A Model for Collective Strategy Diffusion in Agent Social Law Evolution

Transcription

1 A Model for Collective Strtegy Diffusion in Agent Socil Lw Evolution Yichun Jing, Toru Ishid Deprtment of Socil Informtics, Kyoto University Yoshid-Honmchi, Kyoto , Jpn Abstrct Socil lw is perceived s evolving through the competition of individul socil strtegies held by the gents. A strtegy with strong uthority, ccepted by mny gents, will tend to diffuse to the remining gents. The uthority of socil strtegy is determined by not only the number of but lso the collective socil positions of its overlid gents. This pper presents novel collective strtegy diffusion model in gent socil lw evolution. In the model, socil strtegies tht hve strong uthority re impressed on the other gents. The gents will ccept (prtilly or in full) or reject them bsed on their own socil strtegies nd socil positions. The diffusion of socil strtegies proceeds in series of steps nd the finl result depends on the interply between the forces driving diffusion nd the countercting forces. Introduction Coordintion is the key to develop relistic multigent systems [Krus, 997][Jing & Jing, 2005]. The concept of rtificil socil system is presented by [Shohm nd Tennenholtz, 995]; their bsic ide ws to dd mechnism, clled socil lw, into the system to relize coordintion mong gents. Ech gent initilly hs its own strtegy, nd the different strtegies my produce conflict. Therefore, to relize hrmonious gent system, we will need to endow set of socil lws tht cn be ccepted by most gents. A set of socil lws represents restrictions on finl gent strtegies. Previous work on rtificil socil systems [Shohm & Tennenholtz, 997] [Shohm nd Tennenholtz,995] [Fitoussi nd Tennenholtz, 2000] [Boell nd vn der Torre, 2005] mde no systemtic nlyses on the evolution of socil lws from individul socil strtegies, nd the socil lws were creted off-line. Therefore, the socil lws described in previous work re lwys fixed, nd so fil to yield dynmic gent systems. This pper presents tht socil lws ren t fixed over the system s lifetime. A socil lw represents n islnd of stbility nd cn be overwhelmed nd replced. In the frmework presented by this pper, gents strt with their individul socil strtegies; the socil strtegies cn diffuse nd be ccepted in prt or in full by others. The emergence of new dominnt socil strtegy represents the emergence of new socil lw. We initited study on how to evolve individul socil strtegies to globl socil lw through hierrchicl gent diffusion [Jing nd Ishid, 2006][Jing nd Ishid, 2007]. In our originl model, ech gent hs its own socil strtegies t the first stge of the system; for simplicity we restrict the discussion to just one ction/belief. Further, we ssume tht the gents possess socil rnk nd the rnks re known by ll gents. As the system runs, the strtegies of superior gents will tend to diffuse (be dopted by or ccepted by) the junior gents. Given the right conditions nd enough time, globl socil lw my be finlly estblished. A simple exmple is given below: Two businessmen enter the sme conference room. One strts to smoke but the other complins. Upon lerning tht the smoker hs higher position in the sme compny, the compliner chnges his strtegy of smoking is not permitted to go hed. This mens tht the socil lw in the conference room hs become smoking is permitted. [Scenrio : diffusion by rnk] Only the diffusion of the socil strtegies of superior gents to junior gents ws considered in [Jing nd Ishid, 2006][ Jing nd Ishid, 2007]. However, such sitution is not truly representtive of relity. In rel society, there re so mny collective intentions nd prctices [Blzer nd Tuomel, 2003][Pcheco nd Crmo, 2003], nd the socil strtegies shred by mny junior gents cn lso influence the superior gents. The following exmple demonstrtes this: You like smoking very much nd you occupy the highest position in your compny. However, if ll other members dislike smoking, you will probbly stop smoking, i.e. your socil strtegy hs been trumped by tht of the mjority. Therefore, the socil lw of your office is now no smoking. [Scenrio 2: diffusion by numbers] The interply between rnk, strength of strtegy support, nd the numbers of supporters is extremely complex. The emergence of socil lw my not prevent some gents from mintining their originl strtegies or indeed dopting contr-strtegies. For exmple: 353

