player experience [16]. For his purpose, he algorihm responsible for he DDA should be able o adap he game difficuly based on he player experience. In [17], he researchers developed Evoluionary Fuzzy Cogniive Maps o adjus gameplay parameers in real-ime according o he curren player skill XVII SBGames Foz do Iguaçu PR Brazil, Ocober 9h November 1s,

2 level. In a differen research [18], he game difficuly was dynamically adjused considering he emoional sae of he player, using as inpu for he game balance he over behavior and physiological responses of he player. Games wih Evoluionary Algorihm (EA) are he subjec of many sudies [1], [11], [19]. I is common using EA o Procedural Generaion of Conen (PGC) [0], Dynamic Difficuly Adjusmen (DDA) [1] and ohers. In he case of PGC, he conen generaion ends o be complex and cosly, however, EA has been used o dynamically generae conens like maps, visual ars and narraives based on player experience [0]. In oher sudy, EA was used o game sraegy learning. The auhor creaed a heory-inspired game and implemened an EA o generae sraegies based on playsyles [19]. In [1] he auhors propose he DDA based on an Evoluionary Algorihm (EA). The game proposed by hem is called The Cacher (Figure 1), and has been used for rehabiliaion of paiens wih moor deficis. In his game, he player mus conrol he horizonal posiion of a squirrel (he main characer of he game) and, in doing so, reach he arges (nus) ha fall verically on he screen. So, he player has o worry abou moving he conroller in only one dimension. ha has been used in rehabiliaion [1]. This game is similar o he game proposed in [1] bu he difference is ha Whac- A-Mole has a wo-dimensional gameplay, since he player can use he conroller o move horizonally and verically. So, adapaions are required in EA proposed in ha work. Besides ha, observing he resuls we aim o verify he game behavior for each differen profile (Secion V-C). III. METHODS AND MATERIALS This secion presens he mehods and maerials used o perform he game simulaor (Secion III-A) and he player simulaor (Secion III-B). A. The Game Simulaor This secion presens he proposed Wack-a-Mole simulaor, which has been developed in C language. In his ype of game, he player s goal is o conrol he image of a hammer on he screen so i can reach he arges ha appears in random posiions before hey disappear, as illusraed by Figure. Figure. Screensho of a Whac-A-Mole (5 5) ype game creaed in Uniy 3D, bu simulaed in C language. Figure 1. Screensho of he game The Cacher [1] The game difficuly is based on he iniial disance o he arge and he reacion speed, so, he chromosome defined by hem has genes (disance o he arge d and speed of he arge v). The finess of a chromosome is calculaed by he following equaion: F = K d d + K v v K ɛ ɛ. (1) where, K d, K v and K ɛ are coefficiens ha se he impac of all he erms of he equaion. d and v reflec he game disance and velociy, ɛ represens how far from he arge horizonal posiion he player is when he round ends. However, in his paper we adap he proposed EA in [1] for a Whac-A-Mole ype game, which is also a ype of game Four consans are imporan o explain he game: W,H,C and R. W and H represens, respecively, he widh and heigh of he screen in pixels. C represens he number of columns and R represens he number of rows on he screen, relaive o he screen division ha delimis he regions where he arges can appear. To beer undersand i, considering he example in Figure, he respecive game would have 5 columns and 5 rows (C = 5 and R = 5). The simulaor also uses variables: p x and p y, ha represens he player (hammer) posiion on he screen (respecively he coordinaes, in pixels, being p x he hammer posiion horizonally and p y he hammer posiion verically. A he beginning of he game, he hammer is placed a he cener of he screen [ W, ] H. Then, a arge appears a a disance from he hammer given by and (respecively, he disance on he x-axis and on he y-axis) and says on he screen for seconds before i disappears. Noe ha, XVII SBGames Foz do Iguaçu PR Brazil, Ocober 9h November 1s,

