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Extending Hotelling’s location model into Agent-based domain
Název práce v češtině: Multiagentní simulace v Hotellingově modelu prostorové diferenciace
Název v anglickém jazyce: Extending Hotelling’s location model into Agent-based domain
Klíčová slova: Agentní simulace; Hotellingův model prostorové diferenciace; Zpětnovazební učení; Nash-Q učení
Klíčová slova anglicky: Agent-based simulation; Hotelling's location model; Reinforcement learning; Nash-Q learning
Akademický rok vypsání: 2016/2017
Typ práce: bakalářská práce
Jazyk práce: angličtina
Ústav: Institut ekonomických studií (23-IES)
Vedoucí / školitel: PhDr. Mgr. Jiří Kukačka, Ph.D.
Řešitel: skrytý - zadáno vedoucím/školitelem
Datum přihlášení: 15.06.2017
Datum zadání: 15.06.2017
Datum a čas obhajoby: 11.06.2018 09:00
Místo konání obhajoby: Opletalova - Opletalova 26, O105, Opletalova - místn. č. 105
Datum odevzdání elektronické podoby:10.05.2018
Datum proběhlé obhajoby: 11.06.2018
Oponenti: Mgr. Ing. Šarlota Smutná, M.Sc.
Kontrola URKUND:
Seznam odborné literatury
1. D'ASPREMONT, Claude; GABSZEWICZ, J. Jaskold; THISSE, J.-F. On Hotelling's" Stability in competition". Econometrica: Journal of the Econometric Society, 1979, 1145-1150.
2. AHLIN, Christian; AHLIN, Peter D. Product differentiation under congestion: Hotelling was right. Economic Inquiry, 2013, 51.3: 1750-1763.
3. LARRALDE, Hernán; JENSEN, Pablo; EDWARDS, Margaret. Two dimensional Hotelling model: analytical results and numerical simulations. 2006.
4. HELBING, D.; BALIETTI, S. How to do agent based simulations in the future. H. Dirk, & S. Balietti, Modeling Social Mechanisms to Emergent Phenomena and Interactive Systems Design. SFI Working Paper. Retrieved, 2011, 10.25: 2013.
5. HAMILL, Lynne; GILBERT, Nigel. Agent-based modelling in economics. John Wiley & Sons, 2015.
6. VARIAN, Hal R.; REPCHECK, Jack. Intermediate microeconomics: a modern approach. New York: WW Norton & Company, 2010.
7. OSBORNE, Martin J.; PITCHIK, Carolyn. Equilibrium in Hotelling's model of spatial competition. Econometrica: Journal of the Econometric Society, 1987, 911-922.
8. IRMEN, Andreas; THISSE, Jacques-François. Competition in multi-characteristics spaces: Hotelling was almost right. Journal of Economic theory, 1998, 78.1: 76-102.
9. RAILSBACK, Steven F.; GRIMM, Volker. Agent-based and individual-based modeling: a practical introduction. Princeton university press, 2011.
10. ABBEEL, Pieter; QUIGLEY, Morgan; NG, Andrew Y. Using inaccurate models in reinforcement learning. In: Proceedings of the 23rd international conference on Machine learning. ACM, 2006. p. 1-8.
11. SUTTON, Richard S.; BARTO, Andrew G. Reinforcement learning: An introduction. Cambridge: MIT press, 1998.s
12. SIMM, Jaak, et al. Method for creating empirical agent-based models for economics. 2004. PhD Thesis.
Předběžná náplň práce v anglickém jazyce
Research question and motivation
Hotelling’s location model has been discussed for its minimum differentiation principle. The principle states that regardless of starting location, either firm would be motivated to get closer to its opponent to increase its profit. This principle was criticized by D'Aspremont, Gabszewicz and Thisse (1979). In last decades, various adjustments to the model were made to make the model more tractable. Ahlin and Ahlin (2013) showed that Hotelling’s differentiation principle may apply if negative network externalities – “congestion costs” – are present in the model. However, they leave empirical exploration of the congestion – differentiation relationship for future work. We will refer to the model from Ahlin and Ahlin (2013) as to HL congestion model. Inspired by Larralde, Jensen and Edwards (2006), we will extend the HL congestion model with random factor in consumer’s choice through a logit function. Further, we will test the model numerically through agent-based simulation.

Prelimitary working hypotheses are:
• Minimum differentiation principle in Hotelling’s location model with congestion costs can be empirically confirmed.
• Agent-based modelling is a method that can be used instead of empirical testing of microeconomic models. Simm (2004)
• Introducing stochastic consumer’s choice will not contradict the minimum differentiation principle. Larralde, Jensen and Edwards (2006)
• Reinforcement learning is an efficient tool for profit optimization of agents under imperfect information.

This thesis will provide comprehensive overview of development of Hotelling’s location model. Controversy regarding minimum differentiation principle will be briefly discussed and latest development of the model will be summarized. We aim to test and extend the HL congestion model and to provide good starting point for further research in microeconomic spatial analysis. To compensate for unsatisfactory real-world conditions for empirical testing, we will use Agent-Based simulation as a substitute for testing in laboratory conditions.

To empirically test the HL congestion model, we decided to leverage the agent-based modelling (ABM) and reinforcement learning. This will allow us to get closer to reality through imperfect information and bounded rationality of firms as our agents. The agents will only know about their own and their competitor’s position and price. Every round, they will observe certain profit from their last decision and will be able to change their price and location. After sufficient amount of repetition, they will be able to decide on optimal strategy regardless of their starting position. We are hoping, that the observed optimal strategy will sufficiently support the form of Hotelling’s model introduced by Ahlin and Ahlin (2013). Consumers in our model will decide where to shop stochastically, based on their logit function. This way we will try to include unobserved factors that influence consumer’s behaviour. Before running the simulation, a sensitivity analysis and fixed-parameter calibration of the model will be carried out.

Introduction to monopolistic competition
Comprehensive overview of development and literature of Hotelling’s model
Introduction to agent-based modelling and reinforcement learning
Model description
Simulation results and discussion
Conclusion and recommendations for further research
List of references
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