Chapter 7 Models (Introduction to VIABLE modeling)

Introduction to VIABLE (Values and Investments from Agent-Based interaction and Learning in Environmental systems) Modeling, using example model described in Box 7.2.

Download NetLogo (v. 6.2) model

Purpose

The model represents a conceptual and theoretical framework that unifies several complex systems modeling approaches for the purposes of better understanding, representing, exploring, and resolving environmental conflict. This method builds on techniques from agent-based modeling (ABM), evolutionary game theory, and system dynamics (SD) modeling.

General State Variables and Scales

V = value achieved by an agent, e.g., indicating something positive or valuable, such as utility or benefit

V^* = a value goal or target value that an agent aims to achieve

C = rate of total agent investment

C⁺ = the highest rate of investment available for an agent

r^k = fraction of investment (priority; ranges from 0 to 1) committed to action path a^k

f = the efficiency of producing value output for a given unit of investment (also can be thought of as a benefit-cost ratio; v/c)

f_ij = interaction efficiencies describing the mutual couplings of a pair of agents, agent i and j which represent the effect of investment by each agent on the value of each other agent. These mutual efficiencies depend on the allocation of investments and action paths taken by agent i as well as other agents (j=1,…,n).

α = adaptation rate of an agent to change priority r^k for investing in an action path a^k.

β = adaptation rate of an agent to change investment C to a target level C*.

κ = the constant adaptation factor within the logistic growth function that affects the speed at which adaptation rates α or β move from 0 to 1 as r or C increase (given as κ^r or κ^C, in the adaptation rule for r and C, respectively).

τ = (tau) the inverse of the fixed rates (τ = 1/α or τ = 1/b) represented as a delay time needed to adapt.

Process Overview and Scheduling

This model depicts a simple conflict simulation interaction between two (2) agents in a hostile or competitive relationship where each agent invests with an objective to reach a target value but at the same time this kind of investments has a negative impact on the value of the other agent (see Chapter 7, Fig 7.3).

The NetLogo model shows the interactions between two agents in which nine cases (1-7, A and B) were investigated corresponding to the example shown in chapter seven. We have set up the interface of this NetLogo model to allow users to select any of these nine (9) cases prior to the model “setup” function, allowing the model to automatically be parameterized to re-create that case. Alternatively, the values of any of the model’s parameters could be modified either through the control button or internally in the model code. The interface is described in more detail in Table 1 (link to pdf).

Design Concepts

Emergence

VIABLE was developed to simulate a conceptual simple interaction between two (or more) agents through the investment in changing the environment to a condition that helps achieving a target value. This kind of interaction could be in a conflictive or cooperative manner. The concept can be further applied in practical cases (as it is in other chapters of the book). The key outputs of this model are depicted by the fluctuating patterns of investment rate and values that changes as agents change adaptation rates and response times. Therefore, the agents can identify the response time that would support achieving the target value.

Adaptation

The agents adapt in response to the resulting value obtained by either increasing the investment rate or decreasing it.

Fitness

The fitness is measured for each agent according to the difference between their target value and their observed value, which is the result of each of the investments of each of the agents.

Prediction

Agents can predict their future value in case other agents do not change their behavior or their adaptation rate. However, it would be difficult for each agent to predict their future value if other agents behave differently at each time step. In this model, we assume that the interaction efficiency and the delay time are constant throughout the running period.

Interaction

The interactions shown in this model are competitive, but  other types of interactions could be also simulated.

Sensing

Each agent is assumed to know the investment rate of the other agent.

Stochasticity

VIABLE is based on pre-identified variables and does not include random variables.

Observation

No real data/observations are included in this model. We show here a hypothetical example of a conflict between two agents and use the model to explore agent interactions and conflict stability.

Initialization

The model begins with an initial investment rate of both agents equal to $30 million, whereas the maximum investment rate is $60 million. The initial values of agent 1 and agent 2 are 0.3 and -0.3, respectively. Both agents have a target value (V*) of zero (for simplicity). The constant adaptation factor κ is 0.005 for both agents. According to the case to be investigated – as described in the book and in Table 2 below — the values of other variables are given. The differences between the cases are due to applying different values of the interaction efficiencies (f_ii, f_ij) and the response time (τ) parameters. The allocation fraction r = 1 as the investment is targeted to only one action pathway.

Table 2: Interaction efficiencies (f_ii, f_ij) and response time (τ) parameter values for the nine cases explored in the book.

Case	τ	f11	f22	f12	f21
1	0	0.01	0.01	-0.01	-0.01
2	1	0.01	0.01	-0.01	-0.01
3	10	0.01	0.01	-0.01	-0.01
4	35	0.01	0.01	-0.01	-0.01
5	45	0.01	0.01	-0.01	-0.01
6	50	0.01	0.01	-0.01	-0.01
7	60	0.01	0.01	-0.01	-0.01
A	0	0.01	0.01	-0.011	-0.011
B	0	0.011	0.011	-0.01	-0.01

Input

The input values of all variables could be modified at any time step of the model if the user un-selects the “run forever” option on the interface’s “go” button .

Sub-models

The value model
The investment rate model