#include <models.h>

Inheritance diagram for Models::EPEC:

Public Member Functions
	EPEC ()=delete

	EPEC (GRBEnv *env, arma::sp_mat TranspCosts={})

void	testLCP (const unsigned int i)

EPEC &	addCountry (LeadAllPar Params, const unsigned int addnlLeadVars=0)
	Models a Standard Nash-Cournot game within a country More...

EPEC &	addTranspCosts (const arma::sp_mat &costs)
	Adds intercountry transportation costs matrix. More...

unsigned int	getPosition (const unsigned int countryCount, const LeaderVars var=LeaderVars::FollowerStart) const
	Gets position of a variable in a country. More...

unsigned int	getPosition (const std::string countryCount, const LeaderVars var=LeaderVars::FollowerStart) const

EPEC &	unlock ()
	Unlocks an EPEC model. More...

std::unique_ptr< GRBModel >	Respond (const std::string name, const arma::vec &x) const

Game::NashGame *	get_LowerLevelNash (const unsigned int i) const
	Returns a non-owning pointer to the `i` -th country's lower level NashGame. More...

Game::LCP *	playCountry (std::vector< Game::LCP *> countries)

void	write (const std::string filename, const unsigned int i, bool append=true) const

void	write (const std::string filename, bool append=true) const

void	readSolutionJSON (const std::string filename)

void	writeSolutionJSON (std::string filename, const arma::vec x, const arma::vec z) const

void	writeSolution (const int writeLevel, std::string filename) const

const EPECInstance	getInstance () const
	Get the current EPECInstance loaded. More...

void	finalize ()
	Finalizes the creation of a Game::EPEC object. More...

void	findNashEq ()

std::unique_ptr< GRBModel >	Respond (const unsigned int i, const arma::vec &x) const

double	RespondSol (arma::vec &sol, unsigned int player, const arma::vec &x, const arma::vec &prevDev) const

bool	isSolved (unsigned int countryNumber, arma::vec ProfDevn, double tol=51e-4) const

bool	isSolved (double tol=51e-4) const

const arma::vec	getx () const

void	reset ()

const arma::vec	getz () const

const EPECStatistics	getStatistics () const
	Get the EPECStatistics object for the current instance. More...

void	setAlgorithm (Game::EPECalgorithm algorithm)

Game::EPECalgorithm	getAlgorithm () const

void	setRecoverStrategy (Game::EPECRecoverStrategy strategy)

Game::EPECRecoverStrategy	getRecoverStrategy () const

void	setAggressiveness (unsigned int a)

unsigned int	getAggressiveness () const

void	setNumThreads (unsigned int t)

unsigned int	getNumThreads () const

void	setAddPolyMethodSeed (unsigned int t)

unsigned int	getAddPolyMethodSeed () const

void	setIndicators (bool val)

bool	getIndicators () const

void	setPureNE (bool val)

bool	getPureNE () const

void	setBoundPrimals (bool val)

bool	getBoundPrimals () const

void	setBoundBigM (double val)

double	getBoundBigM () const

void	setTimeLimit (double val)

double	getTimeLimit () const

void	setAddPolyMethod (Game::EPECAddPolyMethod add)

Game::EPECAddPolyMethod	getAddPolyMethod () const

unsigned int	getnVarinEPEC () const noexcept

unsigned int	getNcountries () const noexcept

unsigned int	getPosition_LeadFoll (const unsigned int i, const unsigned int j) const

unsigned int	getPosition_LeadLead (const unsigned int i, const unsigned int j) const

unsigned int	getPosition_LeadFollPoly (const unsigned int i, const unsigned int j, const unsigned int k) const

unsigned int	getPosition_LeadLeadPoly (const unsigned int i, const unsigned int j, const unsigned int k) const

unsigned int	getNPoly_Lead (const unsigned int i) const

unsigned int	getPosition_Probab (const unsigned int i, const unsigned int k) const

double	getVal_LeadFoll (const unsigned int i, const unsigned int j) const

double	getVal_LeadLead (const unsigned int i, const unsigned int j) const

double	getVal_LeadFollPoly (const unsigned int i, const unsigned int j, const unsigned int k, const double tol=1e-5) const

double	getVal_LeadLeadPoly (const unsigned int i, const unsigned int j, const unsigned int k, const double tol=1e-5) const

double	getVal_Probab (const unsigned int i, const unsigned int k) const

bool	isPureStrategy (const unsigned int i, const double tol=1e-5) const

bool	isPureStrategy (const double tol=1e-5) const

std::vector< unsigned int >	mixedStratPoly (const unsigned int i, const double tol=1e-5) const

const LCP &	getLcpDescr () const

const GRBModel &	getLcpModel () const

void	writeLcpModel (std::string filename) const

Data Fields
bool	quadraticTax = {false}

Protected Member Functions
bool	warmstart (const arma::vec x)
	Warmstarts EPEC with a solution. More...

bool	hasLCP () const

Protected Attributes
std::vector< std::shared_ptr< Game::NashGame > >	countries_LL {}

std::vector< std::unique_ptr< Game::LCP > >	countries_LCP {}

std::vector< std::shared_ptr< Game::QP_Param > >	country_QP {}
	The QP corresponding to each player. More...

std::vector< std::shared_ptr< Game::QP_objective > >	LeadObjec {}
	Objective of each leader. More...

std::vector< std::shared_ptr< Game::QP_objective > >	LeadObjec_ConvexHull {}

std::unique_ptr< Game::NashGame >	nashgame
	The EPEC nash game. More...

std::vector< unsigned int >	LeaderLocations {}

std::vector< const unsigned int * >	LocEnds {}

std::vector< unsigned int >	convexHullVariables {}

unsigned int	n_MCVar {0}

GRBEnv *	env

bool	finalized {false}

bool	nashEq {false}

std::chrono::high_resolution_clock::time_point	initTime

EPECStatistics	Stats {}
	Store run time information. More...

arma::vec	sol_z
	Solution equation values. More...

arma::vec	sol_x
	Solution variable values. More...

