Game Namespace Reference

Data Structures
class	EPEC
	Class to handle a Nash game between leaders of Stackelberg games. More...
struct	EPECAlgorithmParams
	Stores the configuration for EPEC algorithms. More...
struct	EPECStatistics
	Stores statistics for a (solved) EPEC instance. More...
class	LCP
	Class to handle and solve linear complementarity problems. More...
class	MP_Param
	class to handle parameterized mathematical programs(MP) More...
class	NashGame
	Class to model Nash-cournot games with each player playing a QP. More...
struct	QP_constraints
	struct to handle the constraint params of MP_Param/QP_Param More...
struct	QP_objective
	struct to handle the objective params of MP_Param/QP_Param More...
class	QP_Param
	Class to handle parameterized quadratic programs(QP) More...

Typedefs
typedef struct Game::QP_objective	QP_objective
	struct to handle the objective params of MP_Param/QP_Param More...
typedef struct Game::QP_constraints	QP_constraints
	struct to handle the constraint params of MP_Param/QP_Param More...

Enumerations
enum	EPECAddPolyMethod { EPECAddPolyMethod::sequential, EPECAddPolyMethod::reverse_sequential, EPECAddPolyMethod::random }
enum	EPECsolveStatus {   EPECsolveStatus::nashEqNotFound, EPECsolveStatus::nashEqFound, EPECsolveStatus::timeLimit, EPECsolveStatus::numerical,   EPECsolveStatus::unInitialized }
enum	EPECalgorithm { EPECalgorithm::fullEnumeration, EPECalgorithm::innerApproximation, EPECalgorithm::combinatorialPNE }
enum	EPECRecoverStrategy { EPECRecoverStrategy::incrementalEnumeration, EPECRecoverStrategy::combinatorial }

Functions
bool	isZero (arma::mat M, double tol=1e-6) noexcept
bool	isZero (arma::sp_mat M, double tol=1e-6) noexcept
std::ostream &	operator<< (std::ostream &os, const QP_Param &Q)
std::ostream &	operator<< (std::ostream &ost, const perps &C)
void	print (const perps &C) noexcept
arma::vec	LPSolve (const arma::sp_mat &A, const arma::vec &b, const arma::vec &c, int &status, bool Positivity=false)
unsigned int	ConvexHull (const std::vector< arma::sp_mat *> *Ai, const std::vector< arma::vec *> *bi, arma::sp_mat &A, arma::vec &b, const arma::sp_mat Acom={}, const arma::vec bcom={})
void	compConvSize (arma::sp_mat &A, const unsigned int nFinCons, const unsigned int nFinVar, const std::vector< arma::sp_mat *> *Ai, const std::vector< arma::vec *> *bi, const arma::sp_mat &Acom, const arma::vec &bcom)

Typedef Documentation

QP_constraints

typedef struct Game::QP_constraints Game::QP_constraints

struct to handle the constraint params of MP_Param/QP_Param

Refer QP_Param class for what A, B and b mean.

QP_objective

typedef struct Game::QP_objective Game::QP_objective

struct to handle the objective params of MP_Param/QP_Param

Refer QP_Param class for what Q, C and c mean.

Enumeration Type Documentation

EPECAddPolyMethod

enum Game::EPECAddPolyMethod

strong

Enumerator
sequential	Adds polyhedra by selecting them in order.
reverse_sequential	Adds polyhedra by selecting them in reverse sequential order
random	Adds the next polyhedra by selecting random feasible one.

Definition at line 34 of file epecsolve.h.

EPECalgorithm

enum Game::EPECalgorithm

strong

Enumerator
fullEnumeration	Completely enumerate the set of polyhedra for all followers
innerApproximation	iterations Perfrorm increasingly better inner approximations in
combinatorialPNE	Perform a combinatorial-based search strategy to find a pure NE

Definition at line 408 of file games.h.

EPECRecoverStrategy

enum Game::EPECRecoverStrategy

strong

Enumerator
incrementalEnumeration	Add random polyhedra in each iteration.
combinatorial	Triggers the combinatorialPNE with additional information from innerApproximation

Definition at line 418 of file games.h.

EPECsolveStatus

enum Game::EPECsolveStatus

strong

Enumerator
nashEqNotFound	Instance proved to be infeasible. Set of status in which the solution status of a Game::EPEC can be.
nashEqFound	Solution found for the instance.
timeLimit	Time limit reached, nash equilibrium not found.
numerical	Numerical issues.
unInitialized	Not started to solve the problem.

Definition at line 397 of file games.h.

Function Documentation

compConvSize()

void Game::compConvSize	(	arma::sp_mat &	A,
		const unsigned int	nFinCons,
		const unsigned int	nFinVar,
		const std::vector< arma::sp_mat *> *	Ai,
		const std::vector< arma::vec *> *	bi,
		const arma::sp_mat &	Acom,
		const arma::vec &	bcom
	)

ConvexHull()

unsigned int Game::ConvexHull	(	const std::vector< arma::sp_mat *> *	Ai,
		const std::vector< arma::vec *> *	bi,
		arma::sp_mat &	A,
		arma::vec &	b,
		const arma::sp_mat	Acom = {},
		const arma::vec	bcom = {}
	)

isZero() [1/2]

bool Game::isZero ( arma::mat  M, double  tol = 1e-6  )

noexcept

Checking if a given matrix M is a zero matrix

Parameters

tol	Tolerance, below which a number is treated as 0

Warning

tol < 0 always returns false with no error.

Definition at line 14 of file Games.cpp.

isZero() [2/2]

bool Game::isZero ( arma::sp_mat  M, double  tol = 1e-6  )

noexcept

Checking if a given sparse matrix M is a zero matrix

Parameters

tol	Tolerance, below which a number is treated as 0

Definition at line 26 of file Games.cpp.

LPSolve()

arma::vec Game::LPSolve	(	const arma::sp_mat &	A,
		const arma::vec &	b,
		const arma::vec &	c,
		int &	status,
		bool	Positivity = false
	)

Checks if the polyhedron given by is feasible. If yes, returns the point in the polyhedron that minimizes Positivity can be enforced on the variables easily.

Parameters

A	The constraint matrix
b	RHS of the constraint matrix
c	If feasible, returns a vector that minimizes along this direction
status	Status of the optimization problem. If optimal, this will be GRB_OPTIMAL
Positivity	Should be enforced?

Definition at line 721 of file LCPtoLP.cpp.

operator<<() [1/2]

std::ostream& Game::operator<<	(	std::ostream &	os,
		const QP_Param &	Q
	)

operator<<() [2/2]

std::ostream& Game::operator<<	(	std::ostream &	ost,
		const perps &	C
	)

print()

void Game::print ( const perps &  C )

noexcept

Definition at line 39 of file Games.cpp.