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Two-Person Zero-Sum Matrix

(http://faculty.washington.edu/krumme/450/exercises/gamematrix.html)

(Fig.1) Linear Market with 5 discrete locations:

(and 4 Market Segments each with a demand of 5 units)

a ---- (5) ---- b ---- (5) ---- c ---- (5) ---- d ---- (5) ---- e

(Fig.2) Seller I's Payoff Matrix (Inelastic Demand, Total Market = 40)

SELLER II

SELLER I

a b c d e Maxi Min

a 20 5 10 15 20 5
b 35 20 15 20 25 15

c 30 25 20 25 30 |20|

d 25 20 15 20 35 15

e 20 15 10 5 20 5

(Fig.3) Combined Payoff Matrix for Sellers I and II

					    	             | Seller I's
		           S  E  L  L  E  R   "II"           |  Minima
							     | (Maximin)
        -----------------------------------------------------|=SellerII's
     Loc-  |	     |	       |	 |         |         |  Maxima
      ation|   	a    |    b    |    c	 |    d	   |    e    | (Minimax) 
  S     ---|---------|---------|---------|---------|---------|---------|
	   |  	 20  |     35  |     30  |     25  |     20  |     35  |
	a  |    \    |    \    |    \    |    \    |    \    |    \    |
  E	   |  20     |   5     |  10     |  15     |  20     |   5     |
        ---|---------|---------|---------|---------|---------|---------|
	   | 	  5  |     20  |     25  |     20  |     15  |     25  |
  L	b  |    \    |    \    |    \    |    \    |    \    |    \    |
	   |  35     |  20     |  15     |  20     |  25     |  15     |
        ---|---------|---------|---------|---------|---------|---------|
  L	   |	 10  |     15  |     20  |     15  |     10  |     20  |
	c  |    \    |    \    |    \    |    \    |    \    |    \   <---
	   |  25     |  25     |  20     |  25     |  30     |  20     |
  E     ---|---------|---------|---------|---------|---------|---------|
	   |	 15  |     20  |     25  |     20  |      5  |     25  |
	d  |	\    |    \    |    \    |    \    |    \    |    \    |
  R	   |  25     |  20     |  15     |  20     |  35     |  15     |
	---|---------|---------|---------|---------|---------|---------|
	   |	 20  |     25  |     30  |     35  |     20  |    35   |
 "I"	e  |	\    |    \    |    \    |    \    |    \    |   \     |
	   |  20     |  15     |  10     |   5     |  20     |  5      |
-----------|---------|---------|---------|---------|---------|---------|
Seller's II|      5  |     15  |     20  |     15  |      5  |         |
Minima =   |    \    |    \    |    \    |    \    |    \    |   n.a.  |
Seller's I |  35     |  25     |  20     |  25     |  35     |         |
Maxima     |         |         |         |         |         |         |
------------------------------------^----------------------------------|

(Fig.4) An Interesting Variation: The Minimax Regret Matrix & Strategy

Decision-makers compare their actual payoff with the payoff they could have received
if they would have selected the best possible location given the competitor's locational choice.

SELLER II

SELLER I

	a	b	c	d	e	MiniMax Regret
a	15	20	10	10	15	20
b	0	5	5	5	10	10
c	5	0	0	0	5	\|5\|
d	10	5	5	5	0	10
e	15	10	10	20	15	20