Go Lance - Homework Problem

Consider the following situation:

A group of, say, 20 bike riders are competing in a long road race. In any pack of riders, the leader provides a big benefit to the other riders in the pack, and also receives a slight advantage over riding alone. What happens?

1. Model, using whatever techniques you wish, the above scenario.
2. Explicitly state your model and key assumptions.
3. Summarize key results.
4. Suggest some potentially interesting future directions and questions for the model.
5. Suggest some standard social science scenarios that could be usefully modelled using such a process.

Each biker competing in a single line road race follows a simple set of heuristics(tortoise, hare, free-rider). The model was designed to explore the impact of biker strategy and ability on individual and group (the formation of packs)outcomes.  The program was coded in NetLogo and may be run and explored with different parametrisations below.

Population - set the sliders below the SETUP button to change the number of bikers assuming each strategy. 

Draft effect - the energy credits (equivalent to potential distance travelled) gained by followers (riders immediately behind another agent) and leaders (riders at the front of a pack) are set on the sliders to the right. 

Heterogeneity in ability – incremental energy available to each rider at each time step is a uniformly distributed integer with a lower bound of one and an upper bound set through the "Energy_upper_bound" slider.

Forward vision – Agent’s forward vision (vf) is a linear function of their incremental energy (eave) with a multiplier set by the “Forward_Visibility_Multiplier” (s.t., vf = Forward_Visibility_Multiplier *eave).

Tortoises vision – Because tortoises’ strategy does not encode incentives for the use of their accumulated energy stock we assumed that they switch to hare behaviour upon sight of the finish line. Tortoises may have an enhanced vision for this purpose (while still using standard vision vf before the “end game” mode) set in the slider “Multiplier_Tort_Vf_atEndGame”) st. that “end game vision” = Multiplier_Tort_Vf_atEndGame * vf.

Click on the SETUP button to set up the bikers. 

Click on GO to start the bike riders moving across the race space towards the red finish line. Note that you may need to scroll to the right to follow the riders as they progress beyond the edge of your screen (i.e., therace course display may be longer than your screen). You may also calibrate thespeed at which the model runs using the blue slider on the top left of thescreen.

Here is the NetLogo applet of the model.

created with NetLogo

view/download model file: GoLancefinal9.nlogo

T stands for tortoise – green

H stands for hare – grey

FR stands for free rider - red

Final results:

1.The strategy of the first agent to cross the finish line (marked in red on the race space) is displayed on the "Winner's Strategy" monitor.

2.To the right of that you find monitors for the average final rank of each strategy – note that these computations only become complete (and meaningful)once all agents crossed the finish line.

Observing the race:

1."Breed Distribution" plots a time series of the number of agents per strategy still running s.t. decreases represent bikers crossing the finish line.

2."Average Rank per Breed" is also a times series plot tracking the relative average performance per strategy of the agents still on the racecourse(i.e., as agent’s start to finish the plot only refers to the remaining racers).

1. The model is conceptualised such that riding in a pack confers some benefit (accumulation of energy in a stock est). However, because we assumed that agents cannot share the same spot this benefit comes at some cost - breaking out of a pack requires enough energy (stored or possessed through ability) to overcome all adjacent riders. This assumption attempts to capture bikers’ closing in on competitors that attempt passing at low speeds.

2. As noted, bikers’ forward visibility (vf) varies and is fully correlated with their ability (incremental energy). This assumption is justified by the facts that: a) the faster a biker is riding (controlled by energy) the further ahead they should be able to see; and b) riders with more ability are often better riders with higher awareness of their surroundings. 

3. Schedule - Agent creation and move order follows the sequence T FR H ,…,  T FR H ...until all the population goes through the loop (if the number of agents’ with each strategy differs the last loops are left for the largest populations).

NOTE: Observations are based only on visual inspection of runs with different parameterizations (no rigorous experimentation or sensitivity analysis was conducted).

The most general observation is that there is a lot of variability in outcome by strategy across the tested parameter space.  It seemed that overall there was the following rank: hares, free-riders, and tortoises.  Hares win often. Free-riders sometimes win and tortoises very rarely do.  Overall, all strategies tend to ride in packs. 

Given their full exhaustion strategy  (and free-riders strategy to follow) hares often lead packs. Thus, when the leader energy benefit increases (while the follower benefit is fixed) hares performance improves.

To be successful, free riders need to ride mixed strategy packs long enough to accumulate enough wind draft follower energy credits to win. Naturally, free-riders performance varies positively with the ratio of follower to leader energy credit points. Furthermore, we often observe single strategy free-rider packs stuck in the last position, leading to a significant decrease in the overall average ranking for the strategy.