3 and are values ha define how difficul i is for he player o reach he arge and, for his reason, hey are he ones ha mus be adaped according o he player skill level, as explained in Secion IV. We limi he maximum disance from he player ha he arge can appear on he screen by he half of screen widh and heigh, because, supposing he player is a he cener of he screen, he maximum disance ha he arge may appear from he player is half he screen. Any disance greaer han ha would exceed he screen limi and he value of he chromosome would no represen he real difficuly of he mach. Because of ha, o define he arge posiion we creaed wo variables g x and g y. Firs of all, o calculae he value of hem we defined variables o indicae he arge direcion (λ x and λ y ) will appear from he player, boh of hem have only wo values: 1 or -1. In he case of λ x, -1 indicaes ha he arge is on he lef he player and 1 indicaes ha he arge is on he righ he player. In he case of λ y, -1 indicaes ha he arge is under he player and 1 indicaes ha he arge is above he player, hen, o define he arge posiion we ge he player posiion and depending on he values of λ x and λ y, we subrac or add he value of he respecive disances ha he arge should appear from he player (, in he case of g x and, in he case of g y ). Since he values of and are normalized in he chromosome, we muliply hem by he half of screen size, as is demonsraed on he equaions 3 and 4. To ge he real ime in seconds ha he arge will say on he screen, we defined wo consans MIN and MAX ha represen he minimum and maximum ime, respecively, ha he arge can say on he screen. Afer ha, we creaed a variable g o represen he ime unnormalized, his variable ges he ime from he chromosome and ransforms i o seconds based on MIN and MAX, given by he equaion. g = MIN + ( MAX MIN ) () g x = g y = { px W if λ x = 1 p x + W oherwise { py H if λ y = 1 p y + H oherwise Valid arge posiions are resriced by a screen division given by he recangular areas shown in Figure. Having he hammer posiion and is disance o he arge, we deermine he arge posiion by adding he disance values ( and o he hammer coordinaes (p x and p y ) and verifying in which area of he screen he arge is. Then, we adjus he arge posiion, given by x and y, so he arge is locaed a he cener of is curren area. (3) (4) B. Player Simulaors The consans and variables defined in his secion represen he necessary parameers o sar one game mach. When a arge appears on he screen, he player mus hen use he game conroller o move he hammer and ry o reach he arge. In his paper, we use a mehod o dynamically adjus he difficuly of he maches (Secion IV) adaped from he one proposed in [1] and, for esing i, we use simulaion of players. In Secion V-A, we describe 5 differen player profiles ha we creae o simulae differen kinds of skills. Each profile has 3 aribues (v x, v y and r ), v x defines he maximum speed he player can move horizonally, v y defines he maximum speed he player can move verically and r defines he value ha will be subraced from he ime ha he arge will be visible on he screen, allowing he simulaion of players wih aenion defici ha use some of he ime searching for he arge insead of moving he conroller. Equaion 5 shows how he final ime ( f ) is obained, which is used o calculae he player movemen. { g r if g > r f = (5) 0 oherwise Afer ha, we calculae he maximum disance ha player can move he hammer based on is iniial velociy capaciy and he size of he screen, like he following equaion. Then, we use variables x and y o represen he player movemen capaciy. To calculae i, we muliply v x and v y wih he final ime (Equaion 5), as shown by Equaions 6 and 7. x = (v x W ) f (6) y = (v y H) f (7) So, X is he maximum disance ha he player can move he hammer horizonally and y is he maximum disance ha he player can move he hammer verically. Afer we have he value of x and y, we are able o know if he player can reach he arge, because, we ge he arge posiion and calculae in which recangle on he screen he arge is posiioned. Then, we ge he values of x and y and calculae if he player is able o hi ha square, if yes, he algorihm posiions he player a he cener of he square. If he player is no able o hi he arge, we ge he values of λ x and λ y, and based on his previous posiion (p xn 1 and p xn 1 ), we posiion he player as close o he arge as he can, as shown in equaions 8 and 9: p xn = p xn 1 + x λ x (8) p yn = p yn 1 + y λ y (9) XVII SBGames Foz do Iguaçu PR Brazil, Ocober 9h November 1s,

