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Beyond A-level · 5 of 14

Nash equilibrium and the prisoner's dilemma

Find a Nash equilibrium and say why it can leave both players worse off

Game theory turns oligopoly interdependence into a table of payoffs

At A-level, oligopoly means interdependence: each firm's best move depends on what its rivals do. Game theory makes that exact. It studies situations in which players make decisions and then receive payoffs that depend on what the other players decide. Take two firms choosing whether to advertise. Advertising costs money and mostly wins customers from the rival, so if both advertise the gains cancel out and only the costs remain.

The advertising game: profits in £ million, Firm A firstA two-by-two payoff matrix. Rows are Firm A advertising or not; columns are Firm B advertising or not. Both advertise: 3 and 3. A advertises, B does not: 6 and 2. B advertises, A does not: 2 and 6. Neither advertises: 5 and 5.B: AdvertiseB: Don'tA: AdvertiseA: Don't3, 36, 22, 65, 5
Each cell gives Firm A's profit, then Firm B's, in £ million. Illustrative figures.
Predict first

Two firms can advertise or not. Advertising costs money and mainly steals customers from the rival. What do you think they end up doing?