Listing Fee Calculations

lib/market/ListingFee.R

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+# The Listing Fee Price - Costs and Updates to that Cost
+
+
+GetQStandardDecisions <- function(BranchToAddOn, TauUntillAfterEvent) {
+  # Takes a Branch, finds all the Decisions on that branch, at the right time, of the right type.
+
+  RightBranch <- (Decisions$Branch==BranchToAddOn)
+  RightTime <- (Decisions$TauFromNow==TauUntillAfterEvent)
+  RightType <- (Decisions$Standard==1)
+
+  if( sum(RightBranch,RightTime,RightType)==0 ) return(0)
+
+  QStandardDecisions <- nrow( Decisions[(RightBranch & RightTime & RightType), ] )
+  return( QStandardDecisions )
+
+}
+
+GetSlotInfo <- function(PreviousBaseFee, MaxSlots, Width=2, Log=TRUE) {
+  # How much money did the Branch expect to take in (total Listing Fees, assuming the target was hit perfectly)?
+
+  PentLength <- (MaxSlots/5)
+
+  # Calculate Slot Costs - one of two ways
+  if( Log) SlotPrices <- PreviousBaseFee * c( 1/Width, 1/exp(log(Width)/2),  1, exp(log(Width)/2), Width )
+  if(!Log) SlotPrices <- PreviousBaseFee * c( 1/Width, mean(c(1, 1/Width)),  1, mean(c(1, Width)), Width )
+
+  # Calculate Fee Multiple
+  LogHalf <- exp(log(Width)/2) # log-scale version of "halfway" ...used above
+  if( Log) Multiple <- ( LogHalf / (LogHalf + 1) ) 
+  if(!Log) Multiple <- ( 4/7 )
+
+
+  # Extra Info
+
+  # The target is exactly half of the full Slot-range .. fully through 1 and 2, but only halfway through 3.
+  ExpectedSlotUsage <- c(1, 1, .5, 0, 0) * PentLength 
+  ExpectedSpend <- SlotPrices %*% ExpectedSlotUsage
+
+  # All slots completely used
+  MaxSlotUsage <- c(1, 1, 1, 1, 1) * PentLength 
+  MaxSpend <- SlotPrices %*% MaxSlotUsage
+
+  return( list(SlotPrices, Multiple, ExpectedSpend, MaxSpend) )
+
+}
+
+
+QueryCostToAuthorStandard <- function(BranchToAddOn="Politics", TauUntillAfterEvent=2) {
+  # How much will it cost me to add a Decision to this Branch (at this Tau)
+
+  # Get Branch parameters
+  MaxDecisions <- Branches[ Branches$Name==BranchToAddOn, "MaxDecisions"]
+  BaseFee <- Branches[ Branches$Name==BranchToAddOn, "BaseListingFee"]
+
+  # How many Decisions have already been added
+  ExistingDecisions  <-  GetQStandardDecisions(BranchToAddOn, TauUntillAfterEvent)
+
+  # Check to make sure user is even allowed to Author Standard (are there enough slots?):
+  if(ExistingDecisions==MaxDecisions) {
+    print("Too many Standard Decisions already...you will have to use Overflow Decisions or select a different time (or different Branch).")
+    return(-1)
+  }
+
+  # Which pent are we in?
+  PentLength <- (MaxDecisions/5)
+  Pent <- 1 + floor( ExistingDecisions / PentLength )
+
+  SlotPrices <- GetSlotInfo(BaseFee, MaxDecisions)[[1]]
+  Fee <- SlotPrices[Pent]
+
+  print(paste("You are number",(ExistingDecisions+1),"of",MaxDecisions,", and are in Pentile",Pent,"."))
+  print(paste("This period's base fee is",BaseFee, "so you must pay",Fee, "."))  
+  return(Fee)
+
+}
+
+
+QueryCostToAuthorOverflow <- function(BranchToAddOn="Politics", TauUntillAfterEvent=2) {
+
+  # Get Branch Parameter
+  BaseFee <- Branches[ Branches$Name==BranchToAddOn, "BaseListingFee"]
+
+  print(paste("This period's base fee is", BaseFee, "."))  
+  return(BaseFee)
+
+}
+
+
+
+
+
+# After a Tau is done, it is time to get the new Base Fee.
+
+CalcNewBaseFee <- function(PreviousBaseFee=0.02, MaxSlots=500, UsedSlots=490) {
+
+  PentLength <- (MaxSlots/5)
+
+  # Get Slot Economic Parameters
+  SlotInfo <-  GetSlotInfo(PreviousBaseFee, MaxSlots)
+
+  # Calc ActualSpend
+  MaginalIndex <- UsedSlots - (PentLength * ((1:5)-1)) # The second term is "How many would be used if marginal?"
+  FullSlots <- PentLength < MaginalIndex
+  MarginalSlot <- sum(FullSlots) + 1
+
+  ActualSlotUsage <- rep(0, 5) + ( rep(PentLength, 5) * FullSlots ) # Fill up all full slots
+  ActualSlotUsage[MarginalSlot] <- MaginalIndex[MarginalSlot] # Add last marginal slot
+
+  SlotCosts <- SlotInfo[[1]]
+  ActualSpend <- SlotCosts %*% ActualSlotUsage
+
+
+  # Calc New Fee
+  Multiple <- SlotInfo[[2]]
+  NewFee <- as.numeric( (ActualSpend/PentLength) * Multiple )
+
+  return(NewFee)
+}
+
+UpdateBaseFee <- function(Branch) {
+  # Takes a Branch, Calculates the New Base Fee and Installs it for the next round
+  # Note...only run this once per Tau!
+
+  # Get Parameters
+  UsedSlots <- GetQStandardDecisions(Branch, Tau = 0)
+  cur_PreviousBaseFee <- Branches[Branches$Name==Branch,"BaseListingFee"]
+  cur_MaxSlots <- Branches[Branches$Name==Branch,"MaxDecisions"]
+
+  # Calc Base Fee
+  NewFee <- CalcNewBaseFee(cur_PreviousBaseFee, cur_MaxSlots, UsedSlots)
+
+  # Edit Branch Parameter for next period
+  Branches[Branches$Name==Branch,"BaseListingFee"] <<- NewFee
+}
+
+
+# Tests / Explanation
+
+# Fee constantly retargets based on % of slots used.
+# Below: Many slots were used, fee increases from 0.02 to 0.06351472
+# > CalcNewBaseFee(PreviousBaseFee=0.02, MaxSlots=500, UsedSlots=490)
+# [1] 0.06351472
+# Below: sanity check... ( "Used Slots" = "Target Slots", price does not change )
+# > CalcNewBaseFee(PreviousBaseFee=0.0222, MaxSlots=500, UsedSlots=250) 
+# [1] 0.0222
+
+# Below: Few slots were used, fee decreases from 0.020 to 0.004100505
+# > CalcNewBaseFee(PreviousBaseFee=0.02, MaxSlots=500, UsedSlots=70)
+# [1] 0.004100505
+# Sanity check again:
+# > CalcNewBaseFee(PreviousBaseFee=0.004100505, MaxSlots=500, UsedSlots=250) # sanity check
+# [1] 0.004100505
+
+# Final Example: Fee Increases Marginally
+# > CalcNewBaseFee(PreviousBaseFee=0.02, MaxSlots=500, UsedSlots=280)
+# [1] 0.02351472