4 IV. THE PROPOSED EVOLUTIONARY ALGORITHM We propose a new version of he EA used in [1] for a differen ype of game. In order o do so, we had o make some adapaions o he EA, based on a Whac-a-Mole like game. Since he purpose of our EA is o adjus he difficuly level of he game, he chromosome srucure we use is composed of 3 values,, and, which are he parameers o be used in one mach, direcly defining is difficuly, as explained in Secion III-A. If he EA can adjus hese values accordingly o a specific player profile, i indicaes ha i can adjus he difficuly level for a specific ype of player. The used populaion has a oal of five chromosomes. The chromosomes in he firs populaion are iniialized randomly wih values varying from 0 o 1 for, and one of he following values: 0, 0.4 or 0.8 for and. The 0.4 gap was chosen so hese values represen, respecively, a disance of zero, one or wo recangles from he hammer posiion. As he arge can appear a a maximum disance from he hammer of half he screen, he 0.4 gap was calculaed as C for, and R for, which resuls in 0.4 for boh, since our game presens R = 5 and C = 5. For variaions of he proposed game, where he arge can appear in differen posiions (differen han he 5 5 scene shown in Figure ), hese values can be easily recalculaed. The finess funcion we use is similar o Equaion 1. I considers hree differen facors ha reflecs: i) he ime ha he arge says on he screen (T, Equaion 10), ii) he disance ha he arge is from he player a he sar of he mach (D, Equaion 11) and iii) he disance ha he player is from he arge a he end of he mach (E, Equaion 1). While T and I are values ha he reflecs he mach difficuly, E measures he player success or failure in he mach. When E = 0, he arge was reached, oherwise, E represens how close o he arge he player could ge. Equaion 13 shows he final finess funcion used in our EA. D = ( T = 1 (10) ) (gx p x0 ) + (g y p y0 ) W + H (11) where p x0 and p y0 are he coordinaes of he hammer a he sar of he mach. ( ) (gx p x1 ) + (g y p y1 ) E = (1) W + H where p x1 and p y1 are he coordinaes of he hammer a he end of he mach.. F = K T + K d D K e E (13) K, K d and K e are coefficiens ha se he weigh of he finess elemens, higher values for K and K d se higher conribuion o he finess score of soluions ha represen maches wih higher difficuly. On he oher hand, higher values for K e resuls in higher values for soluions where he player presens a good performance. To find good values for hese coefficiens, we reproduced he ranking sysem used in [11], as repored in he experimens from Secion V-B. To evaluae all he individuals in our populaion, a mach is execued for each chromosome (oal of five maches), using is values as he mach parameers (line 6 from Algorihm 1. Afer ha, each chromosome is associaed wih a finess value. The chromosome wih a higher finess score is seleced, and a new populaion is formed mainaining he seleced chromosome (eliism) and replacing he oher five wih muaed copies of he seleced individual (asexual reproducion) as done in [11] and [1]. The Muaion operaor used works as follows: For he and parameers, a random value beween 0.4, 0 and 0.4 is added. Once again, he 0.4 gap was calculaed based on our curren 5x5 game scene, and should be recalculaed for variaions of he game as previously explained. Afer he randomly generaed value is added, he parameer is adjused o 0, if i is less han 0, or o 0.8, if i is higher han 0.8 (since 0.8 represens he maximum disance of wo regions where he arge can appear). For he ime gene () we generae a random value beween 0 and 1, afer ha, we define randomly if his value will be posiive or negaive, and add i o he original value. If he resuling ime value is bigger han 1, he algorihm ses he value o 1, and if he resuling value is less han 0, he algorihm ses i o 0. The Algorihm 1 presens he execuion of he game using he virual players and he proposed EA. V. EXPERIMENTS AND RESULTS This secion presens he creaed experimens and resuls from esing he proposed EA difficuly adjusmen in our proposed game simulaor. Secion V-A shows he profile seings used in he experimens. Secion V-B presens