Positioning Metrics in Agent Farm

This document defines and explains the various positioning metrics used to analyze how initial agent positioning relative to resources affects outcomes in Agent Farm simulations. These metrics provide complementary perspectives on spatial relationships between agents and resources.

1. Distance-Based Metrics

Distance-based metrics measure the spatial separation between agents and resources, providing insights into resource accessibility.

1.1 Nearest Resource Distance

Definition: The distance from an agent to its closest resource.

Implementation:

• Calculates the Euclidean distance from an agent to each resource
• Takes the minimum of these distances
• Calculated as: min(distances to all resources)

Interpretation:

• Lower values indicate better positioning
• Directly measures immediate resource accessibility
• Strong predictor of early resource acquisition advantage

Strengths:

• Simple and intuitive
• Strongly correlates with early-phase dominance
• Good predictor of initial resource acquisition speed

Limitations:

• Considers only the single closest resource
• Doesn’t account for resource amount or quality
• Ignores competition from other agents

1.2 Average Resource Distance

Definition: The average distance from an agent to all resources in the environment.

Implementation:

• Calculates the Euclidean distance from an agent to each resource
• Takes the mean of these distances
• Calculated as: sum(distances to all resources) / count(resources)

Interpretation:

• Lower values indicate better overall positioning
• Measures general resource accessibility
• Reflects long-term resource acquisition potential

Strengths:

• Provides a broader view of resource accessibility
• Less sensitive to outlier resource positions
• Better predictor of mid-to-late phase performance

Limitations:

• Treats all resources equally regardless of amount
• May overvalue distant resources that are practically inaccessible
• Less predictive of early advantage than nearest distance

1.3 Weighted Resource Distance

Definition: The average distance from an agent to all resources, weighted by resource amount.

Implementation:

• Calculates the Euclidean distance from an agent to each resource
• Weights each distance by the inverse of resource amount
• Calculated as: sum(distance * (1/(resource_amount+1))) / count(resources)

Interpretation:

• Lower values indicate better positioning relative to valuable resources
• Balances distance with resource value
• Reflects quality-adjusted resource accessibility

Strengths:

• Accounts for both distance and resource amount
• Gives more importance to proximity to larger resources
• Better predictor of resource acquisition efficiency

Limitations:

• More complex to interpret
• Sensitive to resource amount distribution
• May undervalue strategic positioning near resource clusters

2. Range-Based Metrics

Range-based metrics focus on resources within an agent’s immediate gathering range, providing insights into immediately accessible resources.

2.1 Resources in Range

Definition: The number of resources within an agent’s gathering range.

Implementation:

• Counts resources where distance to agent is less than or equal to gathering range
• Calculated as: count(resources where distance <= gathering_range)

Interpretation:

• Higher values indicate better immediate resource accessibility
• Directly measures resource options available without movement
• Strong predictor of early-phase resource acquisition diversity

Strengths:

• Directly measures immediate resource accessibility
• Intuitive predictor of early advantage
• Accounts for agent’s gathering capabilities

Limitations:

• Doesn’t consider resource amounts
• Binary inclusion (in range or not) ignores partial accessibility
• Doesn’t account for competition from other agents

2.2 Resource Amount in Range

Definition: The total amount of resources within an agent’s gathering range.

Implementation:

• Sums the amount of all resources within gathering range
• Calculated as: sum(resource_amount where distance <= gathering_range)

Interpretation:

• Higher values indicate better immediate resource wealth
• Measures the quantity of immediately accessible resources
• Strong predictor of early-phase resource acquisition volume

Strengths:

• Combines accessibility with resource quantity
• Better predictor of early resource advantage than simple count
• Accounts for both gathering range and resource wealth

Limitations:

• Doesn’t account for competition from other agents
• May overvalue a single large resource versus multiple smaller ones
• Binary inclusion (in range or not) ignores partial accessibility

3. Relative Advantage Metrics

Relative advantage metrics compare positioning between different agent types, providing insights into competitive advantages.

3.1 Nearest Resource Advantage

Definition: The difference in nearest resource distances between two agent types.

Implementation:

• Compares nearest resource distances between agent types
• Calculated as: agent2_nearest_resource_dist - agent1_nearest_resource_dist

Interpretation:

• Positive values indicate agent1 has an advantage over agent2
• Measures relative proximity advantage to the closest resource
• Predictor of which agent type will acquire resources first

Strengths:

• Directly compares competitive positioning
• Strong predictor of early competition outcomes
• Simple comparative measure

Limitations:

• Considers only the single closest resource
• Doesn’t account for resource amount
• May miss broader positioning advantages

3.2 Resources in Range Advantage

Definition: The difference in the number of resources within gathering range between two agent types.

Implementation:

• Compares the number of accessible resources between agent types
• Calculated as: agent1_resources_in_range - agent2_resources_in_range

Interpretation:

• Positive values indicate agent1 has more resource options than agent2
• Measures relative advantage in immediate resource accessibility
• Predictor of resource acquisition diversity advantage

Strengths:

• Compares immediate resource accessibility
• Accounts for gathering capabilities
• Good predictor of early-phase resource diversity advantage

Limitations:

• Doesn’t consider resource amounts
• Binary inclusion may miss nuanced advantages
• Doesn’t account for resource competition dynamics

3.3 Resource Amount Advantage

Definition: The difference in the total amount of resources within gathering range between two agent types.

Implementation:

• Compares the amount of accessible resources between agent types
• Calculated as: agent1_resource_amount_in_range - agent2_resource_amount_in_range

Interpretation:

• Positive values indicate agent1 has access to more resource wealth than agent2
• Measures relative advantage in immediate resource wealth
• Strong predictor of early-phase resource acquisition volume advantage

Strengths:

• Combines accessibility with resource quantity in comparison
• Most comprehensive relative advantage metric
• Strong predictor of early-phase dominance advantage

Limitations:

• Doesn’t account for competition dynamics
• Binary inclusion may miss nuanced advantages
• May overvalue quantity over strategic positioning

4. Comparison of Positioning Metrics

Each positioning metric highlights different aspects of spatial relationships:

• Nearest Resource Distance answers: “How close is an agent to its nearest resource?”
• Average Resource Distance answers: “How well-positioned is an agent relative to all resources?”
• Weighted Resource Distance answers: “How well-positioned is an agent relative to valuable resources?”
• Resources in Range answers: “How many resources can an agent access without moving?”
• Resource Amount in Range answers: “How much resource wealth can an agent access immediately?”
• Relative Advantage Metrics answer: “Which agent type has better positioning?”

5. Practical Applications

5.1 Predictive Power

Analysis of 500 simulations revealed the following correlations with dominance outcomes:

5.2 Strategic Implications

Understanding positioning metrics helps in:

1. Simulation Design
   • Creating balanced or intentionally imbalanced initial conditions
   • Testing agent resilience to positioning disadvantages
   • Designing environments that test specific agent capabilities
2. Agent Strategy Development
   • Developing adaptive strategies based on initial positioning assessment
   • Prioritizing movement and resource acquisition based on positioning metrics
   • Balancing risk and opportunity based on relative positioning advantages
3. Analysis and Interpretation
   • Explaining simulation outcomes through initial conditions
   • Isolating the effects of positioning from agent characteristics
   • Identifying which positioning aspects most strongly influence outcomes

These positioning metrics provide a comprehensive framework for analyzing spatial relationships in Agent Farm simulations and understanding how initial conditions influence emergent dominance patterns.