Collective actions and expectations

1. Collective actions andexpectations Belev Sergey, Kalyagin Grigory Moscow State University

2. Introduction to problem «Ifthe same individualstake part inthe repeatinggame, the tendency to cooperation increases significantly. And there is no doubtthat repeatingmultiplies the cooperativeresult, involvingthose, whoinsingle-stagegameshowed themselvescautious and suspicious» (McCabe, Rassenti, Smith,1996)

3. Possible solution In repeating games individualsgain experience and according to It form their expectationsconcerningfurther interactions. Individuals learn playing again and again

4. The model for simulation Macy’s learning model (1990): Payoff function of jth individual : Cj– binary choice (to take part (Cj=1)/not to take part (Cj=0) in the collective action), N – group size, J – competitiveness of good (J=0 –full competitiveness, J=1 – no competitiveness), R – payoff of all group members within 100% level of participation in the collective action, L – share of the maximum total payoff (R) received by all group members

5. The model for simulation(2) Macy’s production function L (1990): M – slope parameter (М=1 – approaches linearity, М=10 - s-shaped curve) p – share of volunteers

6. Payoff and participation

7. The model for simulation(3) The innovation to Macy (1990): Individualmakes decision to take part or not, comparingexpectedbenefits:

8. To be or not to be…… a volunteer? To be, if expected payoff is more whenhe or she takes part than when he or she don’t:

9. The model for simulation(4) The expected level of other members’ participation : actual share of volunteers at i period of t-1 periods of interaction. weight of other members’ actual participation at i period. random error of individual calculations, uniformly distributed at [-a;a] shortness of memory (as more, so shortly) δ

10. The example of calculation • δ =0,5 = 0,211* +0,316* +0,474* +

11. Obvious results • The more group size (N) is, the less expected marginal benefits from participation are • The less competitiveness (0→ J →1) is ORthe more the maximum payoff (R) is, than the more the maximum size of group, where the collective action could take place, is

12. Obvious results Individual takes part, if expected level of cooperation is near 0,5, and doesn’t, if he or she expects eitherfull participation or noparticipation at all

13. Conditions of simulations With the help of computer simulations we analyze the impact of shortness of memory, size of random error and initial expected level of cooperation. We vary only the size of J instead of varying M, N, R within J. N=20 is less than maximum group size for certain M, R andJ.

14. Simulations. What are the model conditions when the actual share of volunteers is dynamically stableand equals 0? Assumption 1: if initial expectations (p0) are near 0 or 1 Assumption 2: if size of error (a) is small Assumption 3: if the memory is short (δ is big)

15. Simulations(2). Assumption 1. According to inputted dataindividual takes part if and only if pe € [0,334; 0,616] . p0 ≤ 0,3 (≤ 6 from 20).

16. Expected participation 0,80 0,70 0,60 0,50 0,40 0,30 0,20 0,10 0,00 0 10 20 30 40 50 60 70 80 90 100 Actual participation 1,20 1,00 0,80 0,60 0,40 0,20 0,00 0 10 20 30 40 50 60 70 80 90 100 expected particapation

17. Expectedparticipation 0,30 0,25 0,20 0,15 0,10 0,05 0,00 0 10 20 30 40 50 60 70 80 90 100 Actual participation 0,30 0,25 0,20 0,15 0,10 0,05 0,00 0 10 20 30 40 50 60 70 80 90 100 -0,05

18. Simulations (3). Assumption 1. According to inputted dataindividual takes part if and only if pe € [0,334; 0,616] . p0≥0,65 (≥13из 20).

19. Expected participation 1,00 0,90 0,80 0,70 0,60 0,50 0,40 0,30 0,20 0,10 0,00 0 10 20 30 40 50 60 70 80 90 100 Actual participation 1,20 1,00 0,80 0,60 0,40 0,20 0,00 0 10 20 30 40 50 60 70 80 90 100

20. Simulations (3). New Assumption. If expected level atthe thirditeration is less than critical value (0,334), than we could get at low expectation’s trap. If J=0,15 the interval is [0,395; 0,556]

21. Expected participation 1,00 0,90 0,80 0,70 0,60 0,50 0,40 0,30 0,20 0,10 0,00 0 10 20 30 40 50 60 70 80 90 100 Actual participation 0,80 0,70 0,60 0,50 0,40 0,30 0,20 0,10 0,00 0 10 20 30 40 50 60 70 80 90 100 -0,10

22. Simulations (4). Assumption 2. The impact of the error size. False expectations near critical values could change the destiny of collective action.

23. Expected participation 0,80 0,70 0,60 0,50 0,40 0,30 0,20 0,10 0,00 0 10 20 30 40 50 60 70 80 90 100 Actual participation 0,90 0,80 0,70 0,60 0,50 0,40 0,30 0,20 0,10 0,00 0 10 20 30 40 50 60 70 80 90 100

24. Assumption 3 short memory. The longer memory is, the less possible the high expectation’s trap is Simulations (5).

25. Expected participation • 1,00 0,90 0,80 0,70 0,60 0,50 0,40 0,30 0,20 0,10 0,00 0 10 20 30 40 50 60 70 80 90 100

26. Actualparticipation 0,80 0,70 0,60 0,50 0,40 0,30 0,20 0,10 0,00 0 10 20 30 40 50 60 70 80 90 100 -0,10

27. The decision to take part or not dependsonexpected level of other group member’s cooperation and could be illustrated as U-inverted curve: take part close to 0,5 and notclose to 1 or 0 The impact of initial expectations is crucial: group members could face the low expectation’s trap The high expectation’s trap is possible only if the average expected share of participation at the second iteration is less than crucial value Random errors could help collective action to take place (or not) if expected participation is close to critical value Conclusions

28. Thank you !!!