Tortoises seem to do best in intermediate situations were neither free-riders nor hares have a clear advantage.

Increased heterogeneity in ability (higher upper bound for the incremental energy distribution) seems to results in better free-rider performance.  Perhaps increased heterogeneity facilitates the emergence of more mixed strategy packs, allowing free-riders to cash in on their strategy. Furthermore, because average pack size is smaller, bikers are better able to use their stored energy credits.

Strategies: Add more/different strategies, including strategies that are based on perceptions of others (characteristics and/or strategy) and cooperation. Consider implementing an El Farol type of approach, i.e. endogenous strategy choice.

Sequentiality: Order of agent moves could be random, ranked by position, ranked by average or available energy.

Topologies: Alternative topologies like CA, continuous Cartesian space, realistic space (terrain type, etc.).

Physics: Realistic motion, overcoming, etc.

1. Does the outcome vary depending on number and heterogeneity in ability of bikers; composition of biker strategy; length of race; credit given to followers and leaders?
2. What happens if ability is correlated with strategy chosen?
3. Can strategy choice overcome deficiency in fitness? Is there an optimal choice for a biker with a specified ability (and does the optimal choice vary by ability level)?

The key questions that can be investigated in this model are:
1. In a game with individual prizes but strong interaction effects, how does an individual find an intertemporal balance of cooperation and competition?
2. How to cooperate to exclude competitor group(s) from having a chance to win?
3. When to defect from the cooperative group and compete for individual victory?

Applications:
1. General group formation / cooperation mechanisms (e.g., tags).
2. Perception mechanisms - how to evaluate perceived threat level of opponent and select cooperation group?
3. Applied example - workplace teams with hierarchical remuneration systems.

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In this model, the road is broken into unit spaces. Except for the starting space, two bikers can never occupy the same space. The road is one space wide, so bikers can only pass if they have enough ability to overtake all bikers in front of them. 

Note on Space/Coordinates: the race is run on the integer space {- screen-edge-x,..., 0} from left to right, with 0 as the finish line.

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color color based on strategy (or breed)
eave energy on average (reflects ability)  - random uniform integer  [1 , random energy_up_bound]
est energy stock at t initialized to zero

vf forward visibilityvfMultiplier * eave
move where biker moves ina time step
d_move where biker desires to move
prevPt where biker was before step
toFollow is there a pack to join (yes=1)
rank position at the end of the race

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ticks time step counter initialized to 0
credFollow energy credit for following (to est)
lead energy credit for leading (to est)
nt # of bikers with tortoise strategy
nh # of bikers with hare strategy
nf # of bikers with free-rider strategy
numFinish counter for bikers program stops when = nt+nh+nf

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Tortoise: Maintain average speed - don’t push anything! Travel as close to eave as possible, moving back if spaces are full with no preference for joining packs or riding alone. If the finish line is in sight, use all of est to bolt ahead in the endgame. NOTE: As a “reward” for riding slow and steady throughout the race, the tortoise may be able to see the finish line further than their visibility, allowing them to bolt once the finish line is within “end game vision” = x * vf.

Hare: Give it all you have got - full exhaustion! Travel as close to eave+est as possible, moving back if spaces are full with no preference for joining packs or riding alone

Free-Rider: Take the easy way (ride in the back of packs and bolt ahead when possible)
Join the pack that is as far ahead as possible, but no further than min(biker’s visibility, eave+est). If no pack is available, move eave and save stored energy.

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Agent Creation: Agents are created one at a time in a loop by strategy type: Tortoise; Free-rider, Hare. It is possible to change the code to modify the order of breed creation to investigate any bias created.

Schedule:
1. Move with asynchronous updating, move sequence = creation rank
2. Update energy stock, est
3. Verify if race is completed (if so, assign rank)

4. Calculate rank of agents in the race course.

4. Stopping criteria: if biker crosses the finish line, they die and numFinish is incremented by one. The model should stop running when all agents have crossed the finish line.

5. Visualisations

NOTE: Creation order equals move sequence – In NetLogo, if you “ask turtles”, or “ask a whole breed”, the turtles are scheduled for execution in ascending order by ID number. If you “ask patches”, the patches are scheduled for execution by row: left to right within each row, and starting with the top row.  Once scheduled, an agent's "turn" ends only once it performs an action that affects the state of the world, such as moving, or creating a turtle, or changing the value of a global, turtle, or patch variable (setting a local variable doesn't count). It is referred in the documentation that an option for randomized scheduling is planned for future versions of NetLogo.

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We looked at NetLogo for the very first time here. Although things seem to be working as they should, it is very possible that there are bugs in this program.