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The essence of the Nash-stable is that in the final partition Π f, no player can find a coalition that can further improve its payoff; thus, the player has no incentive to deviate from its current coalition.
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In fact, it can easily be shown that if conditions (13) and (15) hold no change of strategy by a single node improves its payoff.
Assume i is the only node supporting it, then j receives no information from i, while if j makes the link strong at a cost (c<1), j improves its payoff in at least (1-c>0), which contradicts g being a Nash profile.
Pareto optimal profiles are those profiles starting from which no player can improve its own payoff without making another's payoff worse.
Then, it is profitable for player k1 to invite player k3 to join, therefore improving its own payoff from 0.4 to 0.6 and that of player k3 from zero to 0.2.
Cisco can improve its fortunes.
Joseph to improve its team.
Thirdly, France intends to improve its competitiveness.
Indonesia must also improve its ports.
NASA certainly needs to improve its efficiency.
The company pledged to improve its performance.
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