Modelling Self-Organisation of Oligopolistic Markets Using

Genetic ProgrammingEdmund Chattoe

Department of SociologyUniversity of Oxford

edmund.chattoe@sociology.ox.ac.ukhttp://www.sociology.ox.ac.uk/people/chattoe.html

Plan of the Talk

• The research question• Genetic programming• Results of the simulation• Qualifications and conclusions

Oligopoly Pricing• How do firms set prices in a complex

environment?• Simplify by making it a game or assuming

(“gifting”) lots of common knowledge• Third approach is adaptive but this is “too difficult” for simple adaptation

• A possible solution is evolutionary learning: firms adapt by an ex ante undirected mechanism and are selected according to ex post success

• Descriptive and instrumental applications

The Intellectual Appeal of Evolution• Driven by heterogeneity• Open ended: actors don’t need to know

objective function (if there is one)• Works on minimally effective strategies

using relative success• Analogous to situation of firms?• Already observed to produce stable self-

organised heterogeneity in ecosystems

A Brief History• Marshall and the representative firm• Alchian

– Outcomes not intentions– Genotype is firm practices– Phenotype is firm behaviour (and structure)

• Nelson and Winter– Fixed decision rules (link to last week)

• Dosi et al. (1999)

Evolutionary Algorithms• Genetic Algorithms and Genetic Programming• Population of solutions represented as data

structures (lists and trees): Travelling Salesman• Population enrichment by selection (GENITOR

versus HOLLAND)• Genetic operators: Crossover, inversion and

mutation• Shared representation/interpretation of imitation• Justification for using “hill climbing” operators• Exploring full space of grammatical strategies

A Typical GP Price String+

3/

OP1

+ 2

OP2

The Dosi et al. Model• Candidate prices are small set of GP strings• Firms set price probabilistically based on

accumulated (but bounded) profits of candidates• Demand determined by “market” price and

allocated by current market share• Market share updated via set and market prices• Profits are accrued to firm (and strategies)• Firms with losses/minimal market share replaced• New candidates may be generated

Modifications to Dosi et al.• Note: No ability to predict effects of pricing• No exogenous “restarts”• Behavioural interpretation of small set of competing

price strategies• Fair trial assumption: priority to untried strategies

and no profit “inheritance”• Genitor rather than Holland architecture: much

smaller number of candidates• Consistent treatment of imitation in new and

surviving firms

The Operators• Crossover: Take two trees, identify “legal” cut

points and swop “tails”• Mutation: Take one tree and identify “legal” cut

point for new randomly generated tree.• Some completely new trees• Other possibilities?• IF NOT AND OR > < = + - % *• OMP, OMD, OP x OUC, CUC, OS, integer• http://users.ox.ac.uk/~econec/thesis.html

Results: Checking Replication• Replicating the Dosi et al. simulation from

the published description: not an easy task• Check the simulation by learning the

monopoly price• Noise reflects experimentation: wasteful but

only if you know the underlying properties of the search space

• Three replication runs per result: not reproduced here

Monopoly Learning

Results: Dosi et al.

• Main Dosi et al. result is evolution of price following and “cost plus” pricing

• This appears to be sensitive to assumptions made about relatively large and variable unit costs

• Use of “elasticity measures” to confirm this result in a more quantitative way

Dosi et al. Replication

Cost Plus Pricing

Price Following

Much Lower Unit Costs

Results: Salience and Co-ordination• With low and fixed unit costs, market is “speculative”: no fundamentals

• Salience is a property that makes some choices stand out for reasons irrelevant to their payoffs

• 1 2 3 4 5 6 7 8 9 10• Beliefs can make choosing salient options rational• Offer firms “common” (but non optimal) terminal

without multiples• New mode of explanation: neutrality about whether

terminal is used in real strategies or not

Speculative Market: Fixed Unit Cost

Co-ordination Through Salience

The Role of Expectations• Recall the Dosi et al. findings involve “backward

looking” strategies• Feedback to market share produces strong

tendency to monopoly: prices are relatively stable but not co-ordinated and thus not sustainable in the long run

• Firms assess strategies on profit only• Adding a simple linear expectations operator

ensures both stability and co-ordination

Stable But Uncoordinated Market

Market Sustainability

Expectation Formation Terminals

A Mechanism of Tacit Collusion• In a duopoly both firms gain from co-ordinating on

the same price: splitting the market• Both leader and follower might lose profit (via

market share) if one “defected” from this• Expectation terminals give a mechanism for tacit

collusion• The leader “trails their coat”• The follower can use expectations on leader prices

that do not change too sharply• An emergent (and sustainable) property?

Tacit Collusion?

Sustainable Market Shares

Three Firms with Expectations

Changing Firm Goals• Introduce possibility of market share goal• Populations with mixed goals• Profit maximisation doesn’t drive out other

goals (contra Friedman)• “Pure” market share maximisation leads

invariably to monopoly in mixed goal markets

What Next?• Better data collection: ethnographic,

experimental, participatory• More effective sensitivity analysis:

particularly challenging Dosi et al. results• Problem of behavioural interpretation• Experimental programme: Diverse strategy

sets, multiple control variables, different operators and terminals

• Better representation?

Conclusions• GP is a powerful adaptation mechanism• Evolutionary algorithms may also be used

as descriptively plausible models for adaptation in economic systems

• Augmenting the grammar of a GP offers a less “judgmental” experimental approach to firm capabilities

• GP models might contribute to “standard” theory of the firm