Introduction
Spite, in the context of game theory, is a phenomenon that occurs in fair division problems. It is characterized by a player's value of an allocation decreasing when one or more other players' valuation increases. This behavior is counterintuitive, as one would expect a player to prefer an allocation where they receive more. However, in the case of spite, the player's preference is inverted, and they prefer an allocation where others receive less.
Definition and Analysis
Spite is difficult to analyze because it requires assessing two sets of preferences. In the context of fair division problems, a spiteful player must make a trade-off between depriving their opponent of a desirable good and receiving more themselves. This trade-off is not straightforward, as it involves considering the preferences of both the self and the opponent.
History and Context
The concept of spite in game theory is not new and has been studied in various contexts. In the field of sociobiology, spite is used to describe social behaviors that have a negative impact on both the actor and recipient(s). This concept is closely related to the idea of kin selection, where spite is favored when it leads to an indirect benefit to a sufficiently related third party.
Examples and Applications
Spite is not a common phenomenon in everyday life, but it can be observed in various game-theoretic scenarios. For example, in the divide and choose method, a spiteful player would prefer an allocation where their opponent receives less, even if it means receiving less themselves. This behavior can be seen as a form of altruism, where the player's preference is directed towards depriving their opponent rather than receiving more.
Relation to Sociobiology
Spite is also used to describe social behaviors in the context of sociobiology. In this context, spite is favored when it leads to an indirect benefit to a sufficiently related third party. This can be seen in the concept of Wilsonian spite, where spite is directed towards individuals who are not closely related. Hamiltonian spite, on the other hand, is directed towards individuals who are negatively related.
FAQ
What is spite in game theory? Spite in game theory is a phenomenon where a player's value of an allocation decreases when one or more other players' valuation increases.
How is spite related to sociobiology? Spite is related to sociobiology in the context of kin selection, where spite is favored when it leads to an indirect benefit to a sufficiently related third party.
Can spite be observed in everyday life? Spite can be observed in various game-theoretic scenarios, such as the divide and choose method, where a spiteful player would prefer an allocation where their opponent receives less.
What is the difference between Wilsonian spite and Hamiltonian spite? Wilsonian spite is directed towards individuals who are not closely related, while Hamiltonian spite is directed towards individuals who are negatively related.