# Complexity Explorer Santa Few Institute

## Spring 2018 Complexity Challenge

Proposed by: The Santa Fe Institute

Contact email: cxc@complexityexplorer.org

Challenge Question:

### Consider the following system:

Suppose there are fifty (50) agents.  At each time step, each agent must decide to locate at one of three possible pools (investing options) described below. These pools are called: stable, high, and low. Agents must choose their pool without knowing what the other agents have picked, and can only rely on information from prior time steps (in particular, each agent must make their choice knowing only the number of agents (but not their identity) that located at each pool and each pool's payoff for all prior time steps). Agents are allowed to switch pools at the start of any time step, but to do so costs the agent a payment of tau (where 0 <= tau).  You are not charged tau for your first choice of a pool.

Once all agents have selected a pool, each pool provides a payoff for the time step.

• Any agent that locates at the stable pool always receives \$1 at the end of the time step.  The other two pools each pay a random amount (see below) that must be split evenly among all of the agents that selected that particular pool at that time step.  For example, if twenty (20) agents had chosen a pool that paid \$40 that period, each agent would receive a payment of \$2 (\$40/20 agents) for that period.

The payoffs of the remaining two pools are as follows:

• The high pool pays \$80 (that must be split evenly among the residents of that pool) with probability 0.25 and \$0 otherwise (0.75 probability), and the *low* pool pays \$40 (again, split evenly) with probability 0.5 and \$0 otherwise (0.5 probability).   The random payoffs for the high and low pools are independent of one another.

The system runs for 100 time steps, with agents accumulating payoffs at each step.

Explore the general dynamics of the above system, using a diverse set of agents, i.e., agents that have different rules for deciding which pools to invest in.

Analysis of the System

Your analysis should include (but is not limited to):

• What general behaviors arise in this system?  How does the wealth of the agents change over time? At the aggregate level? At the individual level?
• How does the diversity of strategies influence the dynamics of the system?
• Are there generally classes of agent behavior (say, based on what data they use, how they process it, or the agent's overall sophistication) that lead to better performance?
• What happens to the system if you violate one of the original assumptions of the problem and allow the agents to alter their strategies over time by observing the performance and strategic details of the other agents?
• Suppose that meta-agents exist that can coordinate the behaviors of a subset of the agents (and split the resulting payoffs equally across the subset)---how does this impact the system's behavior?
• How do the answers to the above questions change as:
• tau is altered?
• you change the total number of agents in the world?

Solution guidelines: Follow the questions carefully and be sure to address them all in your analysis. Provide a coherent write up and analysis, no longer than five pages, excluding tables and figures, in PDF format. Create a clear, concise video description of the challenge and solution, no longer than three minutes, and no larger than 25mb, in mp4 format. Develop some general theoretical principles of this system. Suggest related literature and future research directions.

### The Tournament

The tournament is a special, optional experience on top of the general Challenge question and submissions.  If you'd like to participate in the tournament, head over to https://www.complexityexplorer.org/challenges/pages/tournament to get instructions. Submission is by June 5th, 2018.

For general Challenge guidelines please go here: https://www.complexityexplorer.org/challenges/pages/guidelines

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Challenge Held:

23 Apr 2018 5pm UTC - 04 Jun 2018 6pm UTC

This challenge is not currently accepting solutions.