Private Member Functions
void	make_obj_leader (const unsigned int i, Game::QP_objective &QP_obj) final

virtual void	updateLocs () override

virtual void	prefinalize () override
	Empty function - optionally reimplementable in derived class. More...

virtual void	postfinalize () override
	Empty function - optionally reimplementable in derived class. More...

bool	dataCheck (const bool chkAllLeadPars=true, const bool chkcountriesLL=true, const bool chkMC_QP=true, const bool chkLeadConses=true, const bool chkLeadRHSes=true, const bool chknImportMarkets=true, const bool chkLocations=true, const bool chkLeaderLocations=true, const bool chkLeadObjec=true) const

bool	ParamValid (const LeadAllPar &Param) const
	Checks the Validity of Models::LeadAllPar object. More...

void	make_LL_QP (const LeadAllPar &Params, const unsigned int follower, Game::QP_Param *Foll, const LeadLocs &Loc) const noexcept
	Makes the lower level quadratic program object for each follower. More...

void	make_LL_LeadCons (arma::sp_mat &LeadCons, arma::vec &LeadRHS, const LeadAllPar &Param, const Models::LeadLocs &Loc={}, const unsigned int import_lim_cons=1, const unsigned int export_lim_cons=1, const unsigned int price_lim_cons=1, const unsigned int activeTaxCaps=0) const noexcept
	Makes the leader constraint matrix and RHS. More...

void	add_Leaders_tradebalance_constraints (const unsigned int i)
	Adds leaders' trade balance constraints for import-exports. More...

void	make_MC_leader (const unsigned int i)
	Makes the market clearing constraint for country `i`. More...

void	make_MC_cons (arma::sp_mat &MCLHS, arma::vec &MCRHS) const override
	Returns leader's Market clearing constraints in matrix form. More...

void	WriteCountry (const unsigned int i, const std::string filename, const arma::vec x, const bool append=true) const

void	WriteFollower (const unsigned int i, const unsigned int j, const std::string filename, const arma::vec x) const

Private Attributes
std::vector< LeadAllPar >	AllLeadPars
	The parameters of each leader in the EPEC game. More...

std::vector< std::shared_ptr< Game::QP_Param > >	MC_QP

arma::sp_mat	TranspCosts
	Transportation costs between pairs of countries. More...

std::vector< unsigned int >	nImportMarkets
	Number of countries from which the i-th country imports. More...

std::vector< LeadLocs >	Locations
	Location of variables for each country. More...

std::map< std::string, unsigned int >	name2nos = {}

unsigned int	taxVars = {0}

std::vector< arma::sp_mat >	LeadConses {}
	Stores each leader's constraint LHS. More...

std::vector< arma::vec >	LeadRHSes {}
	Stores each leader's constraint RHS. More...

Detailed Description

Definition at line 167 of file models.h.

Constructor & Destructor Documentation

◆ EPEC() [1/2]

Models::EPEC::EPEC ( )

delete

◆ EPEC() [2/2]

Models::EPEC::EPEC	(	GRBEnv *	env,
		arma::sp_mat	TranspCosts = `{}`
	)

inline

Definition at line 244 of file models.h.

Member Function Documentation

◆ add_Leaders_tradebalance_constraints()

void Models::EPEC::add_Leaders_tradebalance_constraints ( const unsigned int i )

private

Adds leaders' trade balance constraints for import-exports.

Does the following job:

Counts the number of import markets for the country i to store in Models::EPEC::nImportMarkets - Adds the trade balance constraint. Total quantity imported by country i = Sum of Total quantity exported by each country to country i. - Updates the LeadLocs in Models::EPEC::Locations.at(i)

Definition at line 711 of file Models.cpp.

◆ addCountry()

Models::EPEC & Models::EPEC::addCountry	(	Models::LeadAllPar	Params,
		const unsigned int	addnlLeadVars = `0`
	)

Models a Standard Nash-Cournot game within a country

A Nash cournot game is played among the followers, for the leader-decided values of import export, caps and taxations on all players. The total quantity used in the demand equation is the sum of quantity produced by all followers + any import - any export.

Use $l_i$ to denote the $i$ -th element in costs_lin and $q_i$ for the $i$ -th element in costs_quad. Then to produce quantity $x_i$ , the $i$ -th producer's cost will be

$l_ix_i + \frac{1}{2}q_ix_i^2$

In addition to this, the leader may impose "tax", which could increase $l_i$ for each player.

