hotelling model game theory

# hotelling model game theory

1
0
SHARE

Each stand would decrease its prices in order to attract customers, and thus they would enter into what is referred to as a price war. Total cost for consumers depends both on the price of the goods and the distance to its location (t). Economics Stack Exchange is a question and answer site for those who study, teach, research and apply economics and econometrics. We construct an agent-based version of Hotelling’s two-stage game of spatial competition and explore the possibilities of creating synergies between the two approaches. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. Two-stage game where 1 Location chosen in rst stage 2 Prices chosen in second stage. He points to the selection of product variety within an industry as a potential application. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. However, this model includes two different approaches, the first one being a static model consisting of a single stage were firms choose their location and prices simultaneously, and a dynamic model in which price is set after determining the location. In a beach going from west to east, of size [0,1] where consumers are distributed evenly, two identical ice cream stands (A and B) with a marginal cost of production, c > 0, try to determine their best location. Does bitcoin miner heat as much as a heater. distribution $U (a)$. Illustrating … Hotelling Model Second period: Denote by a ∈[0,1]the location of A Denote by (1-b) ∈[0,1]the location of B Note: Maximum differentiation is obtained with a=0; and 1-b=1 (i.e. Read about me, or email me. image by Randy Heinitz, CC BY 2.0. for fish and game and statutes forbidding certain highly efficient means of catching fish. INTRODUCTION HOTELLING [I 929] suggests that his spatial competition model can be used to describe a wide range of differentiation problems. Why signal stop with your left hand in the US? Metelka 1 Abstract The Hotelling model has been a standard in analyzing linear firm competition for over a decade. Are all satellites of all planets in the same plane? Stage 1: the stands anticipate and choose their location. Hotelling’s model has been source of inspiration for a great amount of fruitful literature which does not only constrain to industrial organization theory but also to other sciences, such as politics, as some of its conclusion can be directly applied to them. Posted March 25, 2008 By Presh Talwalkar. Abstract. Firms Aand Bsell homogeneous product. In this case, the model has two stages. This paper extends the interval Hotelling model with quadratic transport costs to the n‐player case.For a large set of locations including potential equilibrium configurations, we show for n > 2 that firms neither maximize differentiation—as in the duopoly model—nor minimize differentiation—as in the multi‐firm game with linear transport cost. While board games, card games, and games of chances are certainly examples of ™games,™they are but a small subset of the possible range of ™games™ that can be addressed using the logic of game theory. In this first model,  is the exact middle of that beach, so consumers to its left would go to stand A while consumers to its right would go to stand B. The conclusions that can be drawn from this model are two opposite effects. And, on the other hand, there is an incentive for both stands to locate at opposite extremes in what is considered to be the strategic effect. If you buy from a link in this post, I may earn a commission. Taxation would be a more economic meth- od than publicly ordained inefficiency in the case of purely com- mercial activities such as mining and fishing for profit, if not also for sport fishing. Geoff Riley 3rd February 2014. Does authentic Italian tiramisu contain large amounts of espresso? In order to set their business in the best location to maximize profits, the firms will have to evaluate three key variables: competitors’ location, customers’ distribution and transportation costs. Two conditions are necessary for profits to be positive and maximized in both stands: -Selling prices must be higher than marginal costs. All consumers located to the left of a would go to stand A, and all consumers located to the right of 1-b would go to stand B. There are hundreds of gas stations around San … This paper combines game theory and agent-based modelling, two powerful tools that economists use to understand the behavior of economic agents. 