experimens conduced for esing he proper implemenaion of he EA and adjusing he coefficiens used in is finess funcion. Secion V-C shows experimens ha verifies if he difficuly presened in our proposed game is consisen wih he abiliy presened by each esed player profile, when using he EA wih he proper adjused coefficiens. Secion V-D presens experimens wih dynamic player profiles, o see if he EA can properly adjus he game difficuly when he player skills are changed during playime. A. Player Profiles Simulaing differen kinds of players is imporan o observe how he EA can adjus he difficuly of our game for players wih differen se of skills. To simulae differen kinds of players we creaed 5 differen players profiles o XVII SBGames Foz do Iguaçu PR Brazil, Ocober 9h November 1s,

5 Algorihm 1 Whac-A-mole simulaion wih EA Inpu: N G 1, N 1, W > 0, H > 0, C W, R H Oupu: h 1: Load curren player profile values: v x, v y and r : Define iniial hammer posiion as p x w and p y h 3: Randomly iniializes he populaion of he EA 4: Iniialize hi couner h 0 5: for i 0 o i < N G sep 1 do 6: for j 0 o j < N sep 1 do 7: Ge he values, and o be used in his mach 8: Calculae g, g x and g y (Equaions, 3 and 4) 9: Calculae f, p xn and p yn (Equaions 5, 8 and 9) 10: if player is able o reach he arge hen 11: Incremen hi couner h h + 1 1: end if 13: Use Equaion 13 o evaluae chromosome 14: end for 15: Selec chromosome wih higher finess 16: Make N copies of he seleced chromosome 17: Apply muaion operaor in N 1 chromosomes 18: Define as he new populaion he se of N chromosomes obained from he wo previous seps 19: end for use wih our player simulaor, explained in Secion III-B. Profile 1 simulaes a player wih good performance o move he conroller horizonally and bad performance o move he mouse verically, profile simulaes a player wih good performance in moving he conroller verically and bad performance in moving he conroller horizonally, profile 3 simulaes a player which really does no have a good performance in moving he conroller in any axis, profile 4 simulaes a player which has a beer performance han profile 3, however, his profile also does no have a good performance in moving he conroller and he has aenion defici and profile 5 simulaes a player wih good performance in moving he conroller in boh ways, bu has aenion defici. All of hese profiles are represened in Table I. B. EA adjusmens TABLE I PLAYER PROFILES USED IN THE EXPERIMENTS Profile v x v y r Our firs experimen aimed o adjus he K, K d and K e coefficiens of our finess funcion so he EA can work properly. For his purpose, he experimens in [11] were repeaed. Firs, we define ha each coefficien may one of he 5 differen values (1,,4,8,16). Since we have 3 coefficiens o adjus, we have a oal of 15 possible combinaions (5 3 ). For each combinaion, we run a sequence of 30 ess for each player profile. Each es consiss in running 30 generaions of he EA using he given coefficien combinaion. Afer ha, we calculae he player profile skill score (Θ), which is he rae of maches in which he player successfully his he arge, calculaed by Equaion 14, and also he game overall difficuly (Ψ), calculaed by Equaion 15. Θ = h N G N (14) where h is he hi couner, calculaed in line 11 of Algorihm 1. i=0 Ψ = 1 N G 1 N G 3 1 N j=0 N + N j=0 C X = C R Y = R XN + N j=0 Y N (15) (16) (17) where, z is he floor funcion, gives he larges ineger less han or equal o z. Using he obained values, we can plo a do like he ones shown in Figure 3. The closes a do is o he diagonal line in he picure he beer, because he mos likely i is ha he game kep he player in he flow channel area, explained in Secion I) (greaer game difficuly for players wih good skill level, and lower game difficuly for players wih lower skill level). However, a good se of coefficiens should be able o keep all player profiles near he flow channel. So, o obain a good combinaion of values for our coefficiens, he same ranking sysem presened in [11] was used and, from his mehod, we deeced ha he se of coefficiens K =, K d = 4 and K e = 8 was presened in each op 38, 46, 37, 30, 4, coefficiens for every player profile, respecively. Then, we seleced his se of coefficiens o be used in our EA. Figure 3 shows he plo of a do for each player profile obained as previously explained using he given coefficiens se. Figure 4 represens a simple es using profile 5 and he EA wih he adjused coefficiens, in which we can see ha he EA is working as expeced, since he endency line indicaes an improvemen of he finess values as he generaion number increases. The used heurisic aims o find a se of coefficiens ha resuls in dos ha are close o he diagonal line for all he XVII SBGames Foz do Iguaçu PR Brazil, Ocober 9h November 1s,

