Speculative Demand Problem: Solved By Economic Game Theory!

By @AlgoBrain

What is the Speculative Demand Problem?

A Business has 2 Warehouses - 1 local and 1 offshore. The business speculates that there may be higher LOCAL demand than OFFSHORE demand for the same price of the stocked product at that particular time, and in anticipation of higher sales considers shipping stock from its offshore warehouse to its local base.

The penalty for the decision to ship is the payment of freight cost.

Questions Arising

Is the speculation worth it? Will there actually be better sales either way? Will shipping generate higher sales? or lower sales?

The Solution

The solution lies in the adoption of game theory in the form of the speculative demand game. We create a game to model the situation and play for a large number of rounds (say of the order of 10,000 - 100, 000 rounds) to converge at a conclusive result (ship or don't ship).

The Speculative Demand Game

In this 1-player game (the business is the player), the business plays the system. There are only 2 moves for the player (business) - ship or don't ship. In either case the player utilizes fixed resources - demand (local and offshore), stock (local and offshore), price (fixed) and freight cost (fixed penalty for shipping).

Note: Demand is expressed as a weight between 0 and 1


Move 1: Don't Ship

Total Sales = Price*(Local_Demand*Local_Stock + Offshore_Demand*Offshore_Stock)

Move 2: Ship

Total Sales = Price*Local_Demand*(Local_Stock + Offshore_Stock) - Freight


The speculation has value (a win) if for any round of the game one approach yields a greater result than the other. The games must be simulated and played very many times to converge at a definite result.

Demand is modeled as:

demand = lowest _demand + random(1 - lowest_demand)

if demand > 1 then demand = (1+lowest_demand*demand)/(demand - lowest_demand)

Stock is modeled as:

stock = base_stock + random(max_addition)

Of course, price and freight cost are fixed. The games must be played in a binary gaming program such as the  Dimkpa Binary Game Engine.

If we assume the following parameters:

Price = $500
Base Stock  = 10,000 units
Max stock addition = 5,000 units
Lowest demand = 5% of stock = 0.05
Freight cost = $10,000

Then after100,000 rounds of gaming, the Dimkpa Binary Game Engine produced the following results for the speculative demand game:

Game Summary - after 100000 rounds
----------------------------------------
total lost = 50120
lost GOAL = 50120
total WON = 49880
% LOST = 50.12 %
% LOST GOAL = 50.12 %
% WON = 49.88 %
% METHOD 1 PICKED = 50.137 %
% METHOD 2 PICKED = 49.863 %
% METHOD 1 WON = 50.1764234 %
% METHOD 2 WON = 49.8235766 %
% METHOD 1 LOST = 50.0977654 %
% METHOD 2 LOST = 49.9022346 %
% METHOD 1 LOST GOAL = 50.0977654 %
% METHOD 2 LOST GOAL = 49.9022346 %
----------------------------------------

INTERPRETATION:

After 100,000 games, there is a 49.88% chance that the speculation is viable; and a 50.12% chance that it is not viable. If the viability of the speculation is rejected, then either move should yield a similar result. Should the player decide to accept viability of the speculation, then:


MOVE 1: DON'T SHIP

WON: 50.1764234 % of 100,000 games
LOST:  50.0977654 % of 100,000 games

Won MORE times than lost.

MOVE 2: SHIP

WON: 49.8235766 % of 100,000 games
LOST: 49.9022346 %  of 100,000 games

Won LESS times than lost.

VERDICT: DON'T SHIP.