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We uncover a new necessary condition for implementation in iteratively undominated strategies by mechanisms that satisfy the "best element property" where for each agent, there exists a strategy profile that gives him the highest payoff in the mechanism.
In Pareto optimal game, there exists a strategy that increases player's gain without damaging others.
there exists a strategy K-tuple s ∈ DS g (u) such that g(s) = f u) and.
Hence, there exists a strategy K-tuple s ∈ N g (u) such that g(s) = f u).
The mechanism g implements the SCF f in dominant strategy equilibria if for each utility K-tuple u ∈ U K, 1. there exists a strategy K-tuple s ∈ DS g (u) such that g(s) = f u) and 2.
It means that, for any given profile (x in S _{N}) and for every player (iin N), when player i's opponents take (x_{-i}) to play, there exists a strategy (t _{i}in S _{i}) such that player i will optimize his utility at the profile ((t _{i}), (x_{-i})).
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We prove that, if the frequency distribution of actions (fictitious play beliefs) converges, then there exists a pure-strategy equilibrium strategy that is consistent with it.
If (p^{s}_{t}=p^{s}_{t}left (x_{t},mathcal {C}^{t}right)) is such that there exists a superhedging strategy (resp. a strict superhedging strategy) Open image in new window then it is called a superhedging cost (resp. strict superhedging cost) at time t for (mathcal {C}^{t}).
That means not only that there exists, in general, no perfect hedging (i.e. replicating) strategy which is robust with respect to ambiguity on priors, but that in general there might not even exists a replicating strategy in the model with (any) one given probability prior, even without ambiguity.
Our main contributions in this paper are as follows: (1) We prove that there always exists a pure strategy Nash Equilibrium in the game and the optimal solution of our game is a Nash Equilibrium as well.
Dynamic programming, which is used for solving Markovian stochastic viability problems, then yields the set of design states for which there exists a maintenance strategy which guarantees reliability with a confidence level β for a given period of time T. Besides, it leads to a straightforward computation of the date of the first outcrossing, informing on when the system is most likely to fail.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com