Farsightedness (game theory)

In game theory, farsightness refers to players’ ability to consider the long-term consequences of their strategies, beyond immediate payoffs, often formalized as farsighted stability where players anticipate future moves and stable outcomes.^[1]

In static games, players optimize payoffs based on current information, as in the Nash equilibrium,^[2] but farsightedness involves anticipating dynamic or repeated interactions, such as in coalition games like hedonic games where preferences shape long-term alliances.^[3] For example, in a repeated Prisoner's Dilemma, a farsighted player might cooperate to encourage future cooperation, unlike the one-shot case where defection prevails.^[4] Similarly, a player might refuse a small immediate payoff to build a more valuable alliance later.^[1]

Farsightedness assumes significant foresight and computational ability, which may be unrealistic in complex scenarios. In evolutionary settings, myopic strategies might dominate if immediate survival outweighs long-term planning.^[5]

Applications

In evolutionary game theory, farsightedness contrasts with myopic adaptation, where strategies adjust based on immediate fitness.^[6] A farsighted strategy might aim for an evolutionarily stable strategy (ESS) that withstands long-term mutant challenges. In coalition settings, farsighted players assess how current choices affect future stability, rejecting short-term gains for long-term benefits, as seen in hedonic games.^[3] Farsighted stability captures this by modeling chains of responses predicting stable configurations.^[1]

See also

• Evolutionary game theory
• Cooperative game theory
• Hedonic games
• Subgame perfect equilibrium
• Repeated game
• Evolutionarily stable strategy