6 skills in moving he conrol horizonally and poor abiliy o move i verically. As we can see in Figure 5, he average seings for he game maches make he arge appears in a disan posiion in he horizonal axis (high value), close posiion in he verical axis (low value). These seings for he game maches his ype of player skills. The ime () ha he arge says visible is a low value, which is also coheren wih he player skills, since profile 1 does no have aenion defici ( r = 0). Figure 3. Dispersion diagram obained using K =, K d = 4 and K e = 8 for each player profile. Figure 5. Average values for parameers, and used in he maches for player profile 1. Profile is very similar o he firs one, bu wih invered skills: good skills in moving conrol verically and poor abiliy o move horizonally. Figure 6 shows he resuls ha, once again, mach he player profile skills. Figure 4. Finess diagram wih rend line from profile 5. differen player profiles (Figure 3). By doing ha, we expec ha players represened by hese profiles will have a lower chance of feeling frusraed or bored when playing. We can, however, be cerain of ha, since we are no working wih real players, bu simulaed player profiles. Furhermore, we sill can deermine if he ype of difficuly presened by he game is consisen wih he se of abiliies presened by each esed player profile, which is wha we hope o validae from he soluions found by our EA. C. Comparing ypes of challenges found for each player profile Wih he adjused finess funcion for our EA, we go he average values for each chromosome parameer, considering all generaions and all 30 ess run in he previous experimen for each given profile. This reflec he average seings used by he game considering all maches wih he simulaed player. The resuls are shown in Figures 5, 6, 7, 8 and 9. As described on secion V-A, he firs profile has good Figure 6. Average values for parameers, and used in he maches for player profile. The hird player profile does no have good movemen skills. Observing he Figure 7, we can see ha, once again, he algorihm maches he player skill by using low values for he disances in boh axis. XVII SBGames Foz do Iguaçu PR Brazil, Ocober 9h November 1s,

7 Figure 7. Average values for parameers, and used in he maches for player profile 3. Figure 9. Average values for parameers, and used in he maches for player profile 5. The las wo profiles, 4 and 5, represen cases of aenion defici. Figures 8 and 9 presen he resuls of our ess, ha shows ha he EA was able o adap he maches so ha he average ime ha he arge is visible is now, in boh scenarios, higher han in he ime found for he previous profiles (1, and 3). Also, he disance he arge appears is, in average, bigger for profile 5 han for profile 4, which is expeced since profile 5 has beer movemen skills han profile 4. Figure 8. Average values for parameers, and used in he maches for player profile 4. The resuls presened in his secion le us verify ha our curren EA is capable of adjusing he exising challenges in he game o properly adjus o he skill level of a saic player profile (a player whose skill level remains he same during gameplay). D. Change in players skill level during gameplay Players ofen change heir skill level during gameplay, usually improving heir skills as hey learn from he game. To simulae his scenario, an experimen was conduced simulaing a game wih 750 maches, wha corresponds o 150 EA generaions. In order o simulae ha he player improved his abiliies, every 50 generaions we changed he value of v x and v y as follows: Firs 50 generaions: 0.03, generaion 51 o 100: 0.1 and generaion 101 o 150: We kep he value of r as 0 hrough all generaions. The resuls from his experimen are presened in Figures 10 