abSan-eqm: Compute the set of equilibrium values
In squipbar/abSan: Computes the Abreu-Sannikov repeated game algorithm

Description Usage Arguments Value See Also Examples

Calculates the set of values of all subgame-perfect equilibria for a repeated game.

1 2	abSan.eqm(modelName, model, set, pun, tol=1e-12, charts=FALSE, maxIt=150, detail=FALSE, print.output=TRUE, save.solution=FALSE, par=FALSE, cluster, modelOpts)

`modelName`	the model definition function.
`model`	a post-processed model list. Usually created as the output of `model.initiate(modelName)` for some model. Useful when re-computing the same model with different solution options, as prevents re-defining the model each time.
`set`	an (m,2) matrix of vertices of the initial set of continuation values. Must wholly contain the equilibrium set. If missing or `NULL`, the set of stage payoffs is used.
`pun`	a length-2 vector of initial punishments. Must be less than the equilibrium punishment. If missing or `NULL`, the minmax payoff for the stage game is used.
`tol`	numeric convergence tolerance. The threshold Hausdorff difference between successive sets at which the algorithm terminates.
`charts`	Boolean flag for saving charts. Currently only equilibrium set and the sequence of convergent sets are created. These are saved as equilibrium.pdf, and convergence.pdf in the current working directory.
`maxIt`	The maximum number of iterations.
`detail`	Boolean flag for retaining information about the iterations
`par`	Boolean flag for using multicore execution.
`print.output`	Boolean flag for output display.
`save.solution`	Currently inactive.
`cluster`	number of nodes to use in cluster execution. Currently inactive.
`modelOpt`	options to pass to the model.

Returns a list of solution components:

`status`	is `1` if solution converges to required tolerance. Otherwise `0`.
`vStar`	a list containing a description of the equilibrium set. `vStar$mZ` is a 2-column matrix of vertices of the equilibrium set. `vStar$mG` is a 2-column matrix of unit-magnitude normals to the boundary of the equilibrium set, and `vStar$vC` is a vector of intercepts to those normals, such that for every row g of `vStar$mG` and each entry c of `vStar$vC` the conditions g.z≤ c are a necessary and sufficient condition for z to be in the equilibrium set.
`vBar`	the equilibrium punishment
`iterations`	The number of iterations to solution
`lSet`	returned only if `details=TRUE`. The list of sets at each iteration of the algorithm.
`lPun`	returned only if `details=TRUE`. The list of punishments at each iteration of the algorithm.
`time`	time to compute the equilibrium set.

model.initiate

## Compute the Cournot duopoly game
sol <- abSan.eqm( modelName=examples.cournot, modelOpts=list( 'iActs' = 15 ) )
  # Benchmark solution
sol$time
  # Time taken
sol <- abSan.eqm( modelName=examples.cournot, modelOpts=list( 'iActs' = 15 ), print.output=FALSE )
  # Turn off output
sol$time
  # Time taken
sol <- abSan.eqm( modelName=examples.cournot, modelOpts=list( 'iActs' = 40 ) )
  # Using model options to compute a finer discretization
sol$time
  # Time taken
sol <- abSan.eqm( modelName=examples.cournot, modelOpts=list( 'iActs' = 40 ), par=TRUE )
  # Using multicore execution to speed up larger example
sol$time
  # Time taken