1. Network VCM progress report

2. =============================================================== 2009-12-1 =============================================================== Test VCM on 5 different networks, described by Sid in his email, and averaged the contribution of the whole network(20 players), excluding the dummies. So, for each player, his/her utility is calculated only based on his/her 5 neighbors specified by the network graph. In other words, N = 6. The simulation is done for R = 40 runs, T = 10 periods each. Additional parameters: M = 0.4, P = 0.48, B = 22, G = 8 The result is shown in this figure: http://www.cs.sfu.ca/~lshia/personal/econ/vcm_network/presentation/figure_network_all_behavor_all_m0.4_p0.48_b22_g8.pdf http://www.cs.sfu.ca/~lshia/personal/econ/vcm_network/presentation/figure_network_all_behavor_all_m0.4_p0.48_b22_g8.pdf http://www.cs.sfu.ca/~lshia/personal/econ/vcm_network/presentation/figure_network_all_behavor_all_m0.4_p0.48_b22_g8_clean.pdf http://www.cs.sfu.ca/~lshia/personal/econ/vcm_network/presentation/figure_network_all_behavor_all_m0.4_p0.48_b22_g8_clean.pdf (title clean) (exchange.pdf to.eps for the corresponding figures in eps format; exchange.pdf to.txt for the corresponding data) The title of each subplot says which network is used. eg, 4_k_6, 4_k_6_cycle, etc.... In each subplot, three cases were tested: 1) with dummies contributing nothing 2) with no dummies, in place of dummies, put just regular IEL agents. 3) with dummies contributing everything

3. =============================================================== 2010-1-1 =============================================================== Here is the MSE, with respect to the experimental data provided by Sid, given parameters M = 0.4, P = 0.48, B = 22, G = 8: MSE = 0.4221 0.3037 2.3650 2.0102 0.8127 4.1935 0.5976 2.1385 6.8279 2.9767 0.8782 2.0434 1.8821 0.4646 3.6724 where the 5 rows represent 5 networks, 3 columns represent 3 dummy behaviors: dummy = 0; no dummy; dummy = w.

4. ================================================================ 2010-1-23 ================================================================ This time the MSE was calculated by the average of the last 3 periods only, ie. ((ave over last 3) - (predicted over last 3) )^2. All the other parameters were unchanged. Here is the result: MSE = 0.3835 0.0285 0.0450 1.9871 0.6312 0.5644 0.4471 0.1383 1.5037 2.5654 0.3423 0.1386 1.5828 0.1343 1.4769

5. =============================================================== 2010-1-23 =============================================================== After checking equation 6 in that paper, I found some in-consistency in computing MSE. I explained it in following pdf file. http://www.cs.sfu.ca/~lshia/personal/econ/vcm_network/mse.pdf http://www.cs.sfu.ca/~lshia/personal/econ/vcm_network/mse.pdf --- Let's re-compute MSE: Based on equation 1: a) exp10 + exp3 MSE = 1.5976 1.3994 3.8299 3.4006 2.0312 5.8710 1.8713 3.1999 8.1702 4.2628 1.8696 3.3854 3.0093 1.5075 5.0709 b) exp3 only MSE = 1.1782 0.7308 1.0267 2.9876 1.4329 1.7268 1.3297 0.8198 2.4094 3.5076 0.9784 1.0488 2.3778 0.8163 Based on equation 2(As what we have done always): a)exp10 + exp3 MSE = 0.4221 0.3037 2.3650 2.0102 0.8127 4.1935 0.5976 2.1385 6.8279 2.9767 0.8782 2.0434 1.8821 0.4646 3.6724 b) exp3 only MSE = 0.3835 0.0285 0.0450 1.9871 0.6312 0.5644 0.4471 0.1383 1.5037 2.5654 0.3423 0.1386 1.5828 0.1343 1.4769

