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Pareto dominant (Definition)

An outcome $ s^*$ strongly Pareto dominates $ s^\prime$ if:

$\displaystyle \forall i\leq n \left[u_i(s^*)>u_i(s^\prime)\right] $

An outcome $ s^*$ weakly Pareto dominates $ s^\prime$ if:

$\displaystyle \forall i\leq n \left[u_i(s^*)\geq u_i(s^\prime)\right] $

$ s^*$ is strongly Pareto optimal if whenever $ s^\prime$ weakly Pareto dominates $ s^*$, $ \forall i\leq n\left[u_i(s^*)=u_i(s^\prime)\right]$. That is, there is no strategy which provides at least as large a payoff to each player and a larger one to at least one. $ s^*$ is weakly Pareto optimal if there is no $ s^\prime$ such that $ s^\prime$ strongly Pareto dominates $ s^*$.



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Also defines:  strongly Pareto optimal, weakly Pareto optimal, strongly Pareto dominates, strongly Pareto dominant, Pareto dominates, Pareto dominant, weakly Pareto dominates, weakly Pareto dominant
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Cross-references: player, payoff, strategy, outcome
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This is version 3 of Pareto dominant, born on 2002-07-24, modified 2004-04-30.
Object id is 3194, canonical name is ParetoDominant.
Accessed 12854 times total.

Classification:
AMS MSC91A99 (Game theory, economics, social and behavioral sciences :: Game theory :: Miscellaneous)

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Which is correct? by magsfi on 2004-08-28 19:40:51
I often see the definition of Pareto Optimality is expressed as "An outcome of a game is Pareto optimal if there is no other outcome that makes every player at least as well off and at least one player strictly better off."
http://www.gametheory.net/Dictionary/ParetoOptimal.html
http://www.fact-index.com/p/pa/pareto_efficiency.html

This definition is different from the above definition. Which is correct?


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