Total quantity in the market is given by sum of quantities produced by all producers adjusted by imports and exports

${Total\quad Quantity} = \sum_i x_i + x_{imp} - x_{exp}$

The demand curve in the market is given by

${Price} = a-b({Total\quad Quantity})$

Each follower is also constrained by a maximum production capacity her infrastructure allows. And each follower is constrained by a cap on their production, that is imposed by the leader.

Each follower decides $x_i$ noncooperatively maximizing profits.

The leader decides quantity imported $q_{imp}$ , quantity exported $q_{exp}$ , cap on each player, $\tilde{x_i}$ , and the tax for each player $t_i$ .

The leader is also constrained to not export or import anything more than the limits set by export_limit and import_limit. A negative value to these input variables imply that there is no such limit.

Similarly the leader cannot also impose tax on any player greater than what is dictated by the input variable max_tax.

Returns: Pointer to LCP object dynamically created using new.

Parameters

Params	The Parameter structure for the leader
addnlLeadVars	Create columns with 0s in it. To handle additional dummy leader variables.

Definition at line 445 of file Models.cpp.

◆ addTranspCosts()

Models::EPEC & Models::EPEC::addTranspCosts ( const arma::sp_mat & costs )

Adds intercountry transportation costs matrix.

Adds the transportation cost matrix. Entry in row i and column j of this matrix corresponds to the unit transportation costs for sending fuel from country i to country j.

Parameters

costs The transportation cost matrix

Definition at line 639 of file Models.cpp.

◆ dataCheck()

bool Models::EPEC::dataCheck	(	const bool	chkAllLeadPars = `true`,
		const bool	chkcountries_LL = `true`,
		const bool	chkMC_QP = `true`,
		const bool	chkLeadConses = `true`,
		const bool	chkLeadRHSes = `true`,
		const bool	chknImportMarkets = `true`,
		const bool	chkLocations = `true`,
		const bool	chkLeaderLocations = `true`,
		const bool	chkLeadObjec = `true`
	)		const

private

Checks the data in Models::EPEC object, based on checking flags, n is the number of countries in the Models::EPEC object.

Parameters

chkAllLeadPars	Checks if Models::EPEC::AllLeadPars has size `n`
chkcountries_LL	Checks if Models::EPEC::countries_LL has size `n`
chkMC_QP	Checks if Models::EPEC::MC_QP has size `n`
chkLeadConses	Checks if Models::EPEC::LeadConses has size `n`
chkLeadRHSes	Checks if Models::EPEC::LeadRHSes has size `n`
chknImportMarkets	Checks if Models::EPEC::nImportMarkets has size `n`
chkLocations	Checks if Models::EPEC::Locations has size `n`
chkLeaderLocations	Checks if Models::EPEC::LeaderLocations has size `n` and Models::EPEC::nVarinEPEC is set
chkLeadObjec	Checks if Models::EPEC::LeadObjec has size `n`

Definition at line 864 of file Models.cpp.

◆ finalize()

void Game::EPEC::finalize ( )

inherited

Finalizes the creation of a Game::EPEC object.

Performs a bunch of job after all data for a Game::EPEC object are given, namely. Models::EPEC::computeLeaderLocations - Adds the required dummy variables to each leader's problem so that a game among the leaders can be defined. Calls Game::EPEC::add_Dummy_Lead

Makes the market clearing constraint in each country. Calls

Game::EPEC::prefinalize() can be overridden, and that code will run before calling Game::EPEC::finalize()

Game::EPEC::postfinalize() can be overridden, and that code will run after calling Game::EPEC::finalize()

Definition at line 1226 of file Games.cpp.

◆ findNashEq()

void Game::EPEC::findNashEq ( )

inherited

Computes Nash equilibrium using the algorithm set in Game::EPEC::algorithm

Checks the value of Game::EPEC::algorithm and delegates the task to appropriate algorithm wrappers.

Definition at line 2182 of file Games.cpp.

◆ get_LowerLevelNash()

Game::NashGame * Models::EPEC::get_LowerLevelNash ( const unsigned int i ) const

Returns a non-owning pointer to the i -th country's lower level NashGame.

Definition at line 933 of file Models.cpp.

◆ getAddPolyMethod()

Game::EPECAddPolyMethod Game::EPEC::getAddPolyMethod ( ) const

inlineinherited

Definition at line 644 of file games.h.

◆ getAddPolyMethodSeed()

unsigned int Game::EPEC::getAddPolyMethodSeed ( ) const

inlineinherited

Definition at line 624 of file games.h.

◆ getAggressiveness()

unsigned int Game::EPEC::getAggressiveness ( ) const

inlineinherited

Definition at line 611 of file games.h.

◆ getAlgorithm()

Game::EPECalgorithm Game::EPEC::getAlgorithm ( ) const

inlineinherited

Definition at line 601 of file games.h.

◆ getBoundBigM()

double Game::EPEC::getBoundBigM ( ) const

inlineinherited

Definition at line 638 of file games.h.

◆ getBoundPrimals()

bool Game::EPEC::getBoundPrimals ( ) const

inlineinherited

Definition at line 634 of file games.h.

◆ getIndicators()

bool Game::EPEC::getIndicators ( ) const

inlineinherited

Definition at line 628 of file games.h.

◆ getInstance()

const EPECInstance Models::EPEC::getInstance ( ) const

inline

Get the current EPECInstance loaded.

Definition at line 291 of file models.h.

