If the market-as-a-game is played just once allow for a unique payoff of
(2, 2). It can be any number but both players receive exactly the same amount.
Each player knows exactly what they want to do (they have a dominant strategy)
and each player has the easiest of decisions to face – keep prices high and
receive 2. Both players would prefer to be in the top left cell of the matrix
because in four cycles of this game a player could receive a payoff of 8 =
2+2+2+2. However, player A has a dominant strategy of competing to a low
price, trying to do better by obtaining a payoff of 3. But the 3 is only obtainable
if player B continues to keep his prices high.
Signalling, Strategy & Management Type
75

Table 8.1 Prisoners’ Dilemma
In other words, if B keeps prices high, it is because he trusts A to do likewise
and
vice vearsa
.
So B trusts A; but A knowing that, betrays B. Once player B
realises that player A has lowered its price, player B follows and they both
12
find themselves in the lower right cell of the matrix with a payoff of (1,1). Player
A now ends up with 6 = 2+3+1+0 or with 4 = 1+1+1+1 if B punishes A for the
betrayal by always keeping prices low. This is a recognised
punishment strategy
,
signalling to A the payoff 4 in time period t+1 instead of 8. In trying to do better
you can end up worse off! David Hume, an English philosopher, writing in the
18
th
century, captured the idea: ‘we can better satisfy our appetites in an oblique
manner, than by their headlong and impetuous motion’. Remember that the
future is not what it used to be!
Nash equilibrium
In the exchange of prices, players interact with each other by using prices as
signals. An incumbent and entrant, or two incumbents can face classic
coordination problems. Conflicts can arise. In a two-person game, a pair of
strategies will form a Nash equilibrium when each player cannot do better given
the strategy the other player has adopted. A
Nash equilibrium
is a pair of
strategies such that each is a best response to the other. The payoff (1,1) above
is an example of a Nash equilibrium. To test whether a strategy combination
forms a Nash equilibrium just consider the following: let us call the strategy
for the first player x* and the strategy for the second player y*. A pure strategy
equilibrium is a Nash equilibrium in which the equilibrium strategies are played
with certainty or with probability equal to one. When the Nash equilibrium
involves only strategies that are played with certainty, we have a pure strategy
Signalling, Strategy & Management Type
76
High p
Player B
Low p
Player A
High p
2,
2
3,
0
Low p
0,
3
1,
1
12
A cartel between A and B might seem a solution, but with an inherent incentive to cheat or betray,
enforcement of the cooperative solution might prove to be difficult,
vide
the arguments in McNutt
Law, Economics and Antitrust
. Cartels may not last very long. If one player believes that the other
player will always cooperate and keep prices high then there is an incentive to betray or cheat. The