Adaptation of the boundary system in growing firms: an agent-based computational study on the role of complexity and search strategy

Figures & data

Figure 1. Interaction structures and growth stages in the simulation experiments.

Table 1. Overview of the modes of coordination.

	Type of coordination mode
	Decentralized	Sequential	Proposal
Lateral communication	no	yes	no
Vertical communication	no	no	yes
Headquarter intervening	no	no	yes
Re-evaluation of preferences	no	yes	yes
Departments’ final configuration	First preferences ${\mathbf{d}}_t^{r,p1}\forall r\in \left\{1,\dots ,M_s\right\}$	First preferences subject to choices of preceding departments, i.e., ${\mathbf{d}}_t^{r,p1}({\mathbf{d}}_t^{r-1,p1}) \text{for} r>1;{\mathbf{d}}_t^{r,p1} \text{for} r=1$	First [or second] preferences ${\mathbf{d}}_t^{r,p1} \left[\text{or} {\mathbf{d}}_t^{r,p2}\right]\text{if} V({\mathbf{d}}^C)\ge V({\mathbf{d}}_{t-1}),\text{otherwise} {\mathbf{d}}_{t-1}^{r*}$

Table 2. Parameter settings.

Parameter	Values/Types
Subject to variation across experiments
Interaction structures	‘Decomposable’ and ‘non-decomposable’ (see also Figure 1)
Search strategies	‘Exploitation only’: h(d^r^,^a^1) = 1 and h(d^r^,^a^2) = 1 ‘Exploitation and exploration’: h(d^r^,^a^1) = 1 and h(d^r^,^a^2) = 2 ‘Exploration only’: h(d^r^,^a^1) = 2 and h(d^r^,^a^2) = 2
Fixed for all experiments
Observation period	T = 750
Growth stages	s ∈ {1,2,3}
Interval of growth stages	T^G = 250
Number of choices	Ns=1 = 6, Ns=2 = 9,  Ns=3 = 12
Number of departments	in growth stage s = 1: M1 = 2 with d1 = (d1,d2,d3),  d2 = (d4,d5,d6); in growth stage s = 2: M2 = 3 departments as in s = 1  and additionally d3 = (d7,d8,d9); in growth stage s = 3: M3 = 4 departments as in s = 2  and additionally d4 = (d10,d11,d12)
Precision of ex-ante evaluation	σ^r = 0.05 ∀ r and σ^cent = 0.1
Modes of coordination	a^c ∈ {decentralized, sequential, proposal}
Interval of learning	T^L = 10
Aspiration level	v = 0
Learning strength	l = 0.5
Simulation runs	per scenario 5000: 20 runs on 250 performance landscapes

Figure 2. Relative frequencies of types of coordination modes in the course of growth. For parameter settings see Table 2.

Table 3. Condensed results of the simulation experiments. Each row represents averaged/aggregated results of 5000 runs.

	(a) Frequency of coordination  mode a^c in t = 750			(b) Final performance Vt = 750  (confidence interval*)			(c) Frequency of global maximum  found in t = 750			(d) Frequency of false  positive alterations of dt
Scenario	Decent.	Sequ.	Prop.	Decent.	Sequ.	Prop.	Decent.	Sequ.	Prop.	Decent.	Sequ.	Prop.
Decomposable structure
Exploitation only	32.8%	33.1%	34.1%	0.957±0.0035	0.9576±0.0035	0.957±0.0035	19.5%	21.2%	17.2%	2.5%	2.5%	2.8%
Exploitation and exploration	35.8%	39.7%	24.5%	0.9929±0.0012	0.9936±0.0011	0.9899±0.0019	57.7%	60.2%	48.0%	3.1%	2.8%	3.1%
Exploration only	31.4%	34.7%	33.9%	0.9167±0.005	0.919±0.0047	0.9171±0.0047	4.3%	6.1%	4.5%	3.2%	3.3%	2.9%
Non-decomposable structure
Exploitation only	27.2%	34.5%	38.3%	0.899±0.006	0.899±0.0051	0.9091±0.0043	8.2%	6.8%	7.2%	2.1%	2.2%	2.4%
Exploitation and exploration	17.8%	30.2%	52.0%	0.8764±0.0127	0.8973±0.081	0.9306±0.0041	11.0%	13.9%	18.0%	7.2%	7.3%	8.0%
Exploration only	13.7%	22.6%	63.8%	0.833±0.0124	0.844±0.0085	0.8695±0.0036	1.2%	1.7%	2.0%	6.2%	6.3%	5.7%