2 None of the employees in n office like smoking; so the socil lw in the office is no smoking in the office. The boss strts long discussion with the employees. The boss hs hbit: he likes to smoke while giving orders to the stff. Therefore, the boss will smoke even though the socil lw is no smoking in the office. [Scenrio 3: persistence of outliers] In such scenrio, the outlier gent hs very high socil position; so its corresponding socil strtegy my hve high dominnce though the number of overlid gents is few (just one in this cse). All three scenrios re common in rel world socil strtegy diffusion. We think tht the dominnce of socil strtegy is determined by the numbers nd rnking of its supporters reltive to those of other strtegies. A strtegy becomes more dominnt s the number of dopters increses nd/or their rnking increses. The success of socil strtegy supported by mny junior gents over the socil strtegy of superior gents cn be clled collective insurgent diffusion; the reverse is clled collective elite diffusion. In this pper, we explore how socil strtegy cn diffuse mong gents. Our model is explined using the exmple of crowd orienttion. 2. An Exmple nd Relted Concepts 2. Socil Strtegy in Queue Orienttion To explin our model, we use the exmple of n gent system tht reproduces crowd of strngers stnding on soccer field. At the initil stge, the orienttion of ech gent (its strtegy) is quite rndom. Wht we re looking for the emergence of socil lw; most gents fce the sme direction. Figure : The cse of n gent system nd its socil strtegies Ech of the n gents cn stnd with one of the 8 orienttions, see Figure (). The socil strtegy of n gent is its orienttion. Let n be the number of gents, we cn use n rry to denote the socil strtegies of gents. s {,, 8}, i n, represents socil strtegy (i.e. the i () Agent Socil Strtegy (b) b c d e Agent (c) Agent b Agent c Agent d Agent e stnding orienttion) of gent i. The socil strtegies of the gents in (b) re shown s (c). Obviously, the stnding orienttions of the gents in Figure (b) re disorderly. Since our exmple consists of strngers, now we my replce explicit socil rnk with ge. For exmple, if gent c looks older thn e, then e my chnge its orienttion to mtch tht of c. If gents b nd d shre the sme orienttion, c my not be ble to overcome their numericl dvntge. At this time, c my chnge its orienttion to mtch theirs. Let us exmine the emergence of socil lws. We consider five gents, b, c, d nd e, which hve the sme socil rnk. If nd b hve the sme socil strtegy, s b, but the socil strtegies of the other three gents re quite different, then the socil lw cn be written s ll gents re under pressure to follow strtegy s b. As time goes by, if c, d nd e hppen to estblish the sme socil strtegy, s cde, the socil lw would chnge to ll gents re under pressure to follow strtegy s cde. The sitution becomes more complex if the gents do hve explicit socil rnk. For this sitution, we will need to blnce the influence of rnk ginst the weight of sheer numbers. Next we will give some relted concepts to explin the collective diffusion. 2.2 Dominnce of Socil Strtegy If socil strtegy is ccepted by mny gents, its dominnce will be strong. However, different gents will contribute different mounts to the dominnce of socil strtegy. A superior gent strengthens strtegy s dominnce fr more thn junior gent. To llow for comprison, we equte the dominnce of socil strtegy to its rnk. The concept of rnk is used often in the web serch field to denote the importnce of web pges [Hveliwl, 2003]. Now we use it to represent the reltive dominnce of socil strtegies. Definition 2. Socil rnking of gent i cn be function: p i [0, ], where is nturl number. p i p j i hs superior rnk to j. The set of the positions of ll gents in the system cn be denoted s: P [ pi ], where i n, nd n denotes the number of gents in the system. In this pper, our bsic ide is: if gent hs socil strtegy s, is implicitly conferring some importnce to s. Then, how much importnce does n gent confer to its socil strtegy s? Let N be the number of socil strtegies of nd p represent the socil rnk of, gent confers p / N units of rnk to s. As for our instnce, the number of socil strtegies of n gent t one time is only one, therefore, gent confers p units of rnk to s. 2.3 Overly Group of A Socil Strtegy The gents tht shre socil strtegy re clled the overly group of th strtegy. For exmple, in Figure (b), gents b nd d shre socil strtegy 4 nd so form one overly group. Let G(s) represent the overly group of socil strtegy s, we hve: G () s s { u gent u ccepts the socil strtegy s} (2.) 354