◆ getLcpDescr()

const LCP& Game::EPEC::getLcpDescr ( ) const

inlineinherited

Get the Game::LCP object solved in the last iteration either to solve the problem or to prove non-existence of Nash equilibrium. Object is returned using constant reference.

Definition at line 689 of file games.h.

◆ getLcpModel()

const GRBModel& Game::EPEC::getLcpModel ( ) const

inlineinherited

Get the GRBModel solved in the last iteration to solve the problem or to prove non-existence of Nash equilibrium. Object is returned using constant reference.

Definition at line 693 of file games.h.

◆ getNcountries()

unsigned int Game::EPEC::getNcountries ( ) const

inlinenoexceptinherited

Definition at line 651 of file games.h.

◆ getNPoly_Lead()

unsigned int Game::EPEC::getNPoly_Lead ( const unsigned int i ) const

inherited

Get the number of polyhedra used in the inner approximation of the feasible region of the i-th leader.*

Definition at line 2341 of file Games.cpp.

◆ getNumThreads()

unsigned int Game::EPEC::getNumThreads ( ) const

inlineinherited

Definition at line 618 of file games.h.

◆ getnVarinEPEC()

unsigned int Game::EPEC::getnVarinEPEC ( ) const

inlinenoexceptinherited

Definition at line 650 of file games.h.

◆ getPosition() [1/2]

unsigned int Models::EPEC::getPosition	(	const unsigned int	countryCount,
		const LeaderVars	var = `LeaderVars::FollowerStart`
	)		const

Gets position of a variable in a country.

Definition at line 911 of file Models.cpp.

◆ getPosition() [2/2]

unsigned int Models::EPEC::getPosition	(	const std::string	countryCount,
		const LeaderVars	var = `LeaderVars::FollowerStart`
	)		const

◆ getPosition_LeadFoll()

unsigned int Game::EPEC::getPosition_LeadFoll	(	const unsigned int	i,
		const unsigned int	j
	)		const

inherited

Get the position of the j-th Follower variable in the i-th leader Querying Game::EPEC::lcpmodel for x[return-value] variable gives the appropriate variable

Definition at line 2291 of file Games.cpp.

◆ getPosition_LeadFollPoly()

unsigned int Game::EPEC::getPosition_LeadFollPoly	(	const unsigned int	i,
		const unsigned int	j,
		const unsigned int	k
	)		const

inherited

Get the position of the k-th follower variable of the i-th leader, in the j-th feasible polyhedron.

Indeed it should hold that $ j < $ Game::EPEC::getNPoly_Lead(i)

Definition at line 2313 of file Games.cpp.

◆ getPosition_LeadLead()

unsigned int Game::EPEC::getPosition_LeadLead	(	const unsigned int	i,
		const unsigned int	j
	)		const

inherited

Get the position of the j-th Follower variable in the i-th leader Querying Game::EPEC::lcpmodel for x[return-value] variable gives the appropriate variable

Definition at line 2302 of file Games.cpp.

◆ getPosition_LeadLeadPoly()

unsigned int Game::EPEC::getPosition_LeadLeadPoly	(	const unsigned int	i,
		const unsigned int	j,
		const unsigned int	k
	)		const

inherited

Get the position of the k-th leader variable of the i-th leader, in the j-th feasible polyhedron.

Indeed it should hold that $ j < $ Game::EPEC::getNPoly_Lead(i)

Definition at line 2327 of file Games.cpp.

◆ getPosition_Probab()

unsigned int Game::EPEC::getPosition_Probab	(	const unsigned int	i,
		const unsigned int	k
	)		const

inherited

Get the position of the probability associated with the k-th polyhedron (k-th pure strategy) of the i-th leader. However, if the leader has an inner approximation with exactly 1 polyhedron, it returns 0;

Definition at line 2349 of file Games.cpp.

◆ getPureNE()

bool Game::EPEC::getPureNE ( ) const

inlineinherited

Definition at line 630 of file games.h.

◆ getRecoverStrategy()

Game::EPECRecoverStrategy Game::EPEC::getRecoverStrategy ( ) const

inlineinherited

Definition at line 605 of file games.h.

◆ getStatistics()

const EPECStatistics Game::EPEC::getStatistics ( ) const

inlineinherited

Get the EPECStatistics object for the current instance.

Definition at line 599 of file games.h.

◆ getTimeLimit()

double Game::EPEC::getTimeLimit ( ) const

inlineinherited

Definition at line 640 of file games.h.

◆ getVal_LeadFoll()

double Game::EPEC::getVal_LeadFoll	(	const unsigned int	i,
		const unsigned int	j
	)		const

inherited

Definition at line 2418 of file Games.cpp.

◆ getVal_LeadFollPoly()

double Game::EPEC::getVal_LeadFollPoly	(	const unsigned int	i,
		const unsigned int	j,
		const unsigned int	k,
		const double	tol = `1e-5`
	)		const

inherited

Definition at line 2438 of file Games.cpp.

◆ getVal_LeadLead()

double Game::EPEC::getVal_LeadLead	(	const unsigned int	i,
		const unsigned int	j
	)		const

inherited

Definition at line 2428 of file Games.cpp.

◆ getVal_LeadLeadPoly()

double Game::EPEC::getVal_LeadLeadPoly	(	const unsigned int	i,
		const unsigned int	j,
		const unsigned int	k,
		const double	tol = `1e-5`
	)		const

inherited

Definition at line 2456 of file Games.cpp.

