This is my submission for Complexity Explorer's Complexity Challenge 2018.
For this challenge, I created 9 agent strategies, grouped into 3 categories.
No Heuristics
- Stable - Always on the stable pool. Risk averse
- Sticky - Stay in the same pool as the initial
- Random - Doesn’t look at prior payoffs
- Always new - Always change pool
Looks at the # of agents
- Bandwagon - Always choose a pool that has the most number of agents in the previous time step
- Safe - Always choose a pool that had the most agents with payoffs in the previous time step
- Frost - Always choose the least chosen pool (based on average number of agents that have previously chosen it). Inspired by the poem The Road not Taken, hence the name.
Looks at payoffs
- High Roller - Always choose a pool with the highest payoff in the previous time step
- Opportunistic - Always choose a pool with the highest average payoff
For my challenge solution, each experiment has 100 agents and run for 100 timesteps. Because there is randomness in the behavior of some agent strategies, each experiment is repeated 5 times (trials) and the average total wealth is used for analysis.
There are 3 pools: stable, low and high. The stable pool always give a payoff of 1 to all agents in it. The low pool gives a payoff of 0 or 40 with equal probabilities. The high pool has 75% chance of giving 0 payoff and 25% of giving 80 payoffs. Both low and high pools divide the payoff among the agents in them. If agents transfer pools, tau is deducted from their wealth, which has a value of 1. All agents cannot know the wealth of other agents and where they will go next.
Since there are 9 different agent strategies, I played around with different combinations. Aside from running experiments where all agents follow the same strategy, I also run experiments that had 2 to 9 combinations of strategies deployed, with equal distributions. For example, there are experiments with 50-50 random and safe agents, and 33-33-34 random, sticky and safe agents. Overall, there are 511 experiments and in the following sections, we will look at some of the significant behaviors that emerged.
Table 1. Average total wealth of experiments with only 1 strategy.
| Strategy | Average Total Wealth |
|---|---|
| stable | 10,000.00 |
| safe | 9,662.40 |
| sticky | 7,328.60 |
| bandwagon | 5,287.40 |
| opportunistic | 1,139.40 |
| random | 1,015.60 |
| highroller | 348.80 |
| alwaysnew | 167.20 |
| frost | 140.40 |
High Wealth
From Table 1, we can see that the experiment with 100 stable agents got the highest average total wealth because none of the agents were changing pools. The next highest are the safe agents mainly because all of them eventually stayed in the stable pool after some timestep, causing no more transfers. Sticky agents also got a high average total wealth because they weren't moving pools at all. So even though some of them might not get payoffs on some timesteps, the total wealth never dipped because they stayed on the same pool since the beginning. And although the bandwagon agents have high tendencies of moving, only a few of them transfer pools at one time.
Low Wealth
The lowest total wealth among the strategies was from the frost agents because large numbers of agents move at a time, hence the large drop and almost zero wealth. The alwaysnew agents also had very low total wealth because all agents move every timestep. Random agents fared relatively better because they might not move at all, reducing tau deductions. Highroller agents also had low wealth because they are easily attracted to pools that give high payoffs in the previous timestep. In that case, they have a tendency to move often even though they aren't getting the payoff they expected from their choices (i.e. moving to a pool that previously paid 10 but gave 0 in the current timestep). Opportunistic agents almost behave the same but they have the advantage of better hindsight. These agents wouldn't easily go to a pool that previously gave a high payoff because of a low average payoff.
Figure 1. Average total wealth over time of experiments with only 1 strategy.
From Figure 1, we can see that the experiments with pure stable, sticky, safe and bandwagon agents had a steady increase in total wealth over time, with no dips. The all-random and all-opportunistic agent experiments show very minimal increases in total wealth over time. Although the highroller, alwasynew and frost agents had momentary increases in wealth at a hadnful of timesteps, they never really sustained an upward trend. From the figure, we can even see them having slow and steady decreases in weatlh over time.
Figure 2. Distribution of average total wealth from experiments with at least 2 strategies.