3 Obviously, the rnk of socil strtegy is determined by its overly group. Let G(s) be the overly group of socil strtegy s, the rnk of s cn lso be defined s: srnk() s pu / Nu (2.2) As noted bove, in our exmple gents cn hold only one socil strtegy t ny one time, nd so cn only contribute to the dominnce of only one socil strtegy. The rnk of socil strtegy s cn be simplified to: srnk() s pu (2.3) From Equtions (2.2) (2.3), we cn see tht the rnk of socil strtegy is determined by the number nd socil rnks of the members of its overly group. The diffusion strength of socil strtegy s is the monotone incresing function of its rnk, i.e. the higher Rnk(s) is, the higher the diffusion strength is. Let the diffusion strength of socil strtegy s be represented s S(s), we hve: S () s ( Rnk ()) s s (2.4) Where is monotone incresing function. To simplify the question, we cn directly use the uthority of socil strtegy s to represent its diffusion strength. Moreover, we will use the concept of group rnk to represent the socil strtegy rnk, i.e. Rnk( G( s)) Rnk( s ). (2.5) s u Gs u Gs 2.4 Distnce between Agent nd Overly Group It is very simple to compute the distnce between two gents, but not the one between n gent nd group. As stted bove, ech gent in the group strengthens the dominnce of the strtegy to different extent. Therefore, we introduce the fctor of socil rnk into the definition of the distnce between n gent nd group s follows: Definition 2.2 If d(,u) denote the distnce between gent nd gent u, G denote the number of gents in group G, p u denote the socil rnk of gent u, then the distnce between gent nd group G cn be defined s: DG ( pu d(, u)) (2.6) G p u G u u G 2.5 Difference of Two Socil Strtegies In this pper, the ngulr difference of two gent orienttions is used to represent the difference in their socil strtegies. Therefore, we hve the following definition: Definition 2.3 The difference of two socil strtegies i nd j cn be defined s the ngulr distnce between their respective orienttions: j i, if j i 4 (2.7) DLij 8 j i, if j i 4 For exmple, the difference between socil strtegy nd 7 is 2, nd the difference between socil strtegy 3 nd 4 is. 3. The Collective Diffusion Model 3. Diffusion Impct Force from Overly Group to Agent The impct force from n overly group to n gent is determined both by their distnce nd the group s dominnce (i.e. the dominnce of the corresponding socil strtegy). Therefore, we define the impct force from overly group G to gent s: pu Rnk( G) u G IFG f ( ) f ( ) 2Dg 2( ( pu d(, u))) G p u u G (3.) Where f is monotone incresing function, nd re 2 prmeters to determine the reltive importnce of the two fctors. From Eqution (3.), we cn see tht the nerer the gent is to the group nd the higher the group s rnk is, then the gret the impct force of the group is on tht gent. 3.2 Countercting Force from Agent to Overly Group Bsed on rel-world observtions, if gent is not member of overly group G, will instinctively counter such influence. The countercting force from gent to overly group G is determined by the following fctors: ) the socil rnking of gent, 2) the verge socil rnk of overly group G, 3) the distnce of the socil strtegies (i.e. the stnding orienttions) between gent nd overly group G. The higher the socil rnk of gent is, the bigger the difference in socil strtegies is, the lower the verge socil rnk of overly group G is, then the more gent resists dopting the socil strtegy of overly group G. Therefore, if we let the socil strtegy of gent be s nd the socil strtegy of overly group G is s 2, we define the countercting force from gent to overly group G s: p g( DLs s2 2 ( )) (3.2) pu G Where g is monotone incresing function, nd 2 re two weighting prmeters. 3.3 Collective Diffusion Criterion of Socil Strtegy The collective diffusion criterion of gent socil strtegy needs to consider both IF nd G. The more IF G is nd the less is, then the more likely it is tht gent u G u G 355