6. =========================================================== 2010-2-18 =========================================================== Simulations over 5 networks for 3 behaviors for minimizing MSE. Result of grid search: http://www.cs.sfu.ca/~lshia/personal/econ/vcm_network/presentation/gridsearch_report.txthttp://www.cs.sfu.ca/~lshia/personal/econ/vcm_network/presentation/gridsearch_report.txt According to the file above, optimal settings for M = 0.4 are: P = 0.1, B = 24, G = 39. I've generated the plot, using optimal setting : http://www.cs.sfu.ca/~lshia/personal/econ/vcm_network/presentation/figure_network_all_behavor_all_m0.4_p0.10_b24_g39.pdf http://www.cs.sfu.ca/~lshia/personal/econ/vcm_network/presentation/figure_network_all_behavor_all_m0.4_p0.10_b24_g39_clean. pdf (exchange.pdf to.eps for the corresponding figures in eps format; exchange.pdf to.txt for the corresponding data) Each column is different network, each row is different behavior. Green dotted curves are experimental data; red solid lines are simulation result. The corresponding average contributions used to compute mse (data to generate curves) are in the file: http://www.cs.sfu.ca/~lshia/personal/econ/vcm_network/presentation/figure_network_all_behavor_all_m0.4_p0.10_b24_g39.txt

7. ================================================================ 2010-2-28 ================================================================ Modified Initialization: We will use a different type of initialization. Draw initial contributions for t=1 from a normal distribution with mean = 6 and standard deviation = 2.5. Truncate the end points the same way you do it when you do experimentation from the normal distribution. In other words, the initialization was done by drawing from a normal distribution with mean = 6 and standard deviation = 2.5. The values out of range [0,10] were truncated to 0 and 10 respectively. Compute the MSE the same way, using the average over 10 periods, and the average over last 3 periods. We would like to see the numbers, the values for the smallest MSEs, and a graph with 5 subplots, for each of the 5 networks, using P,B, G that result in the min MSE. ---------------------------------------------------------- Result of all 3 behaviors with the new initialization: gridsearch report: http://www.cs.sfu.ca/~lshia/personal/econ/vcm_network/presentation/gridsearch_report_setrandom.txt Plots with the optimal set of P, G, B = [0, 10, 32]: http://www.cs.sfu.ca/~lshia/personal/econ/vcm_network/presentation/figure_network_all_behavor_all_m0.4_p0.00_b10_g32_rand_init.pdf http://www.cs.sfu.ca/~lshia/personal/econ/vcm_network/presentation/figure_network_all_behavor_all_m0.4_p0.00_b10_g32_rand_init_clean.pdf (exchange.pdf to.eps for the corresponding figures in eps format; exchange.pdf to.txt for the corresponding data) Data corresponding to the plots: http://www.cs.sfu.ca/~lshia/personal/econ/vcm_network/presentation/figure_network_all_behavor_all_m0.4_p0.00_b10_g32_rand_init.txt http://www.cs.sfu.ca/~lshia/personal/econ/vcm_network/presentation/figure_network_all_behavor_all_m0.4_p0.00_b10_g32_rand_init.txt

8. ================================================================ 2010-5-11 ================================================================ Level-two neighbors: Basically, one takes into account the payoffs of his neighbors and of the neighbors' neighbors when calculating the payoffs. We do not need to compute MSE, just have IEL sims. The information that subjects had in the experiments does not correspond to what we are now assuming about IEL. I used PGB values = [0.1 24, 39], The following figure was generated for all 3 behavior with level-2 neighboring: http://www.cs.sfu.ca/~lshia/personal/econ/vcm_network/presentation/figure_network_all_behavor_all_m0.4_p0.10_b24_g39_rand_init_level2_n eigh.pdf http://www.cs.sfu.ca/~lshia/personal/econ/vcm_network/presentation/figure_network_all_behavor_all_m0.4_p0.10_b24_g39_rand_init_level2_n eigh_clean.pdf (exchange.pdf to.eps for the corresponding figures in eps format; exchange.pdf to.txt for the corresponding data) And the data used to generate is above figure is at: http://www.cs.sfu.ca/~lshia/personal/econ/vcm_network/presentation/figure_network_all_behavor_all_m0.4_p0.10_b24_g39_rand_init_level2_neigh.txt