Class for solving stochastic games. More...

#include <sgsolver_maxminmax.hpp>

Collaboration diagram for SGSolver_MaxMinMax:

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Public Member Functions
	SGSolver_MaxMinMax ()
	Default constructor.

	SGSolver_MaxMinMax (const SGEnv &_env, const SGGame &_game)
	Constructor. More...

	~SGSolver_MaxMinMax ()
	Destructor.

void	solve_fixed ()
	Solve routine. More...

void	solve ()
	Solve routine. More...

double	iterate ()
	One iteration of the endogenous algorith. More...

double	pseudoHausdorff (const list< SGPoint > &newDirections, const list< vector< double > > &newLevels) const
	Compute approximate Hausdorff distance.

void	initialize ()
	Initializes the solve routines.

std::string	progressString () const

void	robustOptimizePolicy (SGTuple &pivot, vector< double > &penalties, vector< SGActionIter > &actionTuple, vector< SG::Regime > &regimeTuple, vector< bool > &bestAPSNotBinding, SGTuple &bestBindingPayoffs, const SGPoint currDir, const vector< list< SGAction_MaxMinMax > > &actions) const
	Optimizes the policy for the given direction.

double	sensitivity (const SGTuple &pivot, const vector< double > &penalties, const vector< SGActionIter > &actionTuple, const vector< SG::Regime > &regimeTuple, const SGPoint currDir, const vector< list< SGAction_MaxMinMax > > &actions) const

void	policyToPayoffs (SGTuple &pivot, const vector< SGActionIter > &actionTuple, const vector< SG::Regime > &regimeTuple) const
	Converts a policy function to a payoff function using bellman iteration.

void	policyToPenalties (vector< double > &penalties, const vector< SGActionIter > &actionTuple, const vector< SG::Regime > &regimeTuple) const

bool	lexComp (const SGPoint &a, const double aPenalty, const SGPoint &b, const double bPenalty, const SGPoint &dir) const
	Lexicographic comparison of points. More...

bool	computeBestBindingPayoff (const SGActionIter ait, int &bestBindingPlayer, int &bestBindingPoint, const SGPoint &dir) const
	Computes the best binding payoff for an action.

void	updateBestBinding (const vector< SGActionIter > &actionTuple, const vector< SG::Regime > &regimeTuple, const SGPoint &dir, SGTuple &bestBindingPayoffs, vector< bool > &bestAPSNotBinding) const
	Update best binding payoffs and check if best APS is binding.

void	minimizeRegimes (SGTuple &pivot, vector< double > &penalties, const vector< SGActionIter > &actionTuple, vector< SG::Regime > &regimeTuple, const SGPoint &dir, const SGTuple &bestBindingPayoffs, const vector< bool > &bestAPSNotBinding) const
	Switches regimes from binding to non-binding to minimize levels.

bool	lexAbove (const SGPoint &a, const SGPoint &b) const
	Lexicographic comparison of directions. More...

const SGSolution_MaxMinMax &	getSolution () const

Private Attributes
const SGEnv &	env
	SGEnv object to hold parameters.

const SGGame &	game
	Constant reference to the game to be solved.

SGSolution_MaxMinMax	soln
	SGSolution object used by SGApprox to store data.

const double	delta

const int	numPlayers

const int	numStates

const vector< vector< bool > > &	eqActions

const vector< vector< SGPoint > > &	payoffs

const vector< vector< vector< double > > > &	probabilities

const vector< vector< int > >	numActions

const vector< int >	numActions_totalByState

list< SGPoint >	directions

list< vector< double > >	levels

SGTuple	threatTuple

vector< list< SGAction_MaxMinMax > >	actions

const SGPoint	dueEast = SGPoint(1.0,0.0)

const SGPoint	dueNorth = SGPoint(0.0,1.0)

int	numIter

double	errorLevel

Detailed Description

Class for solving stochastic games.

This class implements the max-min-max algorithm of Abreu, Brooks, and Sannikov (2019) for two players. It contains the parameters for the algorithm, the solve method, as well as the data structure produced by solve. It calculates the equilibrium payoff correspondence corresponding to an SGGame object.

Examples: pd_twostate.cpp, and risksharing_maxminmax.cpp.

Constructor & Destructor Documentation

◆ SGSolver_MaxMinMax()

SGSolver_MaxMinMax::SGSolver_MaxMinMax	(	const SGEnv &	_env,
		const SGGame &	_game
	)

Constructor.

Creates a new SGSolver_MaxMinMax object and initializes it with the given game.

Member Function Documentation

◆ getSolution()

const SGSolution_MaxMinMax& SGSolver_MaxMinMax::getSolution ( ) const

inline

Returns a constant reference to the SGSolution_MaxMinMax object storing the output of the computation.

Examples: pd_twostate.cpp.

