Game theory

Why do players in a game sometimes settle for less than winning?

Imagine you're playing a game of chess with a friend. You both want to win, but you notice that if you both try to checkmate each other's king, it could lead to a stalemate. Instead, you both decide to play more cautiously, avoiding risky moves that could lead to a stalemate.

In chess, players aim for the best outcome, but sometimes they choose a safer strategy that might not win them the game outright. They settle for a stable situation where neither can improve unilaterally, known as Nash Equilibrium.

Example

You and your friend agree to stop the game if either of you has a chance to win in the next move. This way, neither of you can improve your position without making the other worse off.

Remember this

Players sometimes choose a stable strategy that benefits them without risking a worse outcome, even if it's not the winning strategy.

Text adapted from Wikipedia, licensed under CC BY-SA 4.0.

Related concepts

a dominant strategy is: optimal regardless of what other players do

A dominant strategy maximizes payoff irrespective of opponents' actions

Nash equilibrium

Nash equilibrium: no unilateral gain

the minimax theorem says: in zero-sum games, there's a saddle point strategy

Minimax theorem guarantees a saddle point strategy in zero-sum games

Prisoner's dilemma

Prisoner's dilemma illustrates how individual rationality can lead to collectively worse outcomes

Zero-sum game

Zero-sum game: one player's gain equals another's loss

Greedy vs dynamic programming: greedy makes locally optimal choices, DP considers all subproblems

Greedy: locally optimal choices; DP: considers all subproblems

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