Sentence examples for response correspondence from inspiring English sources
Before we start, let us introduce the notion of best response correspondence, since it plays a central role in the following analysis.
In particular, the best response correspondence of i ∈ N, denoted by B i : X − i → X i, is B i ( x − i ) = { x i ∗ ∣ ∀ x i ′ ∈ X i : u i ( x i ∗, x − i ) ≥ u i ( x i ′, x − i ) }. Then the joint best response correspondence, denoted by F : X → X, is defined as F ( x ) = ∏ i ∈ N B i ( x − i ).
Then, from the best response correspondence, it holds that ∀ ( k, s ) ∈ K × S, p k, s † = 1 β k − σ 2 + g − k, s p − k, s † g k, s +, (92).
This, in turn, implies that a strategy profile x ∗ ∈ X is a Nash equilibrium if x ∗ ∈ F ( x ∗ ) ; i.e., if it is a fixed point of the joint best response correspondence.
Nash [4] firstly defined the best response correspondence and applied the Berge maximum theorem and Kakutani fixed point theorem to prove the existence of Nash equilibrium points in finite games, where finitely many players may choose from a finite number of pure strategies in finite-dimensional Euclidean spaces.
In half of the trials, stimulus and response positions corresponded (spatial stimulus-response Correspondence), whereas in the other half, stimulus and response positions did not correspond (spatial stimulus-response Noncorrespondence).
In a non-cooperative game described by the 3-tuple K, P k ∀ k ∈ K, u k ∀ k ∈ K, the relation BR k : P − k → P k such that BR k p − k = arg max q k ∈ P k u k q k, p − k, (16). is defined as the best-response correspondence of player k ∈ K, given the actions p−kadopted by all the other players.
Increasing the weight of the response-location code increases the feature overlap with the stimuli, which increases the size of the stimulus-response correspondence effect.
If the other key is operated by another individual, however, as in the joint task version, the Simon effect is back – spatial stimulus-response correspondence improves performance – the joint Simon effect (JSE; Sebanz et al., 2003).
Mean correct reaction times (RTs) and error percentages (PEs) were analyzed by means of repeated-measures analyses of variance (ANOVAs) as a function of Aroma Group (lavender vs. peppermint vs. control) as between-participants factor and spatial stimulus-response Correspondence (correspondence vs. noncorrespondence) as within-participants factor.