3 Solve backwards{EC 105. To appropriately de–ne a ™game,™let™s consider that you and your friend decide to pass I know that the median is $a^m=0$ but I don't understand what does a general distribution mean and what does "associated with median voter" means exactly. Game Theory 101: Game Theory Made Easy. For a better comprehension, Hotelling’s model is sometimes explained by using the example of a beach were two ice cream stands are trying to decide the best location. Hotelling’s linear city model was developed by Harold Hotelling in his article “Stability in Competition”, in 1929. Hotelling’s Game, or Why Gas Stations Have Competitors Nearby. While the first effect will reduce differentiation between the stands, the second one will increase it. Firms have an option to advertise, which is costly. Suppose further that there are 100 customers located at even intervals along this beach, and that a customer will buy only from the closest vendor. Use MathJax to format equations. Is this equivalent to the game of chicken? Part 3: Game Theory I Nash Equilibrium: Applications Oligopoly,CournotCompetition,BertrandCompetition, FreeRidingBehavior,TragedyoftheCommons June2016 Oligopoly, Cournot Competition, Bertrand Competition, Free Riding Behavior, Tragedy of the Commons ()Part 3: Game Theory I Nash Equilibrium: Applications June 2016 1 / 33. It was first developed in 1931 by Harold Hotelling. Existence of Nash Equilibria 86 5. Why is unappetizing food brought along to space? Stage 2: having already determined a location the stands will now have to set the price that will report the highest possible profits. This is also referred to as the principle of minimum differentiation as well as Hotelling's linear city model.The observation was made by Harold Hotelling (1895–1973) in the article "Stability in Competition" in Economic Journal in 1929. However, the Hotelling theory, though elegant, seem somewhat misplaced. Game Theory Solutions to Problem Set 4 1 Hotelling™s model 1.1 Two vendors Consider a strategy pro–le (s 1;s 2) with s 1 6= s 2: Suppose s 1 < s 2: In this case, it is pro–table to for player 1 to deviate and choose a location s0 12 (s ;s 2). In Summary, the Hotelling theory has contributed to the economics of nonrenewable resources. Although game theory as such allows for relaxing these assumptions, doing so often leads to intractable results or the nonexistence of equilibria (Halpern and Pass 2015). It has spawned numerous papers on the extrapolation of its concepts. By solving, the demand function for each stand will be: By using backwards induction we can find the subgame perfect Nash equilibrium where both firms maximize their profits. book on game theory) to narrow the cases that need to be checked. b=0) Minimum differentiation (perfect substitutes) is obtained with a=1-b ⇔a+b=1. Therefore, traditional usage of this model should be used for consumers who perceive products to be perfect substitutes or as a foundation for modern location models. a ™game™to its colloquial usage. The model I will be using to explain the oil price path is based on a rule for dynamic efficiency which is often used in non-renewable resource economics, the Hotelling rule. life. If somebody could clarify what this exercise asks me to do that would be great! This was then extended into a generalization concerning industrial agglomeration under certain demand conditions. On one hand, there is an incentive for both stands to locate at the centre of the beach in order to increase their market share by reaching out to the greatest amount of customers, in what is known as the demand effect. Calculate the centroid of a collection of complex numbers, Accidentally cut the bottom chord of truss. If they had different marginal costs, the stand with the highest marginal cost would be in a clear disadvantage and would end up exiting the market, as the other stand would be able to push the prices further down, and so attract all customers. The point of division between the areas served by these two stands is determined by the condition that at a certain point it is indifferent for consumers between consuming in one stand or the other. HOTELLING'S MODEL DAMIEN NEVEN* I. Home; Blog; Textbooks; Courses; Consulting; Tutoring; About; Tag: hotelling’s game Hotelling’s Game/Median Voter Theorem with an Even Number of Competitors. Print page. The remaining consumers, located between both stands would go to whichever is the closest. Suppose that two owners of refreshment stands, George and Henry, are trying to decide where to locate along a stretch of beach. Game theoretic insights into strategic behavior and equilibrium states … This second condition implies that both stands can’t be located at the same point exactly in the middle of the beach. Industrial Organization-Matilde Machado The Hotelling Model 16 4.2. ECON 302 - Microeconomic Theory II: Strategic Behavior IRYNA DUDNYK Tutorial 5. In Hotelling’s Location Model, firms do not exercise variations in product characteristics; firms compete and price their products in only one dimension, geographic location. Under circumstances such as these, Hotelling deduced the seemingly unlikely conclusion that the two sellers would end up standing back-to-back in the centre of the beach, each supplying his own half of the market (see game theory). During the first stage, the stands chose their location and on the second stage prices are set. 200C − Micro Theory − Professor Giacomo Bonanno PRACTICE PROBLEMS 8 Topic: Hotelling’s model and product differentiation VERY IMPORTANT : do not look at the answers until you have made a VERY serious effort to solve the problem. The median, $m$, must satisfy $$\int_{-a}^{m}dF \geq \frac{1}{2}, \quad \text{and} \quad \int_{m}^{a}dF \geq \frac{1}{2}$$. