Discussion Prompt
In 500 words, write an answer to the following question:
Consider the following game:
1
———^———-
A | x0 | B
| |
2 3
———-^— —-^———-
C | x1 | D E | x2 | F
| | | |
x3 1………..1 x6
$1 ——-^– –^——– $1
$1 G | x4 | H G | x5 | H $1
$1 | | | | $1
x7 x8 x9 x10
$0 $2 $2 $0
$1 $1 $1 $1
$2 $0 $0 $2
This is an ascii-art diagram, but stare at it for a while to make sure you can work out the details. Nodes are labeled as x0, x1, x2, and so on. Players are labeled as numbers. Moves/actions are labeled as capital letters. Payoffs are labeled as dollar amounts. There is a dotted line between nodes x4 and x5. The branches should be evident: x0 branches into x1 and x2, x1 branches into x3 and x4, x2 branches into x5 and x6, x4 branches into x7 and x8, and x5 branches into x9 and x10.
Your task is this: write down the game pictured here in extensive-form.
In your answer, be sure to complete the following tasks:
Write down the list of players, just as is done in the examples in the handout.
Write down the underlying tree structure as a pair of nodes and edges, just as is done in the examples in the handout..
Write down the list of terminal nodes, just as is done in the examples in the
handout.
Write down a function i(*) that maps a player to each non-terminal node of the tree, just as is done in the examples in the handout.
For each player, write down a function Ai(*) that assigns an action set to each non-terminal node for that player, just as is done in the examples in the handout.
For each player, write down a payoff function vi(*) that assigns a payoff to each terminal-node for that player, just as is done in the examples in the handout.