◆ getVal_Probab()

double Game::EPEC::getVal_Probab	(	const unsigned int	i,
		const unsigned int	k
	)		const

inherited

Definition at line 2409 of file Games.cpp.

◆ getx()

const arma::vec Game::EPEC::getx ( ) const

inlineinherited

Definition at line 595 of file games.h.

◆ getz()

const arma::vec Game::EPEC::getz ( ) const

inlineinherited

Definition at line 597 of file games.h.

◆ hasLCP()

bool Game::EPEC::hasLCP ( ) const

inlineprotectedinherited

Definition at line 571 of file games.h.

◆ isPureStrategy() [1/2]

bool Game::EPEC::isPureStrategy	(	const unsigned int	i,
		const double	tol = `1e-5`
	)		const

inherited

Checks if the returned strategy leader is a pure strategy for the leader i. The strategy is considered a pure strategy, if it is played with a probability greater than 1 - tol;

Definition at line 2376 of file Games.cpp.

◆ isPureStrategy() [2/2]

bool Game::EPEC::isPureStrategy ( const double tol = 1e-5 ) const

inherited

Checks if the returned strategy leader is a pure strategy for the leader i. The strategy is considered a pure strategy, if it is played with a probability greater than 1 - tol;

Definition at line 2363 of file Games.cpp.

◆ isSolved() [1/2]

bool Game::EPEC::isSolved	(	unsigned int *	countryNumber,
		arma::vec *	ProfDevn,
		double	tol = `51e-4`
	)		const

inherited

Checks if Game::EPEC is solved, else returns proof of unsolvedness.

Analogous to Game::NashGame::isSolved but checks if the given Game::EPEC is solved. If it is solved, then retruns true. If not, it returns the country which has a profitable deviation in countryNumber and the profitable deviation in ProfDevn. tol is the tolerance for the check. If the improved objective after the deviation is less than tol, then it is not considered as a profitable deviation.

Thus we check if the given point is an $\epsilon$ -equilibrium. Value of $\epsilon$ can be chosen sufficiently close to 0.

Warning: Setting tol = 0 might even reject a real solution as not solved. This is due to numerical issues arising from the LCP solver (Gurobi).

Definition at line 1450 of file Games.cpp.

◆ isSolved() [2/2]

bool Game::EPEC::isSolved ( double tol = 51e-4 ) const

inherited

Definition at line 1491 of file Games.cpp.

◆ make_LL_LeadCons()

void Models::EPEC::make_LL_LeadCons	(	arma::sp_mat &	LeadCons,
		arma::vec &	LeadRHS,
		const LeadAllPar &	Params,
		const Models::LeadLocs &	Loc = `{}`,
		const unsigned int	import_lim_cons = `1`,
		const unsigned int	export_lim_cons = `1`,
		const unsigned int	price_lim_cons = `1`,
		const unsigned int	activeTaxCaps = `0`
	)		const

privatenoexcept

Makes the leader constraint matrix and RHS.

Makes the leader level constraints for a country. The constraints added are as follows:

$\begin{eqnarray} t_i^{I} &\leq& \bar{t_i^{I}}\\ q^{import} - q^{export} &\leq& \bar{q^{import}}\\ q^{export} - q^{import} &\leq& \bar{q^{export}}\\ \alpha - \beta\left(q^{import} - q^{export} + \sum_i q_i \right) &\leq& *\bar{\pi}\\ q^{export} &\leq& \sum_i q_i +q^{import} \end{eqnarray}$

Here $\bar{q^{import}}$ and $\bar{q^{export}}$ denote the net import limit and export limit respectively. $\bar\pi$ is the maximum local price that the government desires to have.

The first two constraints above limit net imports and exports respectively. The third constraint limits local price. These constraints are added only if the RHS parameters are given as non-negative value. A default value of -1 to any of these parameters (given in Models::LeadAllPar Params object) ensures that these constraints are not added. The last constraint is always added. It ensures that the country does not export more than what it has produced + imported!

Parameters

LeadCons	The LHS matrix of leader constraints (for output)
LeadRHS	RHS vector for leader constraints (for output)
Params	All country specific parameters
Loc	Location of variables
import_lim_cons	Does a constraint on import limit exist or no limit?
export_lim_cons	Does a constraint on export limit exist or no limit?
price_lim_cons	Does a constraint on price limit exist or no limit?
activeTaxCaps	Number of active Tax Caps constraints. If strictly positive, tax cap constraint(s) will be enforced

Definition at line 284 of file Models.cpp.

◆ make_LL_QP()

void Models::EPEC::make_LL_QP	(	const LeadAllPar &	Params,
		const unsigned int	follower,
		Game::QP_Param *	Foll,
		const LeadLocs &	Loc
	)		const

privatenoexcept

Makes the lower level quadratic program object for each follower.

Makes Lower Level Quadratic Programs.

Sets the constraints and objective for the lower level problem (i.e., the follower)

Parameters

Params	The Parameters object
follower	Which follower's QP has to be made?
Foll	Non-owning pointer to the Follower QP_Param object
Loc	LeadLocs object for accessing different leader locations.

Definition at line 221 of file Models.cpp.