4 will dopt or move towrds the socil strtegy of group G. Therefore, we use the rtio of IF G to s the diffusion criterion. If the rtio exceeds predefined vlue, then the socil strtegy of gent will chnge by some mount. We cn predefine two prmeters nd ccording to the ctul sitution being simulted. If the vlue of IFG / is more thn, the socil strtegy of will completely switch to tht of G. If the vlue of IFG / is less thn but more thn, then the socil strtegy of will chnge to some extent but not equl tht of G. While the vlue of IFG / is less thn, the socil strtegy of remins unchnged. Let the socil strtegies of G nd before diffusion re m nd n respectively, mn, 8. If m n, the chnge of the stnding orienttion of will be clock-wise; if m n, the chnge of the stnding orienttion of will be nticlock-wise. Therefore, the diffusion criterion, i.e. the chnge criterion of the socil strtegy of cn be defined s: s m, if IF / G if IF G / : IFG / 2m 8 n ( n m 8), if m n 4 IFG / n ( m n), if 0 m n 4 IFG / n ( n m), if 4 m n 0 IFG / 2m 8 n ( m n 8), ifm n 4 (3.3) n, if IFG / Where s is the new socil strtegy of fter one step in the simultion. 3.4 Gol Function of Diffusion Severl socil strtegies my exist even fter the diffusion process reches equilibrium. Simulting ctul situtions will demnd tht we set different gols for the diffusion results. For our exmple of crowd orienttion, we my wnt to identify the conditions under which ll gents finlly dopt the sme orienttion. Moreover, the socil lws re lwys estblished ccording to the more dominnt socil strtegies. Obviously, the more gent numbers the dominnt socil strtegies re ccepted by, the more rtionl the estblished socil lws re. Such ssumption is lso prcticl in relworld situtions, e.g., the lw should be estblished to stisfy the needs of most people in the society. Therefore, we define the performnce criterion of diffusion s mesure of the winnowing of socil strtegies. Let N S be the number of socil strtegies in the system fter diffusion, Gs ( ) be the gent number in the overly group of socil strtegy s, then the performnce criterion of the diffusion cn be defined s: PS ( Rnk( s) G( s) ) (3.4) N S s S Higher vlues of P S indicte tht fewer socil strtegies hve survived nd lso show tht better diffusion performnce cn be gotten. 3.5 Diffusion Progress In the diffusion progress, the socil strtegy with the strongest dominnce will firstly diffuse to other gents tht belong to the other socil strtegies overly groups. After tht, the socil strtegy with second strongest uthority will diffuse to other gents tht belong to the gents with more junior uthority socil strtegy,., until there re no diffusions tke plce. Let A be the gent set of the system, s be the socil strtegy of gent, the diffusion progress cn be shown s Algorithm. Algorithm. Input S; /*the initil set of socil strtegies of the system*/ SL={, 2,, 8}; Do { SL SL ; A A While SL is not empty {Select the socil strtegy with strongest dominnce from SL : s ; Do {For A G( s ) If IF / G ( s ) ( s ) { Gs ( ) Gs ( ) { }; Rnk( s) Rnk( s) p If Gs ( ) {} then SL SL { s }; Compute s ccording to Eqution (3.3); G( s) G( s) { } ; Rnk( s) Rnk( s) p ;} } until the P S doesn t chnge ny more; SL SL { s }; A A G( s ) ;}; } Until the P S doesn t chnge ny more; Output S nd P S. 4. Cse Studies We exmined severl cses to demonstrte nd test our model. Figure 2 is one such cse. From the rnks of socil strtegies, we cn see tht the socil strtegy 3 hs the strongest dominnce. So we compute the IFG / between other gents nd the overly group of socil strtegy 3. The distribution of IFG / is shown s 356

5 Figure 3. As tril, we set nd to 0 nd 4, respectively. This yields diffusion from G(3) to other gents ccording to Eqution (3.3) nd Algorithm, the progress of diffusion is shown in Figures 4-6. P S does not chnge from Figure 6, so diffusion process is finished. The totl number of diffusion steps is 3. From Figure 6, we cn see tht the stnding orienttions of ll gents re identicl fter three diffusion steps, except for the gent in the bottom right corner. Next, we chnge the vlues of nd. At first we decrese them step by step for 4 cses, nd then increse them step by step for nother 4 cses. The diffusion results re given in Tble. From Tble, we cn see tht more steps re needed to rech diffusion termintion when nd increse. Therefore, we should set nd to mtch the ctul sitution being simulted Figure 4: The gent socil strtegies fter the first round diffusion from G(3) to other gents. Where, Rnk ()=0, Rnk(2)=3, Rnk(3)=3, Rnk(4)=2, Rnk(5)=0, Rnk(6)=4, Rnk(7)=2, Rnk(8)=9. P S =393/5. Agent Position Socil strtegy 3 Figure 2: The initil cse of gent socil strtegies. Rnk()=3, Rnk(2)=5, Rnk(3)=3, Rnk(4)=2, Rnk(5)=0, Rnk(6)=7, Rnk(7)=2, Rnk(8)=9. P S =78/7. Figure 5: The gent socil strtegies fter the second round diffusion from G(3) to other gents. Where, Rnk ()=0, Rnk(2)=0, Rnk(3)=49, Rnk(4)=0, Rnk(5)=0, Rnk(6)=0, Rnk(7)=2, Rnk(8)=0. P S = IF/ between G(3) nd gent Upper vlue Lower vlue Agents Figure 3: The IFG / distribution of other gents to the overly group of socil strtegy 3. Figure 6: The gent socil strtegies fter the third round diffusion from G(3) to other gents. Where, Rnk ()=0, Rnk(2)=0, Rnk(3)=49, Rnk(4)=0, Rnk(5)=2, Rnk(6)=0, Rnk(7)=0, Rnk(8)=0. P S =

