Mathematical Predictions on Game Theory

Game Theory is a mathematical proven tool of analysis, in another word, on itself, it does not make further material predictions than arithmetic does. Relating to Game theory, mathematics is a logical sequence which cannot be proven or tested to be right or wrong. Game theory can be used as a model to predict the outcome of an event given suitable assumptions regarding the actions and payoffs, in that sense, the model produces a testable hypothesis. Some hypothesis may turn out to be externally inconsistent and contradicts the theory, but it does not conclude that the theory as a whole is misguided as internally inconsistency with respect to the theory itself, is still yet to be discovered.

Game theory can be applied to multiple occasions in the supermarket industry in the past which are relatively accurate. One example was in 1995, where Tesco escalate expenditure on its marketing and first introduce its national Clubcard system to sustain its customer's loyalty. No doubt, the scheme was incredibly successful, it was able to assemble information like spending habits for current customers and capture those floating shoppers towards Tesco, in fact it had overtaken Sainsbury, the market leader at the time with a 12.

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7 per cent increase in pre-tax profit and 19.1 per cent market share, 0.6 per cent ahead of Sainsbury.

Until to date, Tesco still is the market leader in the grocery supermarket industry, investing huge sums across a range of market initiatives including the introduction of advanced technology as a strategy has been extremely effective, as it was the pioneer to commence the system, it has drawn customers from both similar size and smaller competitors like Asda and Co-op into Tesco.

In this scenario, the best strategy for competitors is to also rise expenditure on marketing development to reach a Nash equilibrium. Another hypothesis that has been occurred is where eight supermarkets were discovered to be colluding by fixing dairy product prices.

According to the Office of Fair Trading, “The cartel used a so-called A-B-C information exchange, where supermarkets indirectly passed information on future prices to each other via dairy processors”. To illustrate this as an example, in figure 1, the table represents a payoff matrix when Tesco and Sainsbury collude by both fixing a high price to maximise profit, they equally obtained £20 million each. However, both parties have a dominant strategy when they lower prices to achieve extra returns of £5m, so most likely one or another will cheat to gain the benefits.

If Tesco found out that Sainsbury was cheating, they would also drop their prices resulting in both companies to operate under Nash equilibrium and may result in a price war. With regards to the case occurred in 2007, a total of a £49.5m fine was imposed between the eight companies but Arla, the whistleblower received immunity from all penalties. There are two types of Game Theory, the traditional game theory which leans towards normative theory, where it uses theoretical models to conclude which preference would assist each player the most without considering other reasons. Since it assumes that all players act rationally in decision making and therefore grant players to forecast their rivals’ tactics effortlessly. On the other hand, Behavioural game theory uses real-life example and experimental data to rationalise the decisions being made.

Overall, Game Theory itself was not intended to make any predictions since it is an instrument that aids social scientists to examine the certain social situation. However, the theory can be applied to real life situations given appropriate assumptions to produce a hypothesis that is testable. The accuracy of the result is dependent by the hypothesis as it varies from one another, some may turn out to be relatively accurate, cases mentioned in the UK supermarket industry, but others may be unpredictable and disprove the theory. Traditional game theory in comparison to behavioural is mainly a normative theory rather than positive.