As mentioned, I played around with different combinations of agent strategies. I will use the highest average total wealth from the 1-strategy experiments as basis of comparison. We can say that a combination performed well if they had an average total wealth above 10,000.
Figure 2 shows the Gaussian distribution of the average total wealth. Most of the combinations had average total wealth between 2,379 to 8,379. In the following sections, I will discuss which groups of agent strategies contributed to the high and low average total wealth from the experiments.
Table 2. The best performing combinations compared to the average total wealth of the all-stable experiment.
| Best Performing Combinations | Average Total Wealth |
|---|---|
| sticky & safe | 11,184.00 |
| stable & sticky | 10,481.00 |
| stable, sticky & bandwagon | 12,062.40 |
| stable, sticky & safe | 11,616.60 |
| sticky, safe & bandwagon | 10,376.00 |
| stable, safe & bandwagon | 10,007.20 |
| stable, sticky, safe & bandwagon | 11,683.60 |
| stable, random, safe & bandwagon | 10,445.20 |
| stable, safe, alwaysnew & bandwagon | 10,013.80 |
| stable, sticky, safe, bandwagon & opportunistic | 11,010.80 |
| stable, sticky, safe, highroller & bandwagon | 10,161.20 |
| stable, sticky, safe, frost & bandwagon | 10,105.80 |
Out of the 502 experiments with more than 1 agent strategy involved, only 12 combinations had an average total wealth over 10,000. Certainly, the presence of risk-averse agents like stable, safe and sticky are keeping the total wealth high which gives risk-taking agent strategies enough leg room to gamble with higher payoffs. However, this is only true if they are majority of the agents in the experiment. If we look at Table 2 for example, even though the combination stable, sticky, safe, frost & bandwagon has the worst performer frost agents, they still managed to amass a lot of wealth because the frost agents never had a chance to drag everyone and cause dips in total wealth value. 5,703 is the lowest average total wealth when majority of the agent strategies are from those three.
Table 3. The worst performing combinations compared to the average total wealth of the all-stable experiment.
| Worst Performing Combinations | Average Total Wealth |
|---|---|
| random & alwaysnew | 805.00 |
| alwaysnew & highroller | 379.00 |
| random, alwaysnew & highroller | 706.00 |
At the bottom of the rankings (Table 3), combinations with majority of random, alwaysnew and highroller agents usually yield low average total wealth. This is mainly due to their randomness and high attraction to good immediate past payoffs. We can say that they represent a sample of the population who are less pragmatic and impulsive.
After looking at all the experiments, I noticed that the bandwagon and opportunistic strategies amplifies the effect of the best and worst performing combinations of agent strategies. For example, 9 out of 12 best performing combinations had bandwagon agents along with best performing stable, safe and sticky agents. If they are not yet the majority, bandwagon agents has helped pull up the total wealth for them. However, I also saw bandwagon and opportunistic agents exacerbating the negative effects of random, alwaysnew and highroller agents.
These experiments were run with just a tau of 1 and the agents never really a threshold for the least amount of wealth they should maintain before taking tau deductions.
From these experiments, I saw how the major presence of stable, safe and or sticky agents can outperform any combination of agent strategies because of their conservative nature. I also saw how the impulsiveness of the random, alwaysnew and highroller agents definitely dragged their performance, with most of their combinations never reaching a wealth of 1,000. There are also the balanced bandwagon and opportunistic strategies that can amplify the effects of whichever class of strategies holds the majority. In a way, we can see that these two strategies promoted cooperation even though the individual wealth of other agents were not known.
The agent-based model is implemented in Python 3.6.6 and the code are written in main.py.
All experiment outputs like total wealth and population per pool per timestep are saved in CSVs and can be found in the /experiments folder.
Total wealth over time for experiments with 2 different agent strategies
Total wealth over time for experiments with 3 different agent strategies
Total wealth over time for experiments with 4 different agent strategies
Total wealth over time for experiments with 5 different agent strategies
Total wealth over time for experiments with 6 different agent strategies
Total wealth over time for experiments with 7 different agent strategies
Total wealth over time for experiments with 8 different agent strategies
Total wealth over time for experiments with 9 different agent strategies
