Games & Strategies

These are the materials for the lecture topic: Lecture 6, Entry, Exit & Selection.

The lecture considers both traditional entry barriers (primarily absolute cost advantages, scale advantages and product differentiation) and strategy entry deterrence (principally Limit Pricing, Predatory Pricing and Brand Proliferation using Game Theory).

The lecture capture for this lecture is available on the Engage system (University of Nottingham), which can be accessed via Moodle.

These are the materials for the lecture topic: Lecture 7, Product Differentiation. The main models explored as the Lancaster Characteristics Model of Product Differentiation and the Hotelling Model of Competition.

Below you will find the lecture slides (available to download from Moodle) and a series of lecture videos. Note that this would have corresponded to 3 hours of the lecture slot in the usual lecture format (i.e. a full two hour lecture plus half of a second two hour lecture).

Detailed Lecture Overview: This lecture considers two main models. The first is the Lancaster Model of Product Characteristics, where product differentiation exists when two products contain the same characteristics (such as mobile calls and data for a mobile phone contact) but in different proportions (some contracts offer a higher ratio of data to minutes than other contracts and this is the differentiating factor). Consumers are assumed to derive utility from the underlying characteristics of the goods rather than the product itself. That is, we don’t typically derive utility from having a particular mobile phone contract – we derive utility from the characteristics (minutes and data) included in the mobile phone contract.

This model is used to outline a formal approach to product differentiation, where consumers are able to obtain their ideal combination of the underlying characteristics of the products by combining different products. We also relate this model to entry opportunities into a market.

The second model considered is the Hotelling Model, which some of you may have covered briefly in other modules. In Bertrand competition it is assumed that consumers always buy from the cheapest seller. Hotelling introduced the idea that consumers will not necessary buy from the cheapest seller once we introduce product differentiation because the additional utility received from the preferred (but more expensive) product may outweigh the difference in the price. That is, consumers are willing to pay a price premium for products they prefer.

The model considers how firms design their products and differentiate their products in the “product space.” It also considers the case where firms must choose the design of their products and the price of their products. The main results show that when firms are operating in a market with minimal price competition, firms will tend not to differentiate their products. However, in markets where price competition would otherwise be fierce, firms differentiate their products to soften price competition by appealing to the consumers who would prefer to buy their product at a premium price.

We also develop the model to consider the case of collusive pricing, one the degree of product differentiation is fixed. We show that in equilibrium the firms may set a collusive price such that not all of the consumers find it worthwhile to buy the product in equilibrium, and this depends on the strength of consumers preferences for particular products (or in the model we refer to this as their “transport cost”).

The lecture is completed with a brief discussion of an empirical application of the Hotelling Model to the airline industry in Norway.

These are the materials for the lecture topic: Lecture 8: Price Dispersion, Consumer Inertia & Firm Strategy. The slides are also available to download from Moodle as usual.

Detailed Lecture Overview

It is widely recognized that identical products are often sold at different prices, referred to as price dispersion. This finding is especially surprising when we think about online markets, where it is generally easy for consumers to identify the lowest price in the market as this should theoretically eradicate price dispersion because the more expensive firm would not make any sales.

In this lecture we will analyse the role of consumer inertia as a primary driver of price dispersion. That is, some consumers display inertia in their decision making in terms of which firm they buy from; they tend to just buy from their local store, their preferred supplier or a random firm that they find in the market, rather than identifying which seller has the lowest price. This violates the assumption of Perfect Competition that all consumers have perfect information and buy at the lowest price. Therefore, in this lecture, we return to the model of Bertrand price competition to understand the consequences of consumer inertia for the pricing strategy of firms.

First, we outline how we can formally model consumer inertia in a simple way. We introduce two types of consumers: Some consumers are “Informed” and buy at the lowest price, whilst others are referred to as “Uninformed” and these consumers don’t know which firm has the lowest price so they choose a seller at random. (We also discuss other interpretations of the two types of consumers in the lecture).

We analyse why the Bertrand Paradox, which states that even with just two firms all firms must set their price equal to marginal cost, will not hold when there is consumer inertia in the market. Instead, firms could choose the same price, but this price is now above marginal cost (a symmetric equilibrium). Or the firms could each choose different prices (an asymmetric equilibrium). We formally demonstrate that in a market with consumer inertia there is no equilibrium where firms choose a single price (formally; no pure strategy price equilibrium), if firms are choosing their price at the same time.

This differs from the standard Bertrand price competition case without consumer inertia, which we analysed in Seminar 4. There, we discussed that there is a unique equilibrium in which all firms must set their price equal to marginal cost.

Secondly, we extend our analysis to Stackelberg competition, where one firm sets their price before the other firm. We show that there now is an equilibrium which involves one firm choosing a very high price and another firm choosing a very low price, referred to as spatial price dispersion.

Thirdly, we develop a second model to understand not only why firms choose different prices, but also why firms change their prices over time. For example, when you visit a supermarket or an online website, the price the firms charge often varies each week. This is referred to as “Inter-temporal Price Dispersion;” Firms choosing different prices each day, and the price each firm chooses varies over time. On one day, firm 1 is cheaper, whilst on another day, firm 2 is cheaper.

To explain this, we explore a “mixed strategy equilibrium” in this market, which essentially involves firms choosing their price randomly from a range of prices. For instance, if the optimal range is £10 to £20, each day the firm randomly chooses a price in this range. The intuition is that Firm 1 wishes to charge a very high price to maximise the profit for each unit it sells. However, firm 1 wishes to charge a very low price to increase the probability that he has the cheapest price in the market, and therefore receives the demand from all of the informed buyers.

If Firm 1 chooses a single price, the competitor (Firm 2) will undercut and choose a slightly lower price, to make sure that firm 2 has the lower price and wins the demand of the Informed consumers. To prevent this from happening, firm 1 needs to randomise their price so that firm 2 cannot predict it and undercut. This type of randomisation process can explain why firms change their price over time, and the firm that has the lowest price will vary.

Towards the end of the lecture, we cover several examples to help us understand how to apply this lecture content to real world examples.

Note that in order to study consumer inertia and mixed strategies, we need to use Cumulative Probability Distribution Functions. You should be familiar with these from your quantitative methods courses. However, to make sure that all of the technical content for this module is self-contained, I have created an additional video covering this mathematical material: “Primer on Cumulative Distribution Functions.” This is clearly marked on the website and you should watch this before Part 7 of the lecture videos. If the lectures had continued in the usual way in the lecture room, this video would have been uploaded for you to watch before this lecture anyway.

In this short lecture we review a small number of the questions from the "review questions" on consumer inertia, price dispersion and firm strategy to discuss how to apply the theory in practice.

We also discuss how consumer inertia can also be an important factor for our previous analysis of barriers to entry and product differentiation. More broadly, we discuss how each of these topics connect together and highlight connections across different modules across the Industrial Economics programme.