burlap.behavior.stochasticgames.solvers

Class GeneralBimatrixSolverTools

java.lang.Object

burlap.behavior.stochasticgames.solvers.GeneralBimatrixSolverTools

public class GeneralBimatrixSolverTools
extends java.lang.Object

A class holding static methods for performing common operations on bimatrix games.

Author:

James MacGlashan

Method Summary

Modifier and Type	Method and Description
static double[]	constantDoubleArray(double constant, int dimension) Returns a double array of a given dimension filled with the same value.
static double	dot(double[] a, double[] b) Returns the dot product of two vectors
static double[]	expectedPayoffs(double[][] payoffRowPlayer, double[][] payoffColPlayer, double[][] jointActionProbabilities)
static double[]	expectedPayoffs(double[][] payoffRowPlayer, double[][] payoffColPlayer, double[] rowPlayerStrategy, double[] colPlayerStrategy) Computes the expected payoff for each player in a bimatrix game according to their strategies.
static double[]	getNegatedArray(double[] a) Returns a negated version of the input array in a new array object.
static double[][]	getNegatedMatrix(double[][] m) Returns a negated version of the input matrix in a new matrix object.
static double[][]	getPositiveMatrix(double[][] m) Creates a new matrix (m2) whose values are the values of m shifted by a constant amount c such that all the values in m2 are positive.
static double[][]	jointActionProbabilities(double[] rowPlayerStrategy, double[] colPlayerStrategy) Computes the joint action probabilities accroding to each player's strategy and returns it as a matrix.
static double[]	marginalizeColPlayerStrategy(double[][] jointActionProbabilities) Returns the column player's strategy by marginalizing it out from a joint action probability distribution represented as a matrix
static double[]	marginalizeRowPlayerStrategy(double[][] jointActionProbabilities) Returns the row player's strategy by marginalizing it out from a joint action probability distribution represented as a matrix
static double[][]	transposeMatrix(double[][] m) Creates and returns a new matrix that is a transpose of m.
static double[]	zero1Array(int index, int dim) Creates an array that is all zeros except one index which has a value of 1.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

expectedPayoffs

public static double[] expectedPayoffs(double[][] payoffRowPlayer,
                                       double[][] payoffColPlayer,
                                       double[] rowPlayerStrategy,
                                       double[] colPlayerStrategy)

Computes the expected payoff for each player in a bimatrix game according to their strategies.

Parameters:

payoffRowPlayer - the payoff for player 1. Rows are player 1's actions; columns player 2's.

payoffColPlayer - the payoff for player 2. Rows are player 1's actions; columns player 2's.

rowPlayerStrategy - the strategy for player 1. Should be array with dimension equal to the number of player 1's actions.

colPlayerStrategy - the stratgy for player 2. Should be array with dimension equal to the number of player 2's actions.

Returns:

a double array of dimension two. Index 0 holds the first player's expected payoff; index 1 holds the second player's expected payoff.

expectedPayoffs

public static double[] expectedPayoffs(double[][] payoffRowPlayer,
                                       double[][] payoffColPlayer,
                                       double[][] jointActionProbabilities)

jointActionProbabilities

public static double[][] jointActionProbabilities(double[] rowPlayerStrategy,
                                                  double[] colPlayerStrategy)

Computes the joint action probabilities accroding to each player's strategy and returns it as a matrix.

Parameters:

rowPlayerStrategy - the strategy of the player whose actions will be represented by the rows of the returned matrix.

colPlayerStrategy - the strategy of the player whose actions will represented by the columns of the returned matrix.

Returns:

the joint action probabilities in a matrix. m[i][j] represents the probability of the row player selecting action i and the column player selecting action j.

marginalizeRowPlayerStrategy

public static double[] marginalizeRowPlayerStrategy(double[][] jointActionProbabilities)

Returns the row player's strategy by marginalizing it out from a joint action probability distribution represented as a matrix

Parameters:

jointActionProbabilities - a matrix of 2-player joint aciton probability distribution

Returns:

the row player's strategy

marginalizeColPlayerStrategy

public static double[] marginalizeColPlayerStrategy(double[][] jointActionProbabilities)

Returns the column player's strategy by marginalizing it out from a joint action probability distribution represented as a matrix

Parameters:

jointActionProbabilities - a matrix of 2-player joint aciton probability distribution

Returns:

the column player's strategy

constantDoubleArray

public static double[] constantDoubleArray(double constant,
                                           int dimension)

Returns a double array of a given dimension filled with the same value.

Parameters:

constant - the constant value with which the double array is filled.

dimension - the dimension of the double array.

Returns:

a double array of size dimension filled with the value constant.

getNegatedMatrix

public static double[][] getNegatedMatrix(double[][] m)

Returns a negated version of the input matrix in a new matrix object. That is, a new 2D double array (m2) is created with the m2[i][j] value set to -1 * m[i][j].

Parameters:

m - the input matrix.

Returns:

the negated matrix.

getNegatedArray

public static double[] getNegatedArray(double[] a)

Returns a negated version of the input array in a new array object. That is, a new double array (b) is created with b[i] value set to -1 * a[i].

Parameters:

a - the input double array

Returns:

a negated version of the input array

getPositiveMatrix

public static double[][] getPositiveMatrix(double[][] m)

Creates a new matrix (m2) whose values are the values of m shifted by a constant amount c such that all the values in m2 are positive. If all entries in m are already postive, then c = 0 (no shift). Otherwise, c = 1 - min(m).

Parameters:

m - the input matrix.

Returns:

a constant shifted version of m that is positive.

transposeMatrix

public static double[][] transposeMatrix(double[][] m)

Creates and returns a new matrix that is a transpose of m.

Parameters:

m - the input matrix.

Returns:

the transposed version of m.

dot

public static double dot(double[] a,
                         double[] b)

Returns the dot product of two vectors

Parameters:

a - first vector

b - second vector

Returns:

the dot product

zero1Array

public static double[] zero1Array(int index,
                                  int dim)

Creates an array that is all zeros except one index which has a value of 1. For example zero1Array(2, 4) will return {0., 0., 1., 0.}.

Parameters:

index - the index which will have a valu of 1

dim - the dimension of the array to create

Returns:

an array that is all zeros except one index which has a value of 1.