◆ iterate()

double SGSolver_MaxMinMax::iterate ( )

One iteration of the endogenous algorith.

Return the new error level.

◆ lexAbove()

bool SGSolver_MaxMinMax::lexAbove	(	const SGPoint &	a,
		const SGPoint &	b
	)		const

Lexicographic comparison of directions.

Returns true if a is above b or a is parallel to b.

◆ lexComp()

bool SGSolver_MaxMinMax::lexComp	(	const SGPoint &	a,
		const double	aPenalty,
		const SGPoint &	b,
		const double	bPenalty,
		const SGPoint &	dir
	)		const

Lexicographic comparison of points.

Returns true if a is above b in the direction dir, or if they are at the same level but a is higher than b in the direction dir rotated 90 degrees clockwise.

◆ policyToPenalties()

void SGSolver_MaxMinMax::policyToPenalties	(	vector< double > &	penalties,
		const vector< SGActionIter > &	actionTuple,
		const vector< SG::Regime > &	regimeTuple
	)		const

Converts a policy function to the associated penalties using bellman iteration, when computing inner approximation

◆ sensitivity()

double SGSolver_MaxMinMax::sensitivity	(	const SGTuple &	pivot,
		const vector< double > &	penalties,
		const vector< SGActionIter > &	actionTuple,
		const vector< SG::Regime > &	regimeTuple,
		const SGPoint	currDir,
		const vector< list< SGAction_MaxMinMax > > &	actions
	)		const

Find the next clockwise direction at which the optimal tuple changes

◆ solve()

void SGSolver_MaxMinMax::solve ( )

Solve routine.

Initializes a new SGApproximation object and iteratively generates it until one of the stopping criteria have been met. Stores progress in the data member.

Generates directions endogenously.

Examples: pd_twostate.cpp.

◆ solve_fixed()

void SGSolver_MaxMinMax::solve_fixed ( )

Solve routine.

Initializes a new SGApproximation object and iteratively generates it until one of the stopping criteria have been met. Stores progress in the data member.

Fixed directions.

Member Data Documentation

◆ actions

vector< list<SGAction_MaxMinMax> > SGSolver_MaxMinMax::actions

private

Actions that can still be played.

◆ delta

const double SGSolver_MaxMinMax::delta

private

The discount factor, copied from SGApprox_V2::game.

◆ directions

list<SGPoint> SGSolver_MaxMinMax::directions

private

List of directions in which the algorithm bounds payoffs.

◆ dueEast

const SGPoint SGSolver_MaxMinMax::dueEast = SGPoint(1.0,0.0)

private

The direction due east.

◆ dueNorth

const SGPoint SGSolver_MaxMinMax::dueNorth = SGPoint(0.0,1.0)

private

The direction due north.

◆ eqActions

const vector< vector<bool> >& SGSolver_MaxMinMax::eqActions

private

Constant refernece to actions that are allowed to be played in equilibrium in the game.

◆ errorLevel

double SGSolver_MaxMinMax::errorLevel

private

The current error level.

◆ levels

list< vector<double> > SGSolver_MaxMinMax::levels

private

List of optimal levels attained in the corresponding directions.

◆ numActions

const vector< vector<int> > SGSolver_MaxMinMax::numActions

private

Number of actions in the game.

◆ numActions_totalByState

const vector< int > SGSolver_MaxMinMax::numActions_totalByState

private

Total number of actions in each state.

◆ numIter

int SGSolver_MaxMinMax::numIter

private

The number of iterations computed thus far.

◆ numPlayers

const int SGSolver_MaxMinMax::numPlayers

private

The number of players, always 2.

◆ numStates

const int SGSolver_MaxMinMax::numStates

private

The number of states, copied from SGApprox_V2::game.

◆ payoffs

const vector< vector<SGPoint> >& SGSolver_MaxMinMax::payoffs

private

Constant reference to payoffs in the game.

◆ probabilities

const vector< vector< vector<double> > >& SGSolver_MaxMinMax::probabilities

private

Constant reference to transition probabilities in the game.

◆ threatTuple

SGTuple SGSolver_MaxMinMax::threatTuple

private

The current threat payoffs.

The documentation for this class was generated from the following files:

src/hpp/sgsolver_maxminmax.hpp
src/cpp/sgsolver_maxminmax.cpp

Public Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ SGSolver_MaxMinMax()

Member Function Documentation

◆ getSolution()

◆ iterate()

◆ lexAbove()

◆ lexComp()

◆ policyToPenalties()

◆ sensitivity()

◆ solve()

◆ solve_fixed()

Member Data Documentation

◆ actions

◆ delta

◆ directions

◆ dueEast

◆ dueNorth

◆ eqActions

◆ errorLevel

◆ levels

◆ numActions

◆ numActions_totalByState

◆ numIter

◆ numPlayers

◆ numStates

◆ payoffs

◆ probabilities

◆ threatTuple