◆ make_MC_cons()

void Models::EPEC::make_MC_cons	(	arma::sp_mat &	MCLHS,
		arma::vec &	MCRHS
	)		const

overrideprivatevirtual

Returns leader's Market clearing constraints in matrix form.

Reimplemented from Game::EPEC.

Definition at line 763 of file Models.cpp.

◆ make_MC_leader()

void Models::EPEC::make_MC_leader ( const unsigned int i )

private

Makes the market clearing constraint for country i.

Writes the market clearing constraint as a Game::QP_Param and stores it in Models::EPEC::MC_QP

Definition at line 801 of file Models.cpp.

◆ make_obj_leader()

void Models::EPEC::make_obj_leader	(	const unsigned int	i,
		Game::QP_objective &	QP_obj
	)

finalprivatevirtual

Makes the objective function of each country.

Parameters

i	The location of the country whose objective is to be made
QP_obj	The object where the objective parameters are to be stored.

Implements Game::EPEC.

Definition at line 955 of file Models.cpp.

◆ mixedStratPoly()

std::vector< unsigned int > Game::EPEC::mixedStratPoly	(	const unsigned int	i,
		const double	tol = `1e-5`
	)		const

inherited

Returns the indices of polyhedra feasible for the leader, from which strategies are played with probability greater than tol.

Definition at line 2391 of file Games.cpp.

◆ ParamValid()

bool Models::EPEC::ParamValid ( const LeadAllPar & Params ) const

private

Checks the Validity of Models::LeadAllPar object.

Checks that the parameter given to add a country is valid. Does not have obvious errors

Checks the following:

Size of FollowerParam.costs_lin, FollowerParam.costs_quad, FollowerParam.capacities, FollowerParam.emission_costs are all equal to Params.n_followers - DemandParam.alpha and DemandParam.beta are greater than zero - name is not empty - name does not match with the name of any other existing countries in the EPEC object.

Parameters

Params Object whose validity is to be tested

Definition at line 188 of file Models.cpp.

◆ playCountry()

Game::LCP* Models::EPEC::playCountry ( std::vector< Game::LCP *> countries )

◆ postfinalize()

virtual void Models::EPEC::postfinalize ( )

inlineoverrideprivatevirtual

Empty function - optionally reimplementable in derived class.

This function can be optionally implemented by the derived class. Code in this class will be run after calling Game::EPEC::finalize().

Reimplemented from Game::EPEC.

Definition at line 173 of file models.h.

◆ prefinalize()

void Models::EPEC::prefinalize ( )

overrideprivatevirtual

Empty function - optionally reimplementable in derived class.

This function can be optionally implemented by the derived class. Code in this class will be run before calling Game::EPEC::finalize().

Does the following:

Adds the trade balance constraint for all leaders. i.e., total import must equal sum of import from each country
Stores the number of import markets for each country in Models::EPEC::nImportMarkets

Reimplemented from Game::EPEC.

Definition at line 679 of file Models.cpp.

◆ readSolutionJSON()

void Models::EPEC::readSolutionJSON ( const std::string filename )

Reads the solution file and load it in the current EPEC instance

Definition at line 1195 of file Models.cpp.

◆ reset()

void Game::EPEC::reset ( )

inlineinherited

Definition at line 596 of file games.h.

◆ Respond() [1/2]

std::unique_ptr<GRBModel> Models::EPEC::Respond	(	const std::string	name,
		const arma::vec &	x
	)		const

◆ Respond() [2/2]

unique_ptr< GRBModel > Game::EPEC::Respond	(	const unsigned int	i,
		const arma::vec &	x
	)		const

inherited

Definition at line 1366 of file Games.cpp.

◆ RespondSol()

double Game::EPEC::RespondSol	(	arma::vec &	sol,
		unsigned int	player,
		const arma::vec &	x,
		const arma::vec &	prevDev = `{}`
	)		const

inherited

Returns the optimal objective value that is obtainable for the player player given the decision x of all other players.

Calls Game::EPEC::Respond and obtains the unique_ptr to GRBModel of best response by player player. Then solves the model and returns the appropriate objective value.

Returns: The optimal objective value for the player player.

Parameters

sol	Optimal response
player	Player whose optimal response is to be computed
x	A vector of pure strategies (either for all players or all other players

Definition at line 1380 of file Games.cpp.

◆ setAddPolyMethod()

void Game::EPEC::setAddPolyMethod ( Game::EPECAddPolyMethod add )

inlineinherited

Definition at line 641 of file games.h.

◆ setAddPolyMethodSeed()

void Game::EPEC::setAddPolyMethodSeed ( unsigned int t )

inlineinherited

Definition at line 621 of file games.h.

◆ setAggressiveness()

void Game::EPEC::setAggressiveness ( unsigned int a )

inlineinherited

Definition at line 608 of file games.h.

◆ setAlgorithm()

void Game::EPEC::setAlgorithm ( Game::EPECalgorithm algorithm )

inherited

Decides the algorithm to be used for solving the given instance of the problem. The choice of algorithms are documented in Game::EPECalgorithm

Definition at line 2274 of file Games.cpp.

◆ setBoundBigM()

void Game::EPEC::setBoundBigM ( double val )

inlineinherited

Definition at line 637 of file games.h.

◆ setBoundPrimals()

void Game::EPEC::setBoundPrimals ( bool val )

inlineinherited

Definition at line 631 of file games.h.