and 11. Figure 10 shows a moving average graph using a subse of size 10 for he average parameers (, and ) in each generaion. We can see ha here is a endency o improve he arge disance as he maches advance, as expeced, since he player skill level is also improving. We can also noice ha here is an increase in on he second se of 50 generaions (profile wih v x and v y wih value 0.1). To beer visualize wha happened, we creaed a second graph (Figure 11), showing he average of he used parameers in each se of 50 generaions, each one corresponding o a differen profile configuraion. I is possible o visualize ha each se of parameers corresponds o he player skill level. Alhough he values of and are slighly higher for he las 50 generaions (101 o 150), we poin ou ha he skill level of he player in hese las 50 generaions are significanly higher han he values used for he profile in generaion 51 o 100, since value 0.36 o v x and v y represens a player who can move he conroller 3 imes faser han a player wih value 0.1 of v x and v y. However, he resuls show ha he difficuly level was improved in he las 50 generaions by decreasing he ime available o he player o reach he arge, as he go faser. To simulae a scenario where he EA should adap he XVII SBGames Foz do Iguaçu PR Brazil, Ocober 9h November 1s,

8 Figure 10. Genes evoluion by moving average 10. Figure 1. Genes evoluion by moving average 10. Average of he 50 generaions used by each profile configura- Figure 11. ion. Average of he 50 generaions used by each profile configura- Figure 13. ion. difficuly level of he game when a player, for some reason, has a severe decrease in his moor abiliies, we repeaed he previous experimen using a differen order in he changes made o he values of he profile every 50 generaion, changing he values of v x and v y as follows: Firs 50 generaions: 0.1, generaion 51 o 100: 0.36 and generaion 101 o 150: Once again, we kep he value of r as 0 hrough all he experimen. The resuls are shown in Figures 1 and 13, and allow us o ge o he same conclusions as before: ha he EA can dynamically adjus he difficuly level based on he player abiliies when hey are changed during gameplay. VI. CONCLUSION The resuls from he performed experimens show ha our iniial proposal is valid. The developed EA can perform he DDA successfully for he simulaed players profiles, adjusing differen elemens which influence he game difficuly according o he skill se of each player profile. In summary, he conclusions we draw from he resuls of his research are: 1) The echnique used in [1] for obaining a DDA can be adaped for differen games; ) The differen game difficuly elemens can be properly adjused according o changes of he player profile skill se during gameplay; Demonsraing ha he research conduced in [11] and [1] can be adaped for differen ypes of games is imporan o he research field of rehabiliaion games. The resuls of he presen research adds o [11] and [1], by showing ha he DDA echnique can be used in he creaion of games ha could help in he player rehabiliaion process by adaping he game parameers o player specific difficulies during playime. We believe ha he resuls are also promising for oher applicaions of serious games, since we can argue ha in educaional games i is also imporan o adjus he game XVII SBGames Foz do Iguaçu PR Brazil, Ocober 9h November 1s,

9 difficuly level according o he player knowledge, and furhermore, adjus differen difficuly levels for differen opics, according o he player knowledge level in each of hese opics. Coninuaions of his research can include: i) performing ess wih real players, evaluaing he impac of our proposal on clinical rehabiliaion sessions; ii) esing he used echnique in an educaional game; iii) he creaion of a larger se of profiles in order o simulae more ypes of players wih more realisic behaviors; and iv) performing ess wih differen sizes of game scenarios. ACKNOWLEDGMENT The auhors would like o hank he scholarship gran awarded o Bruno Ely Reis Garcia by he Insiuional Scholarship Program of Scienific and Technological Iniiaion of he Federal Insiue of Educaion Science and Technology of São Paulo (PIBIFSP) and Fernanda Goular for he English review. REFERENCES [1] K. O. Andrade, R. C. Joaquim, G. A. P. Caurin, and M. K. Crocomo, Evoluionary algorihms for a beer gaming experience in rehabiliaion roboics, Compu. Enerain., vol. 16, no., pp. 4:1 4:15, Apr [Online]. Available: hp://doi.acm.org/ / [] MPAA, 016 Thearical Marke Saisics Repor, Mpaa.Org, 017. [Online]. Available: hp:// MPAA-Thearical-Marke-Saisics-016 Final-1.pdf [3] Newzoo, 018 Global game Marke Repor: Trends, Insighs, and Projecions Towards 01, 018, pp [Online]. Available: hps://resources.newzoo.com/hubfs/repors/ Newzoo 018 Global Games Marke Repor Ligh.pdf [4] G. B. David Wesley, Innovaion and Markeing in he Video Game Indusry avoiding he performance rap, 016. [5] M. Carrozo, How Arificial Inelligence is changing he gaming indusry. [Online]. Available: hps://unbabel.com/ blog/ai-changing-gaming-indusry/ [6] T. Khalil, Y. S. Raghav, and N. Badra, Opimal Soluion of Muli-Choice Mahemaical Programming Problem Using a New Technique, American Journal of Operaions Research, vol. 06, pp , 016. [7] M. W. Masao Konishi, Seiya Okubo, Tesuro Nishino, Decision Tree Analysis in Game Informaics, Springer Inernaional Publishing, 018. [8] S. Y. Chong, M. K. Tan, and J. D. Whie, Observing he Evoluion of Neural Neworks Learning o Play he Game of Ohello, Trans. Evol. Comp, vol. 9, no. 3, pp , 005. [Online]. Available: hp: //dx.doi.org/ /tevc [9] G. A. P. Caurin, A. A. G. Siqueira, K. O. Andrade, R. C. Joaquim, and H. I. Krebs, Adapive sraegy for muli-user roboic rehabiliaion games, Proceedings of he Annual Inernaional Conference of he IEEE Engineering in Medicine and Biology Sociey, EMBS, no. 1, pp , 011. [10] K. D. O. Andrade, G. Fernandes, G. A. Caurin, A. A. Siqueira, R. A. Romero, and R. D. L. Pereira, Dynamic player modelling in serious games applied o rehabiliaion roboics, in Proceedings - nd SBR Brazilian Roboics Symposium, 11h LARS Lain American Roboics Symposium and 6h Roboconrol Workshop on Applied Roboics and Auomaion, SBR LARS Roboconrol Par of he Join Conference on Roboics and Inelligen Sysems, JCRIS 014, oc 015, pp [11] K. O. Andrade, T. B. Pasqual, G. A. P. Caurin, and M. K. Crocomo, Dynamic difficuly adjusmen wih Evoluionary Algorihm in games for rehabiliaion roboics, in 016 IEEE Inernaional Conference on Serious Games and Applicaions for Healh, SeGAH 016, Orlando, FL USA, 016, pp [1] M. Csikszenmihalyi, Flow: The Psychology of Opimal Experience. New York, NY: Harper Perennial, March [Online]. Available: hps:// Flow The Psychology of Opimal Experience [13] J. M. Thomas and R. M. Young, Annie: Auomaed generaion of adapive learner guidance for fun serious games, IEEE Transacions on Learning Technologies, vol. 3, no. 4, pp , 010. [14] P. Langhorne, F. Coupar, and A. Pollock, Moor recovery afer sroke: a sysemaic review, pp , 009. [15] N. A. Borghese, M. Pirovano, R. Mainei, and P. L. Lanzi, An inegraed low-cos sysem for a-home rehabiliaion, in Proceedings of he 01 18h Inernaional Conference on Virual Sysems and Mulimedia, VSMM 01: Virual Sysems in he Informaion Sociey, 01, pp [16] R. Hunicke, The case for dynamic difficuly adjusmen in games, in Proceedings of he 005 ACM SIGCHI Inernaional Conference on Advances in Compuer Enerainmen Technology, ser. ACE 05. New York, NY, USA: ACM, 005, pp [Online]. Available: hp://doi.acm.org/ / [17] L. J. F. Prez, L. A. R. Calla, L. Valene, A. A. Monenegro, and E. W. G. Clua, Dynamic game difficuly balancing in real ime using evoluionary fuzzy cogniive maps, in h Brazilian Symposium on Compuer Games and Digial Enerainmen (SBGames), Nov 015, pp [18] T. J. W. Tijs, D. Brokken, and W. A. IJsselseijn, Dynamic game balancing by recognizing affec, in Fun and Games, P. Markopoulos, B. de Ruyer, W. IJsselseijn, and D. Rowland, Eds. Berlin, Heidelberg: Springer Berlin Heidelberg, 008, pp [19] Guanci Yang, Game Theory-Inspired Evoluionary Algorihm for Global Opimizaion, MDPI, 017. [0] J. Forsblom and J. Johansson, Geneic Improvemens o procedural generaion in games, Universiy of Boras, 017. [1] Y. Tokuyama, R. P. C. J. Rajapakse, S. Miya, and K. Konno, Developmen of a whack-a-mole game wih hapic feedback for rehabiliaion, in 016 Nicograph Inernaional (NicoIn), July 016, pp XVII SBGames Foz do Iguaçu PR Brazil, Ocober 9h November 1s,