The figure below depicts the electric network which connects 11 generators to 11 customers. Generators are placed at dark nodes while customers are placed at light ones. The two numbers beside each customer node are the demands in high and low demand periods. The numbers in transmission lines are capacities and fees to ship one unit of power. The capacity of lines directly connected to generators is 100 units and the fee is 0.01. The capacity of lines directly connected to customers is 80 units and the fee is 0.01. Four tournaments were carried out with slightly different generators (the production capacities took on values 100, 80, 60 and 40, but everything else was unchanged).
Generators cannot accumulated deficit for more than 8 periods in a row (a generator with 8 consecutive negative profit periods is eliminated of the tournament). Similarly, customers with negative bankroll in 8 consecutive periods or bankroll below the maximum debt are eliminated of the tournament.
All generators and customers have the same characteristics as depicted by the tables below.
| Parameter | Value for Tournament | |||
|---|---|---|---|---|
| tourn 1 | tourn 2 | tourn 3 | tourn 4 | |
| production capacity (q2) | 100 | 80 | 60 | 40 |
| fixed cost (fc) | 2.63 | 2.63 | 2.63 | 2.63 |
| units with low cost (q1) | 50 | 40 | 30 | 20 |
| low cost units (u1) | 0.30 | 0.30 | 0.30 | 0.30 |
| high cost units (u2) | 0.40 | 0.40 | 0.40 | 0.40 |
| parameter | value |
|---|---|
| demand for high consumption periods (d1) | 60 |
| demand for low consumption periods (d2) | 30 |
| budget | 50.11 |
| parameter a (carry over) | 0.52 |
| parameter b (penalty) | 0.54 |
| maximum debt | 50.11 |
Agents submitted by 4 groups and the staff traded in the market for 50 periods, where each period has 120 iterations. Their performances are shown in the tables below. Agents with no points were eliminated from the tournament.
| Group | Pair | Player | Profit | Tourn 1 | Tourn 2 | Tourn 3 | Tourn 4 | |||
|---|---|---|---|---|---|---|---|---|---|---|
| Cash | Points | Cash | Points | Cash | Points | Cash | Points | |||
| 1 | 1 | 1 | -16.19 | 0 | -9.80 | 0 | -15.67 | 0 | 137.01 | 3 |
| 1 | 2 | 2 | -17.50 | 0 | -17.35 | 0 | -16.74 | 0 | -17.14 | 0 |
| 1 | 3 | 3 | 1,109.20 | 9 | 1,030.16 | 9 | 820.40 | 8 | 549.89 | 5 |
| 2 | 1 | 4 | -19.67 | 0 | -6.09 | 0 | 226.82 | 6 | 649.86 | 8 |
| 2 | 2 | 5 | -20.10 | 0 | 102.56 | 5 | 199.49 | 5 | 624.05 | 7 |
| 2 | 3 | 6 | -18.74 | 0 | 259.43 | 6 | 198.97 | 4 | 614.18 | 6 |
| 3 | 1 | 7 | 1,042.43 | 7 | 917.17 | 7 | 738.60 | 7 | 472.28 | 4 |
| 3 | 2 | 8 | 1,503.21 | 10 | 1,299.73 | 10 | 1,065.90 | 10 | 775.39 | 10 |
| 3 | 3 | 9 | -17.30 | 0 | -16.04 | 0 | -16.04 | 0 | -17.29 | 0 |
| 4 | 1 | 10 | 1,104.87 | 8 | 1,010.87 | 8 | 845.98 | 9 | 680.40 | 9 |
| staff | 1 | 11 | 1,995.70 | 11 | 1,812.04 | 11 | 1,436.92 | 11 | 985.97 | 11 |
