Signaling

1
Signaling
Tough players

2
The beer quiche model I

• An incumbent monopolist can be either tough or a
  wimp (not tough).
• An incumbent monopolist receives 4 if the entrant
  stays out and 2 if the entrant enters.
• An entrant earns 2 if it enters against a wimp
  incumbent, loses 1 if it enters against a tough
  incumbent, gets 0 if it stays out.

Entrant
Dont Enter
Enter
( 2, -1)
( 4, 0)
Tough
Incumbent
Wimp
( 2, 2)
( 4, 0)
3
Beer Quiche II

• If the entrant sees who is the incumbent
  (complete information)
• Enters if wimp
• Stays out if tough
• The problem is that the entrant can not see
  whether the incumbent is tough or wimp
  (incomplete information).
• In order for this to be a signaling game we are
  going to add a stage where the incumbent can send
  a signal.
• Then we are going to try to understand if this
  strategy of changing the game can actually help
  the incumbent.

4
Beer Quiche III

• Before the entrant enters the incumbent can have
  breakfast in public so the entrant sees his
  behavior.
• He can either order BEER or QUICHE.
• Having beer for breakfast is awful so there is a
  cost for having beer for breakfast
• Having Quiche for breakfast is nice so it
  actually gives a payoff if you have it. Lets
  assume that this payoff is U where U is non
  negative.
• The trick is that tough incumbent do not suffer
  much for having beer they suffer a loss of 1
  while the wimp suffers a loss of 2.

5
The beer quiche model IV
Wimp Incumbent
Tough Incumbent
Entrant
Entrant
Dont Enter
Dont Enter
Enter
Enter
( 2-3, 2)
( 4-3, 0)
( 2-1, -1)
( 4-1, 0)
Beer
Beer
Quiche
Quiche
( 2U, 2)
( 4U, 0)
( 2U, -1)
( 4U, 0)
6
Beer Quiche V

• In this representation we can not incoporate that
  the incumbent moves first
• We need to draw a game tree that incorporates
  this
• To complete the incomplete information set up
  we need to add beliefs
• We are going to assume that the incumbent can be
  tough or wimp with equal probability.

7
Beer Quiche Game Tree I
quiche
beer
½
tough
Incumbent
wimp
½
quiche
beer
8
Beer Quiche Game Tree II
quiche
beer
½
tough
Entrant
Entrant
Incumbent
wimp
½
quiche
beer
9
Beer Quiche Game Tree III
enter
enter
quiche
beer
out
out
½
tough
Entrant
Entrant
Incumbent
enter
wimp
enter
½
quiche
beer
out
out
10
Beer Quiche Game Tree IV
2U,-1
enter
1,-1
enter
quiche
beer
4U,0
3,0
out
out
½
tough
Entrant
Entrant
Incumbent
enter
wimp
enter
½
2U,2
-1,2
quiche
beer
4U,0
1,0
out
out
11
Beer Quiche solution

• Equilibrium Tough incumbent drinks beer wimp
  incumbent eats quiche entrant stays out against
  beer drinkers and entrant enters against quiche
  eaters.

12
Beer Quiche Game Tree IV
2U,-1
enter
1,-1
enter
quiche
beer
4U,0
3,0
out
out
½
tough
Entrant
Entrant
Incumbent
wimp
enter
½
enter
2U,2
-1,2
quiche
beer
4U,0
1,0
out
out
13
Beer Quiche conditions

• For the tough incumbent to play beer we require 3
  to be bigger or equal than 2U.
• If 2Ugt3 then the tough incumbent would try to
  get the quiche instead of signaling his type.
• This equilibrium is not possible for Ugt1.
• What happens when Ugt1
• Tough incumbent will change his behavior
• This will induce the entrant to modify his
  behavior

14
Beer Quiche Tough change
2U,-1
enter
1,-1
enter
quiche
beer
4U,0
3,0
out
out
½
tough
Entrant
Entrant
Incumbent
wimp
enter
½
enter
2U,2
-1,2
quiche
beer
4U,0
1,0
out
out
15
Beer Quiche interpretation
16
Beer Quiche the role of U

• U reflects the utility derived form consuming
  quiche.
• In fact it is just the difference between
  consuming quiche and consuming beer (when we
  incorporate that beer is costly).
• When U increases taking beer is more costly than
  before
• Tough incumbents do not have incentives to
  actually leave quiche in the table and take beer
• It is more difficult to incur a cost in order to
  signal yourself

17
Other Applications

• Settlements in court cases
• Suppose the plaintiff knows the expected damages
  of the case with greater precision than the
  defendant
• Then the settlement offer of the plaintiff can
  signal the strength of the case
• Effective signaling can avoid costly court battles