Everyday is full of small decisions: what to wear, what to eat, what to say. While many of our choices are based on our own preferences, a few, more complex decisions, require us to consider the possible actions and preferences of other people. This is known as strategic decision making, which is often modelled in the form of static or dynamic games (i.e. the players make a decision simultaneously or sequentially).

Here I will focus on the widely used example of a static game, whereby two prisoners face the same choice to confess or to stay silent. Both are guilty, but the authorities lack enough evidence to achieve a full conviction without a confession. The interrogators take the two suspects into separate rooms (to avoid the possibility of the prisoners communicating) and give them an ultimatum: confess to the crime and receive a reduced sentence or stay silent with a chance of receiving a maximum sentence if the other suspect confesses. We can construct the game in a matrix form, with the payoffs of each potential outcome provided: (The numbers denote years in prison for each prisoner)

The best outcome for the prisoners involves both staying silent, however the incentive to cheat (i.e. the possibility of only spending 3 years in prison) will encourage them to change strategies. As both have the incentive to cheat, the worst outcome will occur, i.e. both spend 7 years in prison. This is called the Nash equilibrium whereby, once at this outcome, changing strategy will not result in a better outcome for the player, holding the other player’s strategy constant. For example, when Prisoner A has chosen to confess as a strategy, Prisoner B will always choose to confess as well as 7 years in prison is more appealing than 10.

In this scenario, we are assuming that the prisoners are not altruistic, i.e. they only care about their own prison time and do not care about betraying their partner.

The best outcome for the prisoners can be achieved via collusion, either explicitly or implicitly agreeing to stay silent, however this is not a stable outcome as the incentive to cheat is still present.

This framework can be applied to many useful scenarios, including whether a firm should lower their price relative to a rival and whether to produce a marketing campaign. Imagine an industry with only two equally sized firms and a fixed number of customers. If firm A reduces their price, they will steal business away from firm B and receive higher profits. Firm B will then reduce their price to compete, but now both firms have the same amount of customers as before, but with lower profits (due to the lower price). The second example is the same idea, whereby adverts bring in business but at a financial cost to the firm. These firms may agree to keep prices high etc. but this practice violates EU Competition Policy and may result in a fine or prison time if proven.

By utilising this simple model, we can attempt to predict decision making behaviour of firms and individuals in certain scenarios. This has major implications across many fields with a broad range of potential uses, but it is a key tool in economics to understand strategic firm behaviours.