Incremental and Breakthrough Innovation: An Agent-Based Model of

Firms and Technology Creation

The Technology Evolution Super Team

Jeremy PesnerBrendon Fuhs

Overview

Based on model of technological epochs (Axtell et al., 2013)

– Jeremy presented this. Hopefully you paid attention

Agents now grouped into Zipf-sized firm Agents have access to goods of their coworkers Used to gain a greater understanding of firm size in

the role of technological evolution

Principles of firm size & innovation (Baumol, 2005):

Small, entrepreneurial firms – Breakthrough innovation

Large, corporate firms – Incremental innovation Account for this in the model

Arthur & Beinhocker, Technological Recombination

Technologies have components which are architected towards a specific purpose

Technologies of various fitnesses comprise a fitness landscape, design space

Oftentimes, there is a sudden jump in technological development after a certain point has been reached (Richard Foster)

Creative Destruction – Horse & buggy after car Technological lock-in can prevent adoption of

newer, fitter technologies

Arthur & Beinhocker, Technological Recombination (Part 2)

Many modern technologies are repeatedly used as building blocks for incremental innovation

– Microprocessors

– Chemicals

– Gene manipulation

Breakthrough innovation comes from combining a technology with a physical or social phenomenon

– Physical Phenomena: fire, gravity, air

– Social phenomena: work, friendship, food

– Ex: Google – algorithmic page ranking + human search

Firm Size & Innovation

Different sized firms have different ways of innovating

– Baumol, 2005; Cohen & Klepper, 1996; Stock, Greis & Fischer, 2002

Smaller entrepreneurial firms: Breakthrough innovation

– Crazy ideas

– Nothing to lose, everything to gain

– Doesn't usually work, but when it does...

Larger corporate firms: Incremental innovation

– Want sure bets

– Won't create technologies antithetical to business/organization

– Both needed (Wright Brothers vs Boeing)

Review of Initial Model(just to be nice)

Some number of agents & some number of total goods with randomly distributed fitnesses

Agents can hold and use goods with defined fitnesses. Goods have finite lifetimes

Agents invent a new good by combining 2 existing ones – new fitness value f = [0, g1 + g2]. Some probability that it is marketable

Agents evaluate their own fitness of good = [0, f]. If new good's fitness is greater than least useful good agent owns, will adopt it

Our Model Reimplemented in Python from ground up

– Enables easier visualization

Firms “birth” agents and their goods

– Agents have goods, but considered firm's goods

Agents create their goods from two randomly selected goods within the entire pool of firm goods

– Agents still have their own goods they demand

Firms generate agents with a Zipf probability

– “Zipf Distribution of US Firm Sizes” (Axtell, 2001)

Fitness Boost Large and small firms each need a fitness boost in

order to ascribe to their innovative capabilities

– Formulae included to raise floor for larger firms, ceiling for smaller ones (S = firm size, F = initial fitness):

Playing god, but no other way Large firm's goods will be pretty good, but only so

good Small firm's goods more unpredictable, but could be

game-changing

Experimenting with the model

Case A: No firms

Case B: No firm advantages

Case C: Small firm advantage only

(omega = 0.25)

Case D: Large and Small firm advantages

(omega = 0.25, alpha = 0.5)

Average Market Share vs. Firm Size

Market share of FINAL goods

B: upper right

C: lower left

D: lower right

Average Market Share vs. Firm Size

Market share of ALL goods

B: upper right

C: lower left

D: lower right

Average Market Share vs. Firm Size

Log(avg market share) as a linear function of log(firm size)

Log-slope(exponent in non-logged model)

Log-intercept(multiplier in non-logged model)

R-squared

No advantages, final goods

0.427 0.169 0.0844

No advantages, all goods

0.694 0.0518 0.162

Small firm advantage, final goods

0.1421 0.261 0.00843

Small firm advantage, all goods

0.413 0.0649 0.0531

Both advantages, final goods

0.668 0.125 0.194

Both advantages, all goods

0.879 .03314 0.208

Observations / Interpretation

• Results are a little hairy!

• Smaller slope in experiments indicates small firm advantage

– Particularly notable in experiment B

• However, in experiment D, ω < α

• Small firm success was bounded

– Specific nature of formulae somewhat arbitrary (blame Brendon)

• Future work needed to test different formulae and advantage coefficients