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(http://www.math.ucla.edu/~tom/papers/poker1.pdf) discusses
Borel's and von neumann's models of two-person,
zero-sum poker with bluffing, which were published in the
1930s. John nash's 1950 dissertation (http://www.princeton.
edu/mudd/news/faq/topics/non-Cooperative_Games_nash.
pdf, scan of the original, page 32) contains a simple poker
game in which agents can bluff, opening with some probability
even when they have bad cards. of course, there is nothing
intrinsic in choosing to open that says, "I have good cards;" it
is just an action in the game. And, in equilibrium, your opponent
knows exactly what the probability is that you have
a good hand when you "claim to." The reason that he can't
completely disregard the claim is that you sometimes behave
aggressively when you Do have a good hand. In these simple,
static (one period) models of lying, the credibility of the bluff
is supported by the possibility that it is not a bluff.
The more modern literature has focused on dynamic
(multi-period) models, in which one can tell more elaborate
stories about "building and destroying credibility." one standard
approach can be illustrated by a classic model introduced
by Joel Sobel in the article "A Theory of Credibility" [Review
of Economic Studies (1985) 52(4) pp. 557-573]. There are two
agents: a king and a spy. The king is unsure about the motivations
of the spy, who might want to help the king or might
be a double agent whose motivations are exactly opposed to
those of the king. every month, a diplomatic issue comes up
with its own level of importance. The spy observes what would
be best for the king and advises an action (say, A or B). After
the action, the king learns whether it was the right action to
take.
In equilibrium, a double agent builds credibility by giving
the king good advice for a while. Then he advises the king to
do the wrong thing for the king when a sufficiently important
issue comes up. After that, the double agent has been outed,
but has benefited in one high-stakes issue.
This illustrates many of the standard ingredients in economic
models of deception:
• Asymmetric information: at least one agent's "type" or motivation
is unknown to the other(s).
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