Dr Henry Hexmoor Department of Computer Science Southern Illinois University Carbondale 1122012 1 Collective Action approaches Social structure can be basis of collective action Eg organizational rules ID: 1001032
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1. Collective Action in NetworksDr. Henry HexmoorDepartment of Computer ScienceSouthern Illinois University Carbondale11/2/20121
2. Collective Action approachesSocial structure can be basis of collective action. E.g., organizational rules.Incentives for individual participation by others. If participation > threshold, participate; a person only knows the threshold of neighbor.When threshold is low – weak links cause spread and strong links motivate participation. When threshold is high – if great mass participate, Participate.Consider n people with strategies of r revolt (participate) , s (stay at home)Thresholds: θi is the ith agent threshold.If the number of people participating > θi , then i participates.B(i) = { g ε N | j → I } = i’s neighborhood. i ε B(i) reflex property
3. It is common knowledge that j,k B(i), agent knows whether j →k. Action A = ( a1, ……….., an ) 0 if ai = s 1 if ai= r and | { j ε N | aj =r } > = θi Ui (θi , a1,.., an ) = -Z if ai= r and | { j ε N | aj =r } | < θi ↑ very large penalty-Z < -n (n+1)2
4. Example! n=2 θ1 = θ2 = 1, 2 or 3 ● ●State of the world 2 3 1 2 no connection 1’s threshold 2’s threshold Person 1’s states Person 2’s states → r → s → s ↓ ↓ ↓ r s s11 12 1321 22 2331 32 33112131122232132333
5. Example 2: ● ● 1 2Person 1 2 statesPerson 1’s actions Person2’s action22 is equilibrium with mutual actions r and s. In general, with n agents ᴲ (n+1)n states making it intractable.111213212223313233rrrrrssssrrsrrsrss
6. Example 3:1 2 1 2 1 2● ● ● ● ● ● ● ● ●3 3 3Threshold = 2 , state of the world=222Person1 Person1 Person1 221 r 221 r 221 222 r 222 r 212 223 r 223 r 213 224 r 224 r 214 244S
7. Person2 Person2 Person2 221 r 221 r somewhat as person1 222 r 222 r 223 r 223 r 224 r 224 r Person3 Person3 Person3 122 s 222 r 222 222 s 322 s 422 sss
8. Collection actionConsider 1 4 2 3Square of world 3333, threshold = 3.Person 1 knows about 2&4, but ignorant of person 3.No one can revolt with certainty so they all stay home.Square
9. Collection action 1 3 4 2Kite & square only differ in structure.Up to 3 people may revolt in a kite network.This is more common knowledge in Kite than Square.common knowledge is crucial for collection action…common knowledge is also a determinant for social capital.B(i,q) = {J ∈ N| d(J,I <= q} = neighborhood of radios q centered.If q = time, B (I,t) = time varying neighborhood. Kite
10. ReferencesM. Chwe, 1999. Structure and Strategy in Collective Action, in American Journal of Sociology 105, pp.128-156. D. Siegel, 2009. Social Networks and Collective Action, American Journal of Political Science, Vol. 53, No. 1, pp. 122-138, Midwest Political Science Association.