edu.princeton.repeatedgames.rgsolve
Class InnerApproximation

java.lang.Object
  edu.princeton.repeatedgames.rgsolve.InnerApproximation

public class InnerApproximation
extends java.lang.Object

This class is for inner-approximating the equilibrium set V* from smaller sets, by applying the Abreu-Sannikov operator to sets inside the calculated V*.

Constructor Summary

private

InnerApproximation() private constructor

Method Summary

static RGSolution	getInnerApproximationSolution(Game game, AlgoParameters params, Point[] W0, double scale) This method returns the inner approximation solution implied by the set W0.
static RGSolution	getInnerApproximationSolution(RGSolution soln, double scale) This method returns the inner approximation solution implied by the solution soln.
static Point[]	shrinkSet(Point[] W, double scale) "Shrinks" the set W by contracting each vertex v towards the point q, i.e.

Methods inherited from class java.lang.Object

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

Constructor Detail

InnerApproximation

private InnerApproximation()

private constructor

Method Detail

getInnerApproximationSolution

public static RGSolution getInnerApproximationSolution(RGSolution soln,
                                                       double scale)

This method returns the inner approximation solution implied by the solution soln. In particular, we shrink the set soln.V_star by scale and apply the AS (or APS) operator until convergence.

Parameters:

soln - a solved game

scale - the shrinkage factor

Returns:

the inner approximation solution

getInnerApproximationSolution

public static RGSolution getInnerApproximationSolution(Game game,
                                                       AlgoParameters params,
                                                       Point[] W0,
                                                       double scale)

This method returns the inner approximation solution implied by the set W0. In particular, we shrink the set W0 by scale and apply the AS (or APS) operator until convergence.

Parameters:

game - the game to be solved by inner-approximation

params - solver settings

W0 - initial set, to be shrunken

scale - the shrinkage factor

Returns:

the inner approximation solution

shrinkSet

public static Point[] shrinkSet(Point[] W,
                                double scale)

"Shrinks" the set W by contracting each vertex v towards the point q, i.e. v' = (1-scale) * v + scale * e, where e is the mean of vertices of W.

Parameters:

W - the set (polygon) to shrink

scale - shrinkage parameter in [0,1)

Returns:

the shrunken set