Repeated and sequential games
Many real interactions happen again and again, or in order. These features change strategies and can make cooperation possible.
Repeated games
When a game is played many times with no known end, players can reward cooperation and punish cheating in future rounds. This can sustain cooperation that would collapse in a one-shot game. Firms in long-lasting oligopolies may avoid price wars for this reason, without any explicit agreement.
Tit-for-tat
In computer tournaments run by political scientist Robert Axelrod in the 1980s, a simple strategy called tit-for-tat performed very well: cooperate in the first round, then copy the opponent's previous move. It is nice (never cheats first), retaliatory (punishes cheating), forgiving, and clear.
Trigger strategies
A grim trigger strategy cooperates until the other player cheats once, then never cooperates again. The threat of losing all future cooperation can deter cheating, as long as players value the future enough. If the game has a known final round, cooperation can unravel backward from the end.
Sequential games
In sequential games, players move in turn, knowing earlier moves. They are drawn as game trees showing each decision point. Players solve them by backward induction: start at the end, work out the best final move, then the best move before that, and so on.
Worked example: entry deterrence
An incumbent firm threatens a price war if a rival enters. If a price war would cost the incumbent more than sharing the market, backward induction shows it will not carry out the threat once entry happens, so the threat is not credible, and the rival enters. Threats must be credible to work.
Credible commitments
A firm can make a threat credible by committing in advance, for example by building excess capacity that makes a price war cheaper to carry out. Burning bridges, signing contracts, and public promises can be strategic moves that limit your own options in order to change others' behaviour.
First-mover advantage
In some sequential games, moving first gives an advantage: the first firm to build a large factory or capture network users can shape the market. In others, moving second is better, because you can learn from the first mover's mistakes.
Games beyond business
Game theory is used in auctions (designing spectrum auctions that raised billions for governments), international relations (nuclear deterrence), biology (evolutionarily stable strategies), and everyday negotiation. Several Nobel Prizes in economics have been awarded for game-theoretic work.
Key takeaways
Repeated games allow cooperation through rewards and punishments; tit-for-tat is a simple effective strategy. Known end points can unravel cooperation. Sequential games are solved by backward induction on game trees. Threats must be credible, and commitments can make them so. First-mover advantage exists in some games. Game theory applies to auctions, diplomacy, and biology.
Flashcard
Same game played many times
Check your understanding
An incumbent threatens a price war if a new firm enters, but a price war would cost the incumbent more than sharing the market. What does game theory predict?