Population Initialization and Parameter Sensitivity

Summary

Karakaya et al. (2011) use a structured experimental design where consumer agent parameters are initialized from specified distributions (uniform, mixed) and five decision variables are varied one at a time across experiments, each replicated 100 times. This approach enables systematic assessment of how individual marketing decisions (price, promotion, quality, opinion leader targeting) affect profitability, while replication controls for stochastic variation.

Overview

In any ABM, the initial configuration of the agent population and the experimental design for parameter exploration are critical methodological choices. Karakaya et al. provide a template for how to initialize heterogeneous agent populations and systematically explore the parameter space without the computational cost of a full GA-based calibration.

Main Content

Fixed Model Parameters (Table 1)

Parameter	Notation and Value
Number of time steps	$T=20$
Number of consumers	$N=1000$
Number of opinion leaders	$M=200$
Product characteristics value	$A_1\in (0.1,1)$, $A_2\sim U(0.6,1)$
Cost of the product	$Cost=A_1\times 0.1+A_2\times 0.2$
Buying threshold	$\alpha =0.7$
Exponential smoothing constant	$\beta =0.5$
Smoothing constant for logit	$k=5$

Consumer Parameter Distributions

Agent heterogeneity is created through random initialization:

Parameter	Distribution	Rationale
Product preference $P_{i1}$	Mixed: 60% mid-range (0.4-0.8), 20% low (0.1-0.4), 20% high (0.8-1.0)	Reflects realistic preference distribution for “best match” attributes
Product preference $P_{i2}$	$U(0.6,1)$	“More is better” attribute — all consumers want at least moderate levels
Price sensitivity $PrSe{n}_i$	$U(0.5,1)$	All consumers are at least moderately price-sensitive
Quality sensitivity $K_i$	Randomly assigned	Individual quality importance
Promotion sensitivity $P{r}_i$	Randomly assigned	Individual responsiveness to advertising
Social sensitivity $S_i$	Randomly assigned	Individual susceptibility to WOM

Experimental Design

Five decision variables are manipulated:

1. Price of the product
2. Promotion intensity
3. Product attribute 1 ($A_1$) — quality dimension 1
4. Product attribute 2 ($A_2$) — quality dimension 2
5. Number of opinion leaders targeted

One-at-a-Time (OAT) Design

Each experiment varies one decision variable while holding all others constant at benchmark values. This allows isolation of individual effects but cannot capture interaction effects.

Replication Strategy

Each experiment configuration is replicated 100 times to account for stochastic variation in:

• Random parameter assignment to agents
• Random network formation
• Stochastic purchase decisions (logit randomness)

WOM Toggle

Each experiment is performed twice: once with WOM in effect and once without WOM. This isolates the contribution of WOM to each marketing strategy’s effectiveness.

Benchmark Configuration

The benchmark (Experiment 1) uses a low-quality product with:

• Small size (low $A_1$), low resolution (low $A_2$)
• High price
• Low promotion intensity
• 5 opinion leaders targeted

This worst-case scenario establishes a baseline for measuring the effect of improvements.

Key Sensitivity Findings

From the experimental results:

• Quality improvements: Most significant effect on profitability, especially with WOM active (WOM amplifies quality signals)
• Price reductions: Increase sales volume but can reduce profitability; negative WOM from price-driven but quality-indifferent consumers can offset gains
• Promotion increases: Diminishing returns when WOM is active (organic WOM substitutes for paid promotion)
• Opinion leader targeting: Accelerates diffusion but has complex interactions with quality

Connections

• Parameter distributions create the agent heterogeneity in the Karakaya model
• Parameters feed into the utility function
• This experimental approach contrasts with the GA calibration used in CUBES
• Results inform marketing strategy recommendations

See Also

• ABM Calibration Overview — broader calibration context
• Consumer Utility Function Components — what these parameters parameterize
• Karakaya et al 2011 - Overview — paper context
• Local vs Global Sensitivity Analysis — global complement to this note’s one-at-a-time local SA