Sentence examples for reply correspondence from inspiring English sources
Proof Let F ( ⋅, t ) be the joint best reply correspondence of the game Γ t.
Then, by Theorem 3, the set of fixed points of the joint best reply correspondence, that is, the Nash equilibrium set is a CPO.
Then, by Theorem 2, there exists the least fixed point of the joint best reply correspondence, which is the least Nash equilibrium of the game.
The defect that exists in the method of the best reply correspondence is the discontinuity between the best reply correspondence and the strategy set or payoff function; that is, in such results, it cannot be stated whether the Nash equilibrium is 'stable' with respect to the perturbation of the strategy sets or payoff functions.
This paper proves the existence of a Nash equilibrium for extended (semi-) uniform g-modular games, i.e., non-cooperative games where the strategy space is a complete partially ordered set, and the best reply correspondence satisfies certain monotonicity requirements.
Games with strategic complementarities in which the joint best reply correspondence is Veinott increasing (Veinott [5], Calciano [6]) rely on Zhou's [7] extension of Tarski fixed point theorem (Tarski [8]) to set-valued maps.
We introduce now the collective-best-reply correspondence of (Gamma (X,f)) ([12]).
Although individual agents learn Nash bidding strategies in isolation, the learning of each agent, by flattening the best-reply correspondence of other agents, blocks common learning.
Define (U Xtimes Xrightarrow R) as follows: U x,y)=sum_{iin N} f_{i}(x_{i},y_{-i}) quad x,yin X), then the collective-best-reply correspondence (mathit{CBR}_{Gamma (X,f }:Xrightarrow X) is defined as mathit{CBR}_{Gamma X,f)}(x)=bigl{ yin X|U x,y leq U y,y bigr} quad xin X).
Answer correspondence which simply requires an immediate reply (without any research), fax simple returns immediately.
