Collective actions and expectations Belev Sergey, Kalyagin Grigory Moscow State University

«If the same individuals take part in the repeating game, the tendency to cooperation increases significantly. And there is no doubt that repeating multiplies the cooperative result, involving those, who in single-stage game showed themselves cautious and suspicious» (McCabe, Rassenti, Smith,1996) Introduction to problem

In repeating games individuals gain experience and according to It form their expectations concerning further interactions. In repeating games individuals gain experience and according to It form their expectations concerning further interactions. Individuals learn playing again and again Possible solution

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

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

Payoff and participation

The innovation to Macy (1990): Individual makes decision to take part or not, comparing expected benefits: The model for simulation(3)

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

The expected level of other members’ participation : The model for simulation(4) 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

The example of calculation ,0000,4000,2110,1230,0760,0480,0310,0200,0130,0090,0060,0040, ,0000,6000,3160,1850,1140,0720,0470,0300,0200,0130,0090,0060, ,000 0,4740,2770,1710,1080,0700,0460,0300,0200,0130,0090, ,000 0,4150,2560,1620,1050,0690,0450,0300,0200,0130, ,000 0,3840,2440,1570,1030,0680,0450,0300,0200, ,000 0,3650,2360,1540,1010,0670,0440,0290, ,000 0,3540,2310,1520,1010,0670,0440, ,000 0,3470,2280,1510,1000,0660, ,000 0,3420,2260,1500,1000, ,000 0,3390,2250,1490, ,000 0,3370,2240, ,000 0,3360, ,000 0, ,000  δ =0,5 = 0,211* +0,316* +0,474* +

1.The more group size (N) is, the less expected marginal benefits from participation are 2.The less competitiveness (0→ J →1) is OR the more the maximum payoff (R) is, than the more the maximum size of group, where the collective action could take place, is Obvious results

Individual takes part, if expected level of cooperation is near 0,5, and doesn’t, if he or she expects either full participation or no participation at all Obvious results

Conditions of simulations NMRδJapopo 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 and J.

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

Assumption 1. According to inputted data individual takes part if and only if p e € Assumption 1. According to inputted data individual takes part if and only if p e € [0,334; 0,616]. p 0 ≤ 0,3 (≤ 6 from 20). Simulations(2). NMRδJapopo ,50,251/60,3

NMRδJapopo ,50,251/60,25

Assumption 1. According to inputted data individual takes part if and only if p e € Assumption 1. According to inputted data individual takes part if and only if p e € [0,334; 0,616]. p 0 ≥0,65 (≥13 из 20). Simulations (3). NMRδJapopo ,50,251/6≥0,65

NMRδJapopo ,50,251/61

New Assumption. If expected level at the third iteration is less than critical value New Assumption. If expected level at the third iteration 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] Simulations (3). NMRδJapopo ,50,151/61

NMRδJapopo ,50,151/61

Assumption 2. The impact of the error size Assumption 2. The impact of the error size. False expectations near critical values could change the destiny of collective action. Simulations (4). NMRδJapopo ,50,25 NMRδJapopo ,50,251/60,25

Assumption 3 short memory Assumption 3 short memory. The longer memory is, the less possible the high expectation’s trap is Simulations (5). NMRδJapopo ,050,151/61 NMRδJapopo ,50,151/61

The decision to take part or not depends on expected level of other group member’s cooperation and could be illustrated as U-inverted curve: take part close to 0,5 and not close to 1 or 0The decision to take part or not depends on expected level of other group member’s cooperation and could be illustrated as U-inverted curve: take part close to 0,5 and not close to 1 or 0 The impact of initial expectations is crucial: group members could face the low expectation’s trapThe 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 valueThe 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 valueRandom errors could help collective action to take place (or not) if expected participation is close to critical value Conclusions

Thank you !!!