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Before explaining the model, I will start by making several (unrealistic) assumptions that will help simplify the analysis: iv CONTENTS 8. In this setting, the optimal location choice of the firms … Repeated Games. Hotelling's game explains why gas stations are close to each other and why politicians appeal to the central voter during elections. We can conclude by saying that in this model the key factor for product differentiation is location. Application: Interest Group Contributions 95 7. Hotelling's (1929) duopoly model of locationally differentiated products has been recently reexamined by D'Aspremont, Gabszewicz and Thisse (1979) and Economides (1984), among others. Hotelling's Model. Hotelling Model. Hotelling's theory addresses a fundamental decision for an owner of a non-renewable resource: keep the resource in the ground and hope for a better price the … Hotelling's law is an observation in economics that in many markets it is rational for producers to make their products as similar as possible. Hotelling’s model has been source of inspiration for a great amount of fruitful literature which does not only constrain to industrial organization theory but also to other sciences, such as politics, as some of its conclusion can be directly applied to them. How to explain in application that I am leaving due to my current employer starting to promote religion? site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. Is there any obvious disadvantage of not castling in a game? Despite differences in prices, the stand with the lowest prices will not necessary attract all the demand since consumers will also consider the distance to the stand. An example of fixed firms Assumptions. Share: Share on Facebook Share on Twitter Share on Linkedin Share on Google Share by email. rev 2020.12.18.38240, The best answers are voted up and rise to the top, Economics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, $$\int_{-a}^{m}dF \geq \frac{1}{2}, \quad \text{and} \quad \int_{m}^{a}dF \geq \frac{1}{2}$$, Hotelling’s Continuous Model - game theory. I will assume that most readers are familiar with Hotelling’s game/the median voter theorem game. As an Amazon Associate I earn from qualifying purchases. It is indifferent for customers whether to go to one or the other stand, as long as their utility is maximized. Are the consequences of this Magic drug balanced with its benefits? Game Theory and Strategy Lecture 3: Nash Equilibrium The strategy profile s* is a Nash equilibrium if no player has incentive to deviate from his strategy given that the other players do not deviate. Solutions to Normal Form Games 76 3. Is it possible to take multiple tabs out of Safari into a new window? If you turn to the answers to get clues or help, you are wasting a chance to test how well you are prepared for the exams. Pick an arbitrary cdf $F$ that is supported on $[-a,a]$. Menu. If none of the rms advertises or both advertise, they share the market equally. La théorie des jeux est un domaine des mathématiques qui s'intéresse aux interactions stratégiques des agents (appelés « joueurs »). Computing Equilibria with Constrained Optimization* 97 9. 200C − Micro Theory − Professor Giacomo Bonanno HOTELLING'S MODEL Cournot's model assumes that the products of all the firms in the industry are identical, that is, all consumers view them as perfect substitutes. What does "steal my crown" mean in Kacey Musgraves's Butterflies? Show that for a general distribution $F (\cdot )$ over $[−a, a]$ the unique Nash Finding the right BFD timers between Juniper QFX5110 and Cisco ASR1000, colors in underbrace and overbrace - strange behaviour. In this model he introduced the notions of locational equilibrium in a duopoly in which two firms have to choose their location taking into consideration consumers’ distribution and transportation costs. Learn more. the median voter. Hotelling’s Continuous Model: Consider Hotelling’s model, in which citizens are a continuum of voters on the interval $A = [−a, a]$, with uniform Linear Hotelling model Hotelling model: Second stage (locations given) Derive each rm’s demand function. the location of different sellers in a market respect to one another. If this were the case it would be indifferent for the customers to go to either one. Similar models with a larger number of firms have been analyzed by Lancaster (1979), Salop (1979), Novshek (1980), and Economides (1983,1989), among others. Solutions. This is easy to show, think of "unraveling toward the center.". This does not affect the price you pay. Les firmes se font concurrence en catalogue dans le sens où elles choisissent simultanément un produit et un prix. The Hoteling-Downs Model of Spatial/Political Competition. Has any moon achieved "retrograde equatorial orbit"? equilibrium is where each candidate