bargain_NP_vert_seq: Nash Product for use in vertical model with sequential timing

In mergersim: Merger Simulation and Calibration

Nash Product for use in vertical model with sequential timing

Description

Nash Product for use in vertical model with sequential timing

Usage

bargain_NP_vert_seq(
  w_start,
  product_max,
  price_w,
  own_down,
  own_up,
  alpha,
  delta,
  cost_w,
  cost_r,
  lambda,
  p_R0,
  sigma,
  showAll = FALSE,
  maxJointProfits = FALSE
)

Arguments

w_start	Initial wholesale price for product for which to maximize Nash Product
product_max	Index of product for which to maximize Nash Product
price_w	Upstream or wholesale prices
own_down	Ownership matrix for downstream firms
own_up	Ownership matrix for upstream firms
alpha	Price coefficient
delta	Mean values
cost_w	Marginal costs for upstream firm for each product
cost_r	Marginal costs for downstream firm for each product
lambda	Bargaining power of the buyer/retailer
p_R0	Retail prices starting values
sigma	Contract type; value between 0 and 1 where 0 is linear price, 1 is two-part tariff
showAll	logical; if true, returns gains for trade for every product
maxJointProfits	Experimental option; if true, will maximize joint profits rather than gains from trade

Details

This function calculate the Nash Product from a Nash bargaining model

Value

The first-order conditions

Examples

bargain_NP_vert_seq(w_start = 1.5, product_max = 1,
price_w = c(1.6, 1.6, 1.6, 1.6, 1.6, 1.6),
own_down = paste0("R",rep(c(1,2,3),each=2)),
own_up = paste0("W",rep(c(1,2),3)),
alpha = -0.9, delta = c(0.2, 0.3, 0.9, 1.0, 0.8, 0.9),
cost_w = rep(.2, times = 6),
cost_r = rep(.1, times = 6),
lambda = 0.5, sigma = 0,
p_R0 = c(2.9, 2.9, 3.0, 3.0, 3.0, 3.0))

mergersim documentation built on July 21, 2026, 5:09 p.m.