Deriving the Game

Based on the theory of Sadeghi-Zandieh (2011) and the research assumptions here, the use of game theory will add a competitive dimension to the analysis of the optimal choice of a product portfolio or a given market. The theory and model played out by Sadeghi-Zandieh was a simple two player game with a small set of potential product portfolios; however, as demonstrated in the case study, the UK Motor Insurance market is far more complex. Representation as a Duopoly with few products is non- representative.

This section will cover the methods used to derive the game model, including: defining the set of players, the set of product portfolio strategies and the game mechanisms.

3.4.1. Defining Players

Given the relatively open nature of the UK Motor Insurance industry, there are upwards of 120+ players in the market. To model this type of complexity would make calculation of a Nash Equilibrium time (and processor) consuming, nearing impossible. For this reason we first looked at Porter’s five

competitive forces before using Porter’s Competitive Analysis and Strategic Groupings to simplify the problem.

Using Porter’s five competitive forces (Porter, 1979) to analyse the UK Motor Insurance market, one can see why primarily internal competition is compared. Entry of new competition was not considered but could contain potential issues. High financial cost to enter, tight governmental regulation and the already highly competitive market are strong deterrents to entry and very few players have entered in the past decade. More likely is spin-off niche brands developed by the big insurers to gather more market share. This issue was not taken into account in the game, but these new company types are covered as a competitive strategic group, as discussed later in this section. The threat of substitution is minimal due to government regulation stipulating that all cars must be insured to be on the road. There are no real substitutions to the motor insurance product, unless considering public transportation, which was not undertaken in this research. The market buyer power has been increasing recently with price comparison websites and is one of the driving factors of this research. This factor is taken into consideration in the consumer purchase behaviour derivations. Supplier Power is unique in this industry, in that there are only a few actual insurers. A majority of ‘insurers’ are actually brokerage firms that find the right product and pricing, then label it as their own and managing the insurer relationship. This leaves rivalry as the main driver of competition with the sheer number of competitors, little diversity between competitors, lack of actual product differentiation and low buyer switching costs. This analysis and results are the same as those found by MarketLine (2013).

In-depth competitor analysis requires four diagnostic components (Porter, 2004): future goals, current strategy, assumptions and capabilities. When putting the four components together, the competitor response profile, or offensive and defensive probably reactions, can be anticipated (Porter, 2004; Fleisher & Bensoussan, 2007). These reactions define the mechanisms of the players and can be simplified to the positioning of each company (Porter, 1996).

Strategic Groupings are groups of companies defined as playing in a similar fashion based on visible characteristics uncovered using Competitive Analysis (Porter, 1980). When performing the Strategic Competitive Groupings, the positioning of each company are clustered together to form groups with common positioning strategies. Porter (2008) defines player positioning on two-axis: cost and

differentiation. In the UK Motor Insurance industry players primarily use Pricing, Brand and Customer targeting to draw in customers. Brand and customer targeting are differentiations factors in this commodity-like market. Using these defining features, we can identify four strategic groups: Large Insurance Brands, Big High Street Brands, Other Big Brands and Small & Medium Sized Insurers.

Larger Insurance companies can undercut the competitor in price in the short run, drawing from their reserves to make up the difference. This makes the Large Insurance companies and brands behave in a different fashion to other groups.

Big High Street Brands and Other Big Brands rely on customer relationships, trust image and other branding techniques to attract customers. They are also attached to convenient locations or sources (i.e. Nissan Insurance can be purchased when purchasing your Nissan automobile). The dividing difference in these two players is the weight of the brand and convenience. High Street brands rely on the everyday relationship held with customers, where as the other big brand rely more on specialist relationship (i.e. car ownership for Nissan or banking and other financial services through Nationwide).

The Small and Medium sized Insurers compete through niche pricing and specialised products targeted at a specific market segment. For instance, Endsleigh Insurance targeting fair pricing and specialised products for Students and Academics.

3.4.2. Defining Player Strategies

If using the structure derived from the Sadeghi-Zandieh model, each player strategy is a possible product portfolio. A product portfolio is a collection of products that are released to the market to create a coherent ‘portfolio’ of offerings. In the UK Motor Insurance industry and in the game model represented here, each product is defined as an insurance product at a particular price level with a collection of add- on insurance products.

