Game theory is concerned with predicting the outcome of games of strategy in which the participants (for example two or more businesses competing in a market) have incomplete information about the others' intentions
The Prisoner's Dilemma
Confess or keep quiet? The Prisoner's Dilemma is a classic example of basic game theory in action!
Nash Equilibrium
Nash Equilibrium is an important idea in game theory – it describes any situation where all of the participants in a game are pursuing their best possible strategy given the strategies of all of the other participants.
In a Nash Equilibrium, the outcome of a game that occurs is when player A takes the best possible action given the action of player B, and player B takes the best possible action given the action of player A
Two prisoners are held in a separate room and cannot communicate They are both suspected of a crime They can either confess or they can deny the crime Payoffs shown in the matrix are years in prison from their chosen course of action | Prisoner A | ||
Confess | Deny | ||
Prisoner B | Confess | (3 years, 3 years) | (1 year, 10 years) |
Deny | (10 years, 1 year) | (2 years, 2 years) |
The equilibrium in the Prisoners' Dilemma occurs when each player takes the best possible action for themselves given the action of the other player. The dominant strategy is each prisoners' unique best strategy regardless of the other players' action Best strategy? Confess? A bad outcome! – Both prisoners could do better by both denying – but once collusion sets in, each prisoner has an incentive to cheat! | Prisoner A | ||
Confess | Deny | ||
Prisoner B | Confess | (3 years, 3 years) | (1 year, 10 years) |
Deny | (10 years, 1 year) | (2 years, 2 years) |
Applying the Prisoner's Dilemma to Business Decisions
Consider this example of a simple pricing game:
The values in the table refer to the profits that flow from making a particular output decision. In this simple game, the firm can choose to produce a high or a low output. The profit payoff matrix is shown below.
Firm B's output | |||
High output | Low output | ||
Firm A's output | High output | £5m, £5m | £12m, £4m |
Low output | £4m, £12m | £10m, £10m |
Potential Benefits from Collusion – A Game Theory Example
An industry consists of two firms, X and Y. The Profit-Payoff Matrix in the table below shows how the profits of X and Y vary depending on the prices charged by the two firms
Price charged by Business B | |||
Price Business A = £20 | Price Business A = £8 | ||
Price charged by Business A | Price Business A = £20 | £12m A, £12m B | £16m A, £-2m B |
Price Business A = £8 | £-2m A, £16m B | £0m A, £0m B |
If both businesses chose to collude on price rather than act competitively, the two firms would be able to increase their joint profits by £10m. However, if they agree to collude at the higher price of £20, then there is then an incentive for one business to under-cut the other, charge a lower price of £8 and inflicts a small loss on the other business.
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