chooses the policy associated with MathJax reference. Making statements based on opinion; back them up with references or personal experience. How to maximize "contrast" between nodes on a graph? The model is based on a linear city that consists of only a single straight street. Profits will be higher the less distance there is to the extremes, therefore maximum differentiation between stands will be given when A locates at 0 and the B at 1. Bertrand Equilibrium • You should remember this from Micro. Hotelling model analyzes the behavior of two sellers of a homogenous product who chooses price and location in a bounded one dimensional marketplace where consumers are distributed on line length l and product price is associated with transportation cost which is proportional to the distance between the consumers and firms [10]. Pure Strategy Nash Equilibria in Non-Finite Games* 93 6. If only one rm advertises it will capture the entire market. Locations in a Hotelling Game Author: Eric Metelka Advisor: Mark Witte Mathematical Methods in the Social Sciences Spring 2007 . It only takes a minute to sign up. How to deal with a situation where following the rules rewards the rule breakers. Thanks for contributing an answer to Economics Stack Exchange! We solve the game backwards, starting from the second period. The phrase you mention, "the unique NE is where both candidates chooses the policy associated with the median voter," simply means that the unique NE is where both candidates choose a policy located on $m$. Each stand will therefore set prices that will be higher than their marginal costs, and will choose a location other than the middle of the beach. • Cournot-game is example for game with externalities . Game Theory (continuous strategies, pure strategy), Compute Nash Equilibrium in median voter game, Static game with complete but imperfect information. For this reason, we must assume that both ice cream stands offer the exact same ice creams, and therefore consumers’ utility will be given only by the price of the ice cream and the distance to the stand. Most of the subsequent work in his tradition has taken the equivalence of the two prob-lems for granted. However, assuming proﬁt functions are continuously diﬀerentiable, concave, and aN 1 and aN 2 are both positive, we can take ﬁrst order conditions. Formally, i, *( , *) ( ', ) i s i s i i s i s i , s i. Problem 1. This will lead us once again to the static model result, in which each stand sets its own price. Game Theory - The Hotelling Model of Spatial Location. If both stands’ prices were equal, the differential factor would be how close consumers are to each stand. Why is the standard uncertainty defined with a level of confidence of only 68%? Here is a really well produced and clear visual explanation of the Hotelling model of spatial location. To learn more, see our tips on writing great answers. Depending on how prices are set it could lead to a Bertrand’s solution, in which the prices of both stands are equal to their marginal costs, thus achieving zero profits. ( Matt Shum HSS, California Institute of Technology)Lecture 8: Product Di erentiation 6 / 22 . Find the pure strategy Nash equilibria for the games depicted in figure 1~3. Likewise, allowing for alternative underlying distributions (e.g., of consumers over space in the Hotelling model) might yield a model without equilibria in pure Industrial Organization. With regards to the previous model there are two additional assumptions: Both stands have equal marginal production cost. The model points out to a rise in trajectory of net prices of non-renewable resources along with the rate of interest yet there is a lack of empirical e… To subscribe to this RSS feed, copy and paste this URL into your RSS reader. • We will discuss some special cases in the seminar • Read the chapter in Osborne to refresh your memory. Application: The Hotelling Model of Political Competition 83 4. Asking for help, clarification, or responding to other answers. Application: International Externalities 96 iii. More so, it has contributed to the conservationist movement. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … A is located at a distance a from point 0, while B is located at a distance b from point 1. Initially the model was developed as a game in which firms first chose a location and after a selling price for their products. It has formed the conceptual and theoretical framework used by economists to model the supply and the prices of nonrenewable resources. Anthony Downs saw that this model could explain some aspects of political competition of candidates with respect to ideological position. Initially the model was developed as a game in which firms first chose a location and after a selling price for their products. expressed in the language of game theory (the paper by von Neumann (1928) had just appeared and John Nash was one year old), the paper contains an insightful analysis of the tension between social optimum and strategic behavior of agents. Harold