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# Game Theory

## Game Theory

Use this framework for responding to competitive strategies

Game theory describes how economic equilibrium develops and changes. It became popular following the work of American mathematician, John Nash, who described how mixed strategies among competitors results in a new equilibrium. His work won a Nobel Prize in 1994. In this description I confine the discussion to the philosophy of game theory rather than its mathematical modelling.

Game theory is a framework that can be used to help decision-making. Take for example a duopoly in which two large competing companies have similar prices. From the point of view of one of these companies it may make logical sense to reduce prices and so steal share from its competitor. However, in a world in which emotions may influence actions, the competing company, worried about losing share may well reduce its prices. Both companies lose out.

The framework is often explained by "the prisoner's dilemma". Two prisoners who were complicit in a crime are interrogated separately. If neither confesses and splits on the other, they will both receive a sentence though it will be light and the best outcome (the least number of years in prison for each). However, each prisoner is tempted to confess thinking this will give them a minor sentence. This may be the case if only one confesses and the other does not. However since the temptation will be there for both of them, it is likely that each will make a confession and each will receive a severe sentence. The Nash equilibrium suggests that in a prisoner's dilemma, both players will make the move that they think is best for them individually but since both of them will make the same move, they will both be much worse off.

Let's take a business example and return to the duopoly. Imagine two competitors in a market in which there are only a limited number of customers. In the first scenario each competitor holds its prices and each makes profits of \$50 million as a result. Now let's imagine that competitor 1, in an attempt to win more business, cuts its prices. Competitor 2 does not. Competitor 1 would do very well out of the situation and earn \$60 million profit while competitor 2 would suffer a reduction and make only \$10 million profit. This is however quite an unlikely situation as competitor 2 would almost certainly take defensive action and would cut its prices. In doing so the companies would make only \$20 million profit each, far less than if they had not disturbed the original equilibrium.

In the case of the prisoner's dilemma each prisoner was unaware of what the other was saying and therefore were making a decision in the dark. In the business world we soon become aware of competitors' decisions and will inevitably have to decide what strategy to take in defence. If a competitor disturbs the equilibrium, it usually prompts an aggressive defensive reaction which results in a race to the bottom.

There are many opportunities for game theory in helping business strategy:

Beating the competition: By using game theory, companies can anticipate how competitors are likely to respond to different moves. This understanding helps in formulating proactive strategies to stay ahead of the competition.

Pricing: Game theory is often applied to analyse pricing strategies in competitive markets. Companies can model how changes in their prices and the prices of competitors impact market share and profitability.

Customer choice: Game theory helps companies analyze the positioning of their products relative to competitors. Understanding how product positioning affects consumer choices and competitor reactions can inform marketing strategies.

Customer loyalty: Analysing customer loyalty and retention as strategic interactions can help companies design programs and incentives to retain customers in the face of competitive challenges.

Promotional impact: Game theory models the impact of advertising and promotional strategies on market share. Companies can optimize their marketing efforts by considering how competitors might respond to different advertising approaches.

Market entry: When considering entering or exiting a market, game theory can help companies assess the potential reactions of existing competitors. This analysis aids in making informed decisions about market expansion or contraction.

Innovation: Game theory helps in analyzing innovation strategies and the adoption of new technologies. Companies can model how their decisions to innovate or adopt new technologies influence their competitive position.

Legal: Game theory can also be applied to assess the impact of regulatory and legal actions on market dynamics. Understanding potential legal reactions of competitors can inform compliance strategies.