◆ setIndicators()

void Game::EPEC::setIndicators ( bool val )

inlineinherited

Definition at line 627 of file games.h.

◆ setNumThreads()

void Game::EPEC::setNumThreads ( unsigned int t )

inlineinherited

Definition at line 614 of file games.h.

◆ setPureNE()

void Game::EPEC::setPureNE ( bool val )

inlineinherited

Definition at line 629 of file games.h.

◆ setRecoverStrategy()

void Game::EPEC::setRecoverStrategy ( Game::EPECRecoverStrategy strategy )

inherited

Decides the algorithm to be used for recovering a PNE out of the innerApproximation procedure.

Definition at line 2282 of file Games.cpp.

◆ setTimeLimit()

void Game::EPEC::setTimeLimit ( double val )

inlineinherited

Definition at line 639 of file games.h.

◆ testLCP()

void Models::EPEC::testLCP ( const unsigned int i )

Definition at line 1595 of file Models.cpp.

◆ unlock()

Models::EPEC & Models::EPEC::unlock ( )

Unlocks an EPEC model.

A finalized model cannot be edited unless it is unlocked first.

EPEC::finalize() performs "finalizing" acts on an object.

Warning: Exclusively for debugging purposes for developers. Don't call this function, unless you know what you are doing.

Definition at line 942 of file Models.cpp.

◆ updateLocs()

void Models::EPEC::updateLocs ( )

overrideprivatevirtual

This function is called after make_country_QP()

Implements Game::EPEC.

Definition at line 1018 of file Models.cpp.

◆ warmstart()

bool Game::EPEC::warmstart ( const arma::vec x )

protectedinherited

Warmstarts EPEC with a solution.

Todo:: Game::EPEC::warmstart - to complete implementation?

Definition at line 2060 of file Games.cpp.

◆ write() [1/2]

void Models::EPEC::write	(	const std::string	filename,
		const unsigned int	i,
		bool	append = `true`
	)		const

◆ write() [2/2]

void Models::EPEC::write	(	const std::string	filename,
		bool	append = `true`
	)		const

◆ WriteCountry()

void Models::EPEC::WriteCountry	(	const unsigned int	i,
		const std::string	filename,
		const arma::vec	x,
		const bool	append = `true`
	)		const

private

Definition at line 1456 of file Models.cpp.

◆ WriteFollower()

void Models::EPEC::WriteFollower	(	const unsigned int	i,
		const unsigned int	j,
		const std::string	filename,
		const arma::vec	x
	)		const

private

Definition at line 1520 of file Models.cpp.

◆ writeLcpModel()

void Game::EPEC::writeLcpModel ( std::string filename ) const

inlineinherited

Writes the GRBModel solved in the last iteration to solve the problem or to prove non-existence of Nash equilibrium to a file.

Definition at line 696 of file games.h.

◆ writeSolution()

void Models::EPEC::writeSolution	(	const int	writeLevel,
		std::string	filename
	)		const

Writes the computed Nash Equilibrium in the EPEC instance writeLevel is an integer representing the write configuration. 0: only Json solution; 1: only human readable solution; 2:both

Definition at line 1237 of file Models.cpp.

◆ writeSolutionJSON()

void Models::EPEC::writeSolutionJSON	(	std::string	filename,
		const arma::vec	x,
		const arma::vec	z
	)		const

Writes the computed Nash Equilibrium in the standard JSON solution file filename dictates the name of the .JSON solution file

Definition at line 1122 of file Models.cpp.

Field Documentation

◆ AllLeadPars

std::vector<LeadAllPar> Models::EPEC::AllLeadPars

private

Initial value:

=

{}

The parameters of each leader in the EPEC game.

Definition at line 179 of file models.h.

◆ convexHullVariables

std::vector<unsigned int> Game::EPEC::convexHullVariables {}

protectedinherited

Definition at line 512 of file games.h.

◆ countries_LCP

std::vector<std::unique_ptr<Game::LCP> > Game::EPEC::countries_LCP {}

protectedinherited

Definition at line 494 of file games.h.

◆ countries_LL

std::vector<std::shared_ptr<Game::NashGame> > Game::EPEC::countries_LL {}

protectedinherited

Definition at line 493 of file games.h.

◆ country_QP

std::vector<std::shared_ptr<Game::QP_Param> > Game::EPEC::country_QP {}

protectedinherited

The QP corresponding to each player.

Definition at line 497 of file games.h.

◆ env

GRBEnv* Game::EPEC::env

protectedinherited

Definition at line 515 of file games.h.

◆ finalized

bool Game::EPEC::finalized {false}

protectedinherited

Definition at line 516 of file games.h.

◆ initTime

std::chrono::high_resolution_clock::time_point Game::EPEC::initTime

protectedinherited

Definition at line 518 of file games.h.

◆ LeadConses

std::vector<arma::sp_mat> Models::EPEC::LeadConses {}

private

Stores each leader's constraint LHS.

Definition at line 194 of file models.h.

◆ LeaderLocations

std::vector<unsigned int> Game::EPEC::LeaderLocations {}

protectedinherited

Location of each leader

Definition at line 506 of file games.h.

◆ LeadObjec

std::vector<std::shared_ptr<Game::QP_objective> > Game::EPEC::LeadObjec {}

protectedinherited

Objective of each leader.

