Costbenefit Module

class powergama.costbenefit.CostBenefit

Experimental class for cost-benefit calculations.

Currently including allocation schemes based on “cooperative game theory”

Methods

gameIsMonotone(values)	Returns true if the game/valueFunction is monotonic.
gameIsSuperadditive(values)	Returns true if the game/valueFunction is superadditive.
gamePayoffHasNullplayer(player_list, values, …)	Return true if the payoff vector possesses the nullplayer property.
gamePayoffIsEfficient(player_list, values, …)	Return `true if the payoff vector is efficient.A payoff vector v is efficient if the sum of payments equal the total value provided by a set of players.sum_{i=1}^N lambda_i = v(Omega);.
gamePayoffIsSymmetric(values, payoff_vector)	Returns true if the resulting payoff vector possesses the symmetry property.
gameShapleyValue(player_list, values)	compute the Shapley Value from cooperative game theory
getBinaryCombinations(num)	Returns a sequence of different combinations 1/0 for a number of decision variables.
nCr(n, r)	calculate the binomial coefficient, i.e.
power_set(List)	function to return the powerset of a list, i.e.

gameSetup

gameIsMonotone(values)

Returns true if the game/valueFunction is monotonic. A game G = (N, v) is monotonic if it satisfies the value function of a subset is less or equal then the value function from its union set: v(C_2) geq v(C_1) for all C_1 subseteq C_2

gameIsSuperadditive(values)

Returns true if the game/valueFunction is superadditive. A characteristic function game G = (N, v) is superadditive if it the sum of two coalitions/subsets gives a larger value than the individual sum: v(C_1 cup C_2) geq v(C_1) + v(C_2) for all C_1, C_2 subseteq 2^{Omega} such that C_1 cap C_2 = emptyset.

gamePayoffHasNullplayer(player_list, values, payoff_vector)

Return true if the payoff vector possesses the nullplayer property. A payoff vector v has the nullplayer property if there exists an i such that v(C cup i) = v(C) for all C in 2^{Omega} then, lambda_i = 0. In other words: if a player does not contribute to any coalition then that player should receive no payoff.

gamePayoffIsEfficient(player_list, values, payoff_vector)

Return `true if the payoff vector is efficient. A payoff vector v is efficient if the sum of payments equal the total value provided by a set of players. sum_{i=1}^N lambda_i = v(Omega);

gamePayoffIsSymmetric(values, payoff_vector)

Returns true if the resulting payoff vector possesses the symmetry property. A payoff vector possesses the symmetry property if players with equal marginal contribution receives the same payoff: v(C cup i) = v(C cup j) for all C in 2^{Omega} setminus {i,j}, then x_i = x_j.

gameSetup(grid_data)

gameShapleyValue(player_list, values)

compute the Shapley Value from cooperative game theory

getBinaryCombinations(num)

Returns a sequence of different combinations 1/0 for a number of decision variables. E.g. three cable investments; (0,0,0), (1,0,0), (0,1,0), and so on.

nCr(n, r)

calculate the binomial coefficient, i.e. how many different possible subsets can be made from the larger set n

power_set(List)

function to return the powerset of a list, i.e. all possible subsets ranging from length of one, to the length of the larger list