| Total | 6,645.91 | 45 | 6,382.68 | 56 | 5,484.63 | 60 | 5,454.60 | 63 | ||
| Group | Pair | Player | Profit | Tourn 1 | Tourn 2 | Tourn 3 | Tourn 4 | |||
|---|---|---|---|---|---|---|---|---|---|---|
| Cash | Points | Cash | Points | Cash | Points | Cash | Points | |||
| 1 | 1 | 12 | 985.74 | 10 | 867.23 | 10 | 594.55 | 3 | 39.12 | 3 |
| 1 | 2 | 13 | 988.50 | 11 | 867.33 | 11 | 575.26 | 2 | 37.94 | 2 |
| 1 | 3 | 14 | 16.10 | 1 | 16.10 | 1 | 16.10 | 1 | 16.10 | 1 |
| 2 | 1 | 15 | 765.91 | 4 | 732.24 | 4 | 795.39 | 7 | 487.17 | 6 |
| 2 | 2 | 16 | 786.43 | 7 | 770.56 | 9 | 806.82 | 9 | 557.45 | 8 |
| 2 | 3 | 17 | 777.15 | 6 | 753.50 | 6 | 787.57 | 5 | 585.26 | 9 |
| 3 | 1 | 18 | 696.18 | 2 | 633.64 | 2 | 659.57 | 4 | 284.58 | 4 |
| 3 | 2 | 19 | 774.93 | 5 | 762.23 | 8 | 806.84 | 10 | 585.40 | 10 |
| 3 | 3 | 20 | 787.38 | 8 | 759.08 | 7 | 803.02 | 8 | 608.21 | 11 |
| 4 | 1 | 21 | 762.60 | 3 | 743.41 | 5 | 793.44 | 6 | 484.23 | 5 |
| staff | 1 | 22 | 849.02 | 9 | 716.46 | 3 | 840.36 | 11 | 535.34 | 7 |
| Total | 8,189.94 | 66 | 7,621.78 | 66 | 7,478.92 | 66 | 4,220.80 | 66 | ||
| Group | Pair | Generator | Customer | Total | |||||
|---|---|---|---|---|---|---|---|---|---|
| Player | Cash | Points | Player | Cash | Points | Cash | Points | ||
| 1 | 1 | 1 | 95.35 | 3 | 12 | 2,486.64 | 26 | 2,581.99 | 29 |
| 1 | 2 | 2 | -68.73 | 0 | 13 | 2,469.03 | 26 | 2,400.30 | 26 |
| 1 | 3 | 3 | 3,509.65 | 31 | 14 | 64.40 | 4 | 3,574.05 | 35 |
| 2 | 1 | 4 | 850.92 | 14 | 15 | 2,780.71 | 21 | 3,631.63 | 35 |
| 2 | 2 | 5 | 906.00 | 17 | 16 | 2,921.26 | 33 | 3,827.26 | 50 |
| 2 | 3 | 6 | 1,053.84 | 16 | 17 | 2,903.48 | 26 | 3,957.32 | 42 |
| 3 | 1 | 7 | 3,170.48 | 25 | 18 | 2,273.97 | 12 | 5,444.45 | 37 |
| 3 | 2 | 8 | 4,644.23 | 40 | 19 | 2,929.40 | 33 | 7,573.63 | 73 |
| 3 | 3 | 9 | -66.67 | 0 | 20 | 2,957.69 | 34 | 2,891.02 | 34 |
| 4 | 1 | 10 | 3,642.12 | 34 | 21 | 2,783.68 | 19 | 6,425.80 | 53 |
| staff | 1 | 11 | 6,230.63 | 44 | 22 | 2,941.18 | 30 | 9,171.81 | 74 |
Allocative efficiency of markets can be defined as the total profit actually earned by all the traders divided by the maximum total profit that could have been earned by all the traders (i.e., the sum of producer and consumer surplus). The table below depicts the allocative efficiency of the markets where the agents played as traders.
| Market or Tournament | Actual Profits | Maximum Profits | Efficiency | ||||
|---|---|---|---|---|---|---|---|
| Generators | Customers | Total | Generators | Customers | Total | ||
| tourn1 | 6,645.91 | 8,189.94 | 14,835.85 | 7,613.10 | 9,703.10 | 17,316.20 | 85.67% |
| tourn2 | 6,382.68 | 7,621.78 | 14,004.46 | 7,370.22 | 9,703.10 | 17,073.32 | 85.64% |
| tourn3 | 5,484.63 | 7,478.92 | 12,963.55 | 7,096.10 | 9,703.10 | 16,799.20 | 77.15% |
| tourn4 | 5,454.60 | 4,220.80 | 9,675.40 | 5,819.00 | 8,756.00 | 14,575.00 | 66.38% |