edu.princeton.repeatedgames.rgsolve.polygon
Class GameExtremePoint

java.lang.Object
  edu.princeton.plot.Point
      edu.princeton.repeatedgames.rgsolve.polygon.GameExtremePoint

All Implemented Interfaces:

java.io.Serializable, java.lang.Cloneable

public class GameExtremePoint
extends Point
implements java.io.Serializable

This class extends the Point class. A GameExtremePoint described a vertex of V*, and how it is generated

See Also:

Serialized Form

Nested Class Summary

static class

GameExtremePoint.CONSTRAINT An enum type for the player identity of binding incentive constraints

Field Summary

int	a1 Player 1 action generating this point
int	a2 Player 2 action generating this point
GameExtremePoint.CONSTRAINT	continConstraint Identity of binding I.C.
int	continIndex1 index of point in extreme-point-table used in constructing continuation value
int	continIndex2 index of point in extreme-point-table used in constructing continuation value
private static long	serialVersionUID Serialization ID
GameExtremePoint.CONSTRAINT	stageConstraint Identity of binding I.C.
double	weight1 Indicates the probability weight on the Extreme Point in continIndex1.

Fields inherited from class edu.princeton.plot.Point

x, y

Constructor Summary

GameExtremePoint(double x, double y)
Simple constructor which sets x- and y-coordinate, leaving other fields uninitialized.

GameExtremePoint(double x, double y, int a1, int a2, int continIndex1, int continIndex2, double weight1, GameExtremePoint.CONSTRAINT stageConstraint, GameExtremePoint.CONSTRAINT continConstraint)
Full constructor of a GameExtremePoint detailing a vertex of V* and how it is generated.

Method Summary

void	contract(double g1, double g2, double discount) This method contracts this point towards g=(g1,g2), i.e.
GameExtremePoint	getContraction(double g1, double g2, double discount) This method contracts this point towards g=(g1,g2), i.e.
Point	getPoint() "Upcasts" this GameExtremePoint and returns an instance of Point with the same coordinates.

Methods inherited from class edu.princeton.plot.Point

affineCombo, angleRadians, angleRadiansAbs, clone, deepCopy, dot, dot, equals, euclidDistance, euclidDistance, get, getClockwiseNormal, getNaN, getX, getY, hashCode, interpXonY, interpYonX, isCloseTo, L1norm, L2norm, linearCombo, LInfnorm, minus, norm, normalize, plus, rotate, roundEquals, roundPointList, set, setX, setY, supDistance, supDistance, supNorm, times, toArray, toString, toString

Methods inherited from class java.lang.Object

finalize, getClass, notify, notifyAll, wait, wait, wait

Field Detail

serialVersionUID

private static final long serialVersionUID

Serialization ID

See Also:

Constant Field Values

a1

public int a1

Player 1 action generating this point

a2

public int a2

Player 2 action generating this point

continIndex1

public int continIndex1

index of point in extreme-point-table used in constructing continuation value

continIndex2

public int continIndex2

index of point in extreme-point-table used in constructing continuation value

weight1

public double weight1

Indicates the probability weight on the Extreme Point in continIndex1. This vertex equals (1-delta) g(a1,a2) + delta * (weight1 * continIndex1 + (1-weight1) * continIndex2).

stageConstraint

public GameExtremePoint.CONSTRAINT stageConstraint

Identity of binding I.C. constraints at the stage payoff supporting this point

continConstraint

public GameExtremePoint.CONSTRAINT continConstraint

Identity of binding I.C. constraints at the continuation payoff supporting this point

Constructor Detail

GameExtremePoint

public GameExtremePoint(double x,
                        double y)

Simple constructor which sets x- and y-coordinate, leaving other fields uninitialized.

Parameters:

x - x-coordinate

y - y-coordinate

GameExtremePoint

public GameExtremePoint(double x,
                        double y,
                        int a1,
                        int a2,
                        int continIndex1,
                        int continIndex2,
                        double weight1,
                        GameExtremePoint.CONSTRAINT stageConstraint,
                        GameExtremePoint.CONSTRAINT continConstraint)

Full constructor of a GameExtremePoint detailing a vertex of V* and how it is generated.

Parameters:

x - x-coordinate

y - y-coordinate

a1 - action of player 1

a2 - action of player 2

continIndex1 - index of continuation value

continIndex2 - index of continuation value

weight1 - the weight on continIndex1

stageConstraint - binding IC constraints at stage payoff

continConstraint - binding IC constraints for continuation value

Method Detail

getContraction

public GameExtremePoint getContraction(double g1,
                                       double g2,
                                       double discount)

This method contracts this point towards g=(g1,g2), i.e. (x',y') <-- (1-discount) * g + discount * (x,y), and returns the returns the new point (x',y')

Parameters:

g1 - stage payoff to 1

g2 - stage payoff to 2

discount - the discount rate

Returns:

(1-discount) * (g1,g2) + discount * (x,y)

contract

public void contract(double g1,
                     double g2,
                     double discount)

This method contracts this point towards g=(g1,g2), i.e. (x,y) <-- (1-discount) * g + discount * (x,y)

Parameters:

g1 - stage payoff to 1

g2 - stage payoff to 2

discount - the discount rate

getPoint

public Point getPoint()

"Upcasts" this GameExtremePoint and returns an instance of Point with the same coordinates.

Returns:

the Point (x,y)