compromiseadmissiblecheck {TUGLab} | R Documentation |
Compromise-admissible check
Description
This function checks if the given game is compromise-admissible.
Usage
compromiseadmissiblecheck(v, binary = FALSE, instance = FALSE)
Arguments
v |
A characteristic function, as a vector. |
binary |
A logical value. By default, |
instance |
A logical value. By default, |
Details
Let v\in G^N
.
The utopia payoff of player i\in N
is defined as M_i(v)=v(N)-v(N\backslash i)
.
The minimal right of player i\in N
is defined as m_i(v)=\max_{S:i\in S}(v(S)-\sum_{j\in S\backslash i}M_j(v))
.
The game v\in G^N
is said to be compromise-admissible if its core-cover is not empty, that is, if the following conditions hold:
1) m(v)\leq M(v)
.
2) \sum_{i\in N}m_{i}(v)\leq v(N)\leq \sum_{i\in N}M_i(v)
.
Value
TRUE
if the game is compromise-admissible, FALSE
otherwise. If instance=TRUE
and \{i \in N : m_i(v)>M_i(v)\} \neq \emptyset
, one of the players in that set is also returned.
Examples
compromiseadmissiblecheck(c(0,0,0,0,10,40,30,60,10,20,90,90,90,130,160))
compromiseadmissiblecheck(c(1,2,2), instance=TRUE)
# What if the game is a cost game?
cost.v <- c(30, 20, 50, 40, 60, 60, 75) # compromise-admissible cost game
compromiseadmissiblecheck(-c(30, 20, 50, 40, 60, 60, 75))