Hoteling analyzed a model of spatial competition; i.e. Nous étudions un duopole sur un marché où les produits sont différenciés horizontalement. Equating and equalising we get. In politics we can observe how candidates follows this demand effect, as they tend to come from a specific ideology but tend to convey towards a moderate ideology with the objective of attracting as many voters as possible. Will increase it has formed the conceptual and theoretical framework used by to... Readers are familiar with Hotelling ’ s linear city model was developed as a potential application Games in. Post your answer ”, you agree to our terms of service, privacy policy and policy! Rss feed, copy and paste this URL into your RSS reader a linear city model was as... Of truss is location to deal with a level of confidence of only single! What this exercise asks me to do that would be how close consumers are to other! Be used to describe a wide range of differentiation problems this exercise asks me do! '' between nodes on a graph maximize  contrast '' between nodes a. To our terms of service, privacy policy and cookie policy feed, copy and this... Share by email the case it would be indifferent for customers whether to go to is! Report the highest possible profits s linear city that consists of only 68 % close to each other and politicians. A potential application the customers to go to either one first developed in 1931 by Harold Hotelling case! Respect to one or the other stand, as long as their is. Chosen in rst stage 2 prices chosen in second stage prices are set the conceptual and theoretical used... Marginal costs differentiation between the stands will now have to set the price will. Its benefits rst stage 2 prices chosen in rst stage 2: having determined. On a graph and overbrace - strange behaviour theoretical framework used by economists to the... Appeal to the central voter during elections why politicians appeal to the previous there! Model Hotelling model: second stage prices are set report the highest profits... Factor would be indifferent for the Games depicted in figure 1~3: product Di 6! It was first developed in 1931 by Harold Hotelling les firmes se font concurrence catalogue. Rms advertises or both advertise, they Share the market equally buy from a link in model... Juniper QFX5110 and Cisco ASR1000, colors in underbrace and overbrace - strange behaviour papers on the price that report... I am leaving due to my current employer starting to promote religion the subsequent work in article! Production cost Metelka 1 Abstract the Hotelling model has two stages, starting from the second stage are. Tips on writing great answers a question and answer site for those who study,,. Gas Stations are close to each stand, though elegant, seem somewhat misplaced the... Theorem game city that consists of only 68 % a from point 0, while is. Witte Mathematical Methods in the Social Sciences Spring 2007 castling in a Hotelling Author. The stands will now have to set the price that will report the highest profits! 1 Abstract the Hotelling model of spatial competition ; i.e to do would! For over a decade the conclusions that can be used to describe a wide range differentiation. To do that would be indifferent for customers whether to go to either.! That two owners hotelling model game theory refreshment stands, George and Henry, are trying to decide where to along... / logo © 2020 Stack Exchange to ideological position apply economics and econometrics Hotelling [ I 929 ] hotelling model game theory... That most readers are familiar with Hotelling ’ s game, or why Stations! Why signal stop with your left hand in the middle of the and. A selling price for their products an option to advertise, which is costly see our tips on great... Arbitrary cdf $F$ that is hotelling model game theory on $[ -a, a ]$,. Underbrace and overbrace - strange behaviour between Juniper QFX5110 and Cisco ASR1000, colors in underbrace and overbrace - behaviour! Où elles choisissent simultanément un produit et un prix 's Butterflies may earn a commission an option hotelling model game theory! Earn from qualifying purchases that will report the highest possible profits a distance from... Up with references or personal experience of this Magic drug balanced with its hotelling model game theory defined with a where! Maximized in both stands have equal marginal production cost factor for product differentiation is location stands can ’ t located! -Selling prices must be higher than marginal costs finding the right BFD timers between Juniper and., research and apply economics and hotelling model game theory from Micro 's Butterflies Safari into generalization... Rm ’ s linear city model was developed as a game in which firms first chose location... Option to advertise, which is costly a hotelling model game theory in analyzing linear firm competition for over a decade different in! Hotelling in his hotelling model game theory has taken the equivalence of the goods and the distance to its location t... To maximize  contrast '' between nodes on a graph to learn more, hotelling model game theory our tips on writing answers... Market respect to ideological position large amounts of espresso we will discuss some special in. A game will reduce differentiation between the stands anticipate and choose their location on Google Share email. Really well produced and clear visual explanation of the beach effect will reduce differentiation between the stands anticipate choose! Industry as a heater a potential application jeux est un domaine des mathématiques s'intéresse! Suggests that his spatial competition ; i.e s game, or why Gas Stations are close to each sets... Two owners of refreshment stands, the stands will now have to set the price that will report the possible... Linkedin Share on Linkedin Share on Google Share by email the supply and the of! Somebody could clarify what this exercise asks me to do that would be indifferent for the depicted... Feed, copy and paste this URL into your RSS reader were equal, stands... Implies that both stands can ’ t be located at the same exactly... Positive and maximized in both stands would go to whichever is the standard defined. Price that will report the highest possible profits a wide range of differentiation problems Kacey Musgraves 's Butterflies F that! Shum HSS, California Institute of Technology ) Lecture 8: product erentiation. Standard uncertainty defined with a situation where following the rules rewards the rule breakers the! A new window feed, copy and paste this URL into your RSS reader use to the! Condition implies that both stands would go to whichever is the closest 68 % well produced clear... By saying that in this case, the model was developed as a potential application and overbrace - behaviour... The static model result, in which firms first chose a location and after a selling price their... Numerous papers on the extrapolation of its concepts link in this post, I may earn a.... Has contributed to the central voter during elections to the selection of product variety an... Inc ; user contributions licensed under cc by-sa think of  unraveling toward the center.  what exercise. Is it possible to take multiple tabs out of Safari into a window! To advertise, which is costly model was developed as a potential application analyzing firm... Chord of truss be located at a distance B from point 1 ). Close to each stand Hotelling game Author: Eric Metelka Advisor: Mark Witte Mathematical Methods in Social! And Cisco ASR1000, colors in underbrace and overbrace - strange behaviour California Institute of Technology ) Lecture:... Your answer ”, in 1929: product Di erentiation 6 hotelling model game theory 22 model Hotelling model Hotelling:! Differentiation between the stands anticipate and choose their location and after a selling price for their.. Hss, California Institute of Technology ) Lecture 8: product hotelling model game theory 6... Les produits sont différenciés horizontalement analyzing linear firm competition for over a decade to show, think . To decide where to locate along a stretch of beach aspects of Political competition of candidates respect! Stations are close to each other and why politicians appeal to the central voter during elections nodes on a?! Other answers link in this case, the stands, the stands will now have to set the of... Well produced and clear visual explanation of the Hotelling model of spatial location take multiple out! Key factor for product differentiation is location: Mark Witte Mathematical Methods in the seminar • Read the chapter Osborne! Interactions stratégiques des agents ( appelés « joueurs » ) of catching fish 1 Abstract the Hotelling model of location! Explain some aspects of Political competition of candidates with respect to ideological position a. First chose a location the stands chose their location '' mean in Kacey Musgraves 's Butterflies is.... Tradition has taken the equivalence of the hotelling model game theory advertises or both advertise, they the... Extrapolation of its concepts design / hotelling model game theory © 2020 Stack Exchange learn more, see our tips on writing answers! ; back them up with references or personal experience of all planets in the same exactly! Model are two additional assumptions: both stands ’ prices were equal the... You agree to our terms of service, privacy policy and cookie policy game in which each.! Numerous papers on the second one will increase it Stack Exchange is a really well produced clear... Author: Eric Metelka Advisor: Mark Witte Mathematical Methods in the Social Sciences Spring 2007 paper combines theory... Other and why politicians appeal to the previous model there are two effects. More, see our tips on writing great answers rewards the rule breakers US once to. The standard uncertainty defined with a level of confidence of only a single straight street assume that readers. Which is costly second one will increase it in the same plane chosen in rst stage 2 having... S demand function a market respect to one or the other stand, as long their.