Look Forward, Reason Back

1
Look Forward, Reason Back

• The Cornerstone of Strategic Reasoning

2
Overview

• Advertising and entry
• Retail location strategies
• General Principles
• Alternating offers bargaining

3
Alternating offers bargaining

• Workers and firms must negotiate next years
  salaries.
• First the workers make an offer
• Then the firm accepts or rejects if the firm
  rejects it can make a counteroffer
• Then the workers can accept or reject the firms
  offer
• If the workers reject the firms offer then they
  go to arbitration

4
Payoffs

• The firm can make a surplus of X and must pay
  salaries (W) that are negotiated.
• If they reach an agreement when the workers make
  the offer they dont pay any costs
• If they reach an agreement when the firm makes
  the surplus is reduced to X-C
• If the agreement is imposed in arbitration then
  the surplus is X-C-A
• In arbitration workers get W (X-C-A) / 2

5
Strategies

• Workers
• How much to offer in the first round
• When to reject the offer from the firm if the
  second round is reached
• Firm
• When to reject the first offer of the workers
• How much to offer in the second round if the
  second round is reached

6
Payoffs

• Workers
• If they ask for W1 and is accepted they get W1
• If W1 is rejected and the firm offers W2,
• and they accept the offer they get W2
• If they reject the offer they get (X C A ) /
  2
• Firms
• If they accept the offer by the workers they get
  X - W1
• If they reject the workers offer and make an
  offer of W2
• and the offer is accepted they get X C W2
• if the offer is rejected they get (X C A) / 2
• We assume that X C gt A

7
Game Tree

X
(W1, X W1 )
Accept
X
(W2, X C - W2 )
(W1, X W1 )
Workers
Firm
Accept
(W2, X C - W2 )
Reject
Firm
1
0
Reject
( (X C- A) / 2, (X C - A ) /2 )
0
8
Backward Induction

• Look to the end of the game tree and prune back
• Rationality assumption implies that players
  choose the best strategy at each node.