This section will cover how the product portfolio strategies were derived, and then simplified to create a representative set of player strategies that provided a full spectrum of marketable product portfolio strategies but so as not to overwhelm the calculation of the Nash Equilibrium.

3.4.2.1.

Product Portfolio Strategies

Using the product definitions used in the survey, for each company (3 insurance level, 1 brands, 4 price levels and 7 insurance add-ons), there are a possible 1,536 ( ) products available. This would imply there are a possible ( ) product portfolios. If each strategy is a product portfolio, this would be an unreasonable game size to calculate the Nash Equilibrium.

Many of the product insurance add-ons did not have statistically significant values for the customer utilities. Therefore, many of the total number of products would not yield unique results. For this reason, we can narrow down the number of product add-ons to three: Legal Cover, Protected No-Claims

3 1 ⇤ 1 1 ⇤ 4 1 ⇤27

2

1,536

Bonus and Key Cover. This would yield 96 unique products. The total number of product portfolios from this, although significantly smaller, is still unreasonable for calculation purposes ( ).

3.4.2.2.

Game Strategies

If using product portfolios, rather than just products, there are too many possibilities for calculating using all possible portfolio strategies; Therefore, methods were employed to create a subset of representative product portfolios.

The representative product portfolio strategies, , where must demonstrate the full range of possible portfolios. Creating the full range includes from very basic portfolios of just one product, to the full portfolio of all possible products. For the other product portfolios, interviews, market data and rank pricing was used to create a total of 21 possible portfolios.

Based on the interviews and insurance market reporting, many insurance companies create products specifically targeted and offered to a niche group. These product offerings are specialty product portfolios and, to avoid confusion with the game product portfolio strategies, will be referred to as Targeted Portfolios. The interviews also revealed insurance company’s desire to have a variety of products available. This was represented using Targeted Portfolios that have more varied collections of products, shifting price points to reflex a shift in the number of add-ons or the insurance level.

Finally, price ranking was used to create portfolios of products that include most all products, but insure consistency in the pricing based on the number of add-ons and the insurance level. Also, it was expressed in the interviews, and demonstrated in market research, that most companies do not provide the ‘Third Party Only’ Insurance Level Option. For this reason, the price ranked portfolios were also created with ‘Comprehensive’ and ‘Third Party, Theft and Fire’ (TPTF) only.

The full list of product strategies are included in Appendix B.

3.4.3. Defining Player Utility

The utility function to be utilised in the game theory model is the utility to the player (competitive strategic group) when using a given product portfolio. As discussed in the Literature Review chapter, the game definition is based on the Sadeghi & Zandieh theory of using game theory to optimise product portfolio management (Sadeghi & Zandieh, 2011). In this model the player utility is derived as the expected market value of the portfolio given the consumer purchase preferences. The final player utility values will then be used in the game matrix to enable to calculation of the Nash Equilibrium of the game.

7.923_⇤10

The consumer utility functions for a given product were calculated using choice-based conjoint analysis and can be used to calculate consumer purchase behaviour. Therefore, the utility needs to be transformed from the consumer utility for a single product to the expected market value of a group of products.

This transformation has many forms, each for a different purpose. The general form was first published by Green and Krieger (1985). Since then there have been more specific functions created for engineering (Jiao & Zhang; 2005) and marketing (Yano & Dobson; 1998). There has even been some work in the insurance industry incorporating risk (Li, 1995).

The customer utility functions, are used to determine the market choice probability, , for a given market segment, as defined in the Multi-nominal Logit (MNL) model. This is done by comparing the utility of the product over the utility of all other available products in the market (Kamakura & Russell, 1989). Thus:

Where ! is a product released by player ! , in the market pure product portfolio strategy combination, , where there are competing products, , by all other players, ,

where for is a set containing all products released by all players in product portfolio strategy combination . Therefore, we may represent the set containing all products release by player in pure product portfolio strategy combination as , where .

For the mth player and a product portfolio strategy, , the expected market value, E, can be calculated with the following, as adapted from Li (1995):

!

Where the market pure product portfolio strategy, ! , is defined by the player pure product portfolio strategies , with released products . Market segments,

and ! are adjusted for using market segment size, ! , and market segment insurance portfolio risk ratio,! . Finally, each product is weighted for its potential profit by inclusion of the product price, ! .

P