Modelling Self-Organisation of Oligopolistic Markets Using Genetic Programming
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This document discusses using genetic programming to model self-organization in oligopolistic markets. It describes replicating previous work showing the evolution of cost-plus pricing and price following. The model is then modified to explore how salience and expectations can lead to coordination. Specifically, adding expectation terminals provides a mechanism for tacit collusion where firms trail prices without changing sharply, leading to stable and sustainable market shares. Overall, genetic programming is proposed as a useful tool for modeling adaptive behavior and self-organization in economic systems.
Modelling Self-Organisation of Oligopolistic Markets Using Genetic Programming
- 1. Modelling Self-Organisation of Oligopolistic Markets Using Genetic Programming Edmund Chattoe Department of Sociology University of Oxford edmund.chattoe@sociology.ox.ac.uk http://www.sociology.ox.ac.uk/people/chattoe.html
- 2. Plan of the Talk • The research question • Genetic programming • Results of the simulation • Qualifications and conclusions
- 3. 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
- 4. 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
- 5. 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)
- 6. 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
- 7. A Typical GP Price String + 3/ OP1 + 2 OP2
- 8. 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
- 9. 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
- 10. 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
- 11. 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
- 13. 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
- 14. Dosi et al. Replication
- 16. Price Following
- 17. Much Lower Unit Costs
- 18. 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
- 19. Speculative Market: Fixed Unit Cost
- 21. 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
- 22. Stable But Uncoordinated Market
- 25. 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?
- 26. Tacit Collusion?
- 28. Three Firms with Expectations
- 29. 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
- 30. 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?
- 31. 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