Definition at line 499 of file games.h.

◆ LeadObjec_ConvexHull

std::vector<std::shared_ptr<Game::QP_objective> > Game::EPEC::LeadObjec_ConvexHull {}

protectedinherited

Objective of each leader, given the convex hull computation

Definition at line 501 of file games.h.

◆ LeadRHSes

std::vector<arma::vec> Models::EPEC::LeadRHSes {}

private

Stores each leader's constraint RHS.

Definition at line 195 of file models.h.

◆ Locations

std::vector<LeadLocs> Models::EPEC::Locations

private

Initial value:

=

{}

Location of variables for each country.

Definition at line 188 of file models.h.

◆ LocEnds

std::vector<const unsigned int *> Game::EPEC::LocEnds {}

protectedinherited

Number of variables in the current player, including any number of convex hull variables at the current moment. The used, i.e., the inheritor of Game::EPEC has the responsibility to keep this correct by implementing an override of Game::EPEC::updateLocs.

Definition at line 511 of file games.h.

◆ MC_QP

std::vector<std::shared_ptr<Game::QP_Param> > Models::EPEC::MC_QP

private

Initial value:

=

{}

The QP corresponding to the market clearing condition of each player

Definition at line 181 of file models.h.

◆ n_MCVar

unsigned int Game::EPEC::n_MCVar {0}

protectedinherited

Definition at line 513 of file games.h.

◆ name2nos

std::map<std::string, unsigned int> Models::EPEC::name2nos = {}

private

Definition at line 191 of file models.h.

◆ nashEq

bool Game::EPEC::nashEq {false}

protectedinherited

Definition at line 517 of file games.h.

◆ nashgame

std::unique_ptr<Game::NashGame> Game::EPEC::nashgame

protectedinherited

The EPEC nash game.

Definition at line 504 of file games.h.

◆ nImportMarkets

std::vector<unsigned int> Models::EPEC::nImportMarkets

private

Initial value:

=

{}

Number of countries from which the i-th country imports.

Definition at line 186 of file models.h.

◆ quadraticTax

bool Models::EPEC::quadraticTax = {false}

If set to true, a term for the quadratic tax is added to each leader objective

Definition at line 237 of file models.h.

◆ sol_x

arma::vec Game::EPEC::sol_x

protectedinherited

Solution variable values.

Definition at line 520 of file games.h.

◆ sol_z

arma::vec Game::EPEC::sol_z

protectedinherited

Solution equation values.

Definition at line 520 of file games.h.

◆ Stats

EPECStatistics Game::EPEC::Stats {}

protectedinherited

Store run time information.

Definition at line 519 of file games.h.

◆ taxVars

unsigned int Models::EPEC::taxVars = {0}

private

Definition at line 192 of file models.h.

◆ TranspCosts

arma::sp_mat Models::EPEC::TranspCosts

private

Initial value:

=

{}

Transportation costs between pairs of countries.

Definition at line 184 of file models.h.

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

Public Member Functions

Data Fields

Protected Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ EPEC() [1/2]

◆ EPEC() [2/2]

Member Function Documentation

◆ add_Leaders_tradebalance_constraints()

◆ addCountry()

◆ addTranspCosts()

◆ dataCheck()

◆ finalize()

◆ findNashEq()

◆ get_LowerLevelNash()

◆ getAddPolyMethod()

◆ getAddPolyMethodSeed()

◆ getAggressiveness()

◆ getAlgorithm()

◆ getBoundBigM()

◆ getBoundPrimals()

◆ getIndicators()

◆ getInstance()

◆ getLcpDescr()

◆ getLcpModel()

◆ getNcountries()

◆ getNPoly_Lead()

◆ getNumThreads()

◆ getnVarinEPEC()

◆ getPosition() [1/2]

◆ getPosition() [2/2]

◆ getPosition_LeadFoll()

◆ getPosition_LeadFollPoly()

◆ getPosition_LeadLead()

◆ getPosition_LeadLeadPoly()

◆ getPosition_Probab()

◆ getPureNE()

◆ getRecoverStrategy()

◆ getStatistics()

◆ getTimeLimit()

◆ getVal_LeadFoll()

◆ getVal_LeadFollPoly()

◆ getVal_LeadLead()

◆ getVal_LeadLeadPoly()

◆ getVal_Probab()

◆ getx()

◆ getz()

◆ hasLCP()

◆ isPureStrategy() [1/2]

◆ isPureStrategy() [2/2]

◆ isSolved() [1/2]

◆ isSolved() [2/2]

◆ make_LL_LeadCons()

◆ make_LL_QP()

◆ make_MC_cons()

◆ make_MC_leader()

◆ make_obj_leader()

◆ mixedStratPoly()

◆ ParamValid()

◆ playCountry()

◆ postfinalize()

◆ prefinalize()

◆ readSolutionJSON()

◆ reset()

◆ Respond() [1/2]

◆ Respond() [2/2]

◆ RespondSol()

◆ setAddPolyMethod()

◆ setAddPolyMethodSeed()

◆ setAggressiveness()

◆ setAlgorithm()

◆ setBoundBigM()

◆ setBoundPrimals()

◆ setIndicators()

◆ setNumThreads()

◆ setPureNE()

◆ setRecoverStrategy()