6 Tble. The diffusion results for different nd. CASE STEPS S P S , , , , , , Discussion nd Conclusion A socil strtegy ccepted by mny gents will hve high dominnce nd my diffuse to other gents. The dominnce of socil strtegy is determined by not only the number of dherents but lso their socil positions. Tht is, superior gent strengthens the dominnce of socil strtegy drsticlly, while the ddition of mny junior gents cn lso strengthen the dominnce of socil strtegy. This pper presents collective strtegy diffusion model in gent socil lw evolution. The model shows us tht the socil strtegy of superior gent my be chnged by the socil strtegy shred by mny gents, which is n exmple of collective insurgent diffusion. Section 4 showed tht it ws possible for one gent of quite high rnk to retin its socil strtegy even fter ll other gents hve dopted the sme socil strtegy, i.e. the countercting force of the lone gent overrides the collective diffusion force of ll other gents. Moreover, if we increse the socil rnk of the lone gent significntly, it is possible tht its socil strtegy will diffuse to ll other gents, which is n exmple of collective elite diffusion. We note tht rel world situtions re often chrcterized by multiple strtegies. For exmple, commnding officer my wlk mong his troops in formtion, nd so hs completely different orienttion to everyone else. The troops understnd the sitution nd so unify their own orienttion nd do not blindly trck the officer s orienttion. In nother simple exmple, the commnder hs n bsolute power nd cn order ll soldiers to follow his direction; the soldiers hve to obey the order. Though we explined our forml frmework using the exmple of crowd orienttion, it offers strong generlity. The frmework nd lgorithms described re quite generl nd cn be pplied in mny other cses simply by mking smll djustments. Our gent socil strtegy diffusion model is bsed on the diffusion of strtegy from collective gents to one gent step by step. This involves significnt time costs when the number of gents is lrge. Such diffusion model my be prcticl in some rel-world situtions, however, which re not fully representtive of relity s whole. In rel-world situtions, there re mny concurrent diffusion movements between groups. Therefore, in our future works, we will explore the concurrent diffusion from collective gents to collective gents. Acknowledgements This work is supported by JSPS Reserch Grnt No References [Blzer nd Tumel, 2003] Wolfgng Blzer, Bimo Tuomel. Collective intentions nd the mintennce of socil prctices. Autonomous Agents nd Multi-Agent Systems, 6: 7-33, [Boell nd vn der Torre, 2005]. Guido Boell, Leendert vn der Torre. The evolution of rtificil socil systems. Proceeding of the Nineteenth Interntionl Joint Conference on Artificil Intelligence (IJCAI05), pges , [Fitoussi nd Tennenholtz, 2000] Dvid Fitoussi, Moshe Tennenholtz. Choosing socil lws for multi-gent systems: Minimlity nd simplicity. Artificil Intelligence, 9: 6-0, [Hveliwl, 2003] Ther H.Hveliwl. Topic-sensitive pgernk: context-sensitive rnking lgorithm for web serch. IEEE Trnsctions on Knowledge nd Dt Engineering, 4 (5): , July/August [Jing nd Jing, 2005] Yi-Chun Jing, J.C.Jing. A Multigent coordintion model for the vrition of underlying network topology. Expert Systems with Applictions, 2(29): , [Jing nd Ishid, 2006] Yichun Jing, Toru Ishid. Evolve individul socil lws to globl socil convention by hierrchicl immedite diffusion. Proceedings of the AAMAS-06 Workshop on Mssively Multi-Agent Systems, pges:25-38, [Jing nd Ishid, 2007] Yichun Jing, Toru Ishid. Locl interction nd non-locl coordintion in gent socil lw diffusion. Expert Systems with Applictions, (34), [Krus, 997] Srit Krus. Negotition nd coopertion in multi-gent environment. Artificil Intelligence, 94: 79-97, 997. [Pcheco nd Crmo, 2003] Olg Pcheco, Jose Crmo. A role bsed model for the normtive specifiction of orgnized collective gency nd gents interction. Autonomous Agents nd Multi-Agent Systems, 6: 45-84, [Shohm nd Tennenholtz, 995] Yov Shohm, Moshe Tennenholtz. On socil lws for rtificil gent societies: off-line design. Artificil Intelligence, 73: , 995. [Shohm nd Tennenholtz, 997] Yov Shohm, Moshe Tennenholtz. On the emergence of socil conventions: Modeling, nlysis nd simultions. Artificil Intelligence, 94: 39-66,