This page describes methods that may be used to explore how a merger affects firms' incentives to collude.
# S4 method for Bertrand
calcProducerSurplusGrimTrigger(object,coalition,
discount,preMerger=TRUE,isCollusion=FALSE,...)Let k denote the number of products in the market, and let c denote the number of firms in a coalition
An instance of one of the classes listed above.
A length c vector of integers indicating the index of the products participating in the coalition.
A length k vector of values between 0 and 1 that represent the product-specific discount rate for all products produced by firms particiapting in the coalition. NAs are allowed
TRUE returns pre-merger result, FALSE returns post-merger results. Default is TRUE.
TRUE recalculates demand and cost parameters under the assumption that the coalition specified in ‘coalition’ is operating pre-merger. FALSE (the default) uses demand and cost parameters calculated from the ‘ownerPre’ matrix.
Additional argument to pass to calcPrices
calcProducerSurplusGrimTrigger returns a data frame with rows
equal to the number of products produced by any firm participating in
the coalition and the following 5 columns
Discount:The user-supplied discount rate
Coord:Single period producer surplus from coordinating
Defect:Single period producer surplus from defecting
Punish:Single period producer surplus from punishing using Bertrand price
IC:TRUE if the discounted producer surplus from coordinating across all firm products are greater than the surplus from defecting across all firm products for one period and receiving discounted Bertrand surplus for all subsequent periods under Grim Trigger.
calcProducerSurplusGrimTrigger calculates ‘preMerger’ product
producer surplus (as well as other statistics -- see below), under the
assumption that firms are playing
an N-player iterated Prisoner's Dilemma where in each period a
coalition of firms decides whether to cooperate with
one another by setting the joint surplus maximizing price on some
‘coalition’ of their products, or defect from the coalition by setting all
of their products'
prices to optimally undercut the prices of the coalition's
products. Moreover, firms are assumed
to play Grim Trigger strategies where each firm cooperates in the
current period so long as every firm in the coalition cooperated last period and
defects otherwise. product level ‘discount’ rates are then employed to determine
whether a firm's discounted surplus from remaining in the coalition are greater than
its surplus from optimally undercutting the coalition prices' for one
period plus its discounted surplus when all firms set Nash-Bertrand prices in
all subsequent periods.