Lying and Deception in Games Joel Sobel August 2, 2016 Lying and Deception Sobel
What is the Talk About? Definitions: 1. Lying 2. Deception 3. Bluff and simple properties. Lying and Deception Sobel
Why do this? 1. Coherence 2. To facilitate scholarly communication 3. To identify and separate characteristics of strategic communication 3.1 Common Language 3.2 Theory of Mind 3.3 Who Gains from Behavior Lying and Deception Sobel
Today’s Talk 1. The basic model 2. A definition of Lying 3. A quick, self-serving look at an enormous literature 4. Properties of Lying 5. A definition of beliefs 6. A definition of deception 7. Many small results Lying and Deception Sobel
But First . . . In mathematics, names are free. It is perfectly allowable to call a self-adjoint operator an elephant, and a spectral resolution a trunk. One can then prove a theorem, whereby all elephants have trunks. What is not allowable is to pretend that this result has anything to do with certain large gray animals. Lying and Deception Sobel
But First . . . In mathematics, names are free. It is perfectly allowable to call a self-adjoint operator an elephant, and a spectral resolution a trunk. One can then prove a theorem, whereby all elephants have trunks. What is not allowable is to pretend that this result has anything to do with certain large gray animals. Hector Sussman, quoted in Ivar Ekeland, “Mathematics and the Unexpected” Lying and Deception Sobel
But First . . . In mathematics, names are free. It is perfectly allowable to call a self-adjoint operator an elephant, and a spectral resolution a trunk. One can then prove a theorem, whereby all elephants have trunks. What is not allowable is to pretend that this result has anything to do with certain large gray animals. Hector Sussman, quoted in Ivar Ekeland, “Mathematics and the Unexpected” So conclusions of the form: “Deception is possible in equilibrium” are only as insightful if my definition is appropriate. Lying and Deception Sobel
. . . and What I shall have to say here is neither difficult nor contentious; the only merit I should like to claim for it is that of being true, at least in parts. The phenomenon to be discussed is very widespread and obvious, and it cannot fail to have been already noticed, at least here and there, by others. Yet I have not found attention paid to it specifically. Lying and Deception Sobel
. . . and What I shall have to say here is neither difficult nor contentious; the only merit I should like to claim for it is that of being true, at least in parts. The phenomenon to be discussed is very widespread and obvious, and it cannot fail to have been already noticed, at least here and there, by others. Yet I have not found attention paid to it specifically. J. L. Austin, “How to Do Things with Words” Lying and Deception Sobel
. . . and What I shall have to say here is neither difficult nor contentious; the only merit I should like to claim for it is that of being true, at least in parts. The phenomenon to be discussed is very widespread and obvious, and it cannot fail to have been already noticed, at least here and there, by others. Yet I have not found attention paid to it specifically. J. L. Austin, “How to Do Things with Words” sometimes is it useful to state the obvious Lying and Deception Sobel
. . . and What I shall have to say here is neither difficult nor contentious; the only merit I should like to claim for it is that of being true, at least in parts. The phenomenon to be discussed is very widespread and obvious, and it cannot fail to have been already noticed, at least here and there, by others. Yet I have not found attention paid to it specifically. J. L. Austin, “How to Do Things with Words” sometimes is it useful to state the obvious but sometimes it isn’t. Lying and Deception Sobel
A Basic Model 1. Two players: Sender and Receiver. 2. Sender observes θ ∈ Θ 3. Sender sends message m ∈ M . 4. Receiver hears m . 5. Receiver takes action y ∈ Y . 6. Preferences U i ( θ, m , y ); U R ( · ) typically independent of m . 7. Prior P ( θ ). 8. All sets are finite (unless I want them to be infinite). Lying and Deception Sobel
Model Includes . . . 1. Standard (Spence) signaling. 2. Cheap talk. 3. Some sequential Games with Incomplete Information. Lying and Deception Sobel
Variations 1. Many Players 2. Noisy Messages 3. Incompletely informed Sender 4. (*) Sender takes payoff relevant action (*) No time today. Lying and Deception Sobel
Common Language 1. For each Θ 0 ⊂ Θ, there exists a message m Θ 0 ∈ M and there is a common understanding that m Θ 0 means “ θ ∈ Θ 0 .’ 2. Exactly one such message for each subset. 3. m has accepted meaning if m = m Θ 0 . 4. Some messages may have no accepted meaning. Lying and Deception Sobel
Comments 1. S need not tell the truth. 2. There may be costs associated with lying (or telling the truth). 3. All definitions can be interpreted from S ’s perspective. Lying and Deception Sobel
Lying: Definitions Lying arises when the Sender says something that she believes to be false. Definition (Lying) 1. The message m is a lie given θ if m = m Θ 0 and θ / ∈ Θ 0 . 2. The message m is a lie of omission given θ if m = m Θ 0 and { θ } � Θ 0 . 3. The message m is true given θ if m = m θ . Lying and Deception Sobel
Observations 1. Lying does not depend on preferences. 2. Lying does not depend on R ’s behavior (or S ’s beliefs about R ’s behavior) 3. Definition depends on only on support of the distribution. (So there is not word for “ A and B are equally likely.”) Lying and Deception Sobel
Other Approaches Philosophy, theology, legal studies, evolutionary biology, computer science, . . . I’ll only say: St. Augustine provides taxonomy (eight types of lie). He asks: Is it ever moral to lie? Dishonest statements told in jest are not lies according to St. Augustine. Lying and Deception Sobel
Linguistic Anthropology Coleman and Kay argue that one evaluates whether a statement is a lie by assessing the extent to which it satisfies three criteria: 1. the statement is false 2. the speaker believes the statement to be false 3. the intention of the speaker is to deceive Experimentally people classify statements as lies using the second criterion. Lying and Deception Sobel
Another Voice It takes two to speak truth – one to speak and another to hear. Lying and Deception Sobel
Another Voice It takes two to speak truth – one to speak and another to hear. Henry David Thoreau, “A Week on the Concord and Merrimack Rivers: Wednesday” Lying and Deception Sobel
Lies in Cheap-Talk Games Simple cheap-talk game : 1. Θ = [0 , 1]; Y = R 2. for i = S , R , U i ( θ, y ) is continuous, strictly concave in a , and satisfies U i 12 > 0; 3. y i ( θ ) ≡ arg max U i ( θ, y ) is well defined; 4. y S ( θ ) > y R ( θ ). Lying and Deception Sobel
Results Proposition In a cheap-talk game with a common language, there always exist equilibria involving lies. Proposition In a cheap-talk game with a common language, any non-trivial equilibrium type-action distribution can be induced by an equilibrium in which each agent’s message is a lie. Proposition In a simple cheap talk game, there is a positive probability of lying every equilibrium. Proposition In a simple cheap-talk game with a common language, every equilibrium type-action distribution can be supported as an equilibrium with only lies of omission. Lying and Deception Sobel
Observations 1. Expect exaggeration. 2. Banning lies benefit both players. Lying and Deception Sobel
Honest Equilibria Honesty is typically incompatible with strategic behavior, but if there is no conflict of interest between the players, there is a possibility that the Sender will report honestly in equilibrium. 1. y R ( θ, m ) be a solution to max U R ( θ, y , m ); 2. let m ( θ ) solve: max U S ( θ, y R ( θ, m ) , m ) . (1) 3. When m ( · ) is single valued and one-to-one, the game is potentially revealing . Proposition In any potentially revealing game in which U S = U R , there exists a specification of language under which an honest equilibrium exists. Lying and Deception Sobel
Beliefs Each m ′ induces a posterior distribution µ ( θ | m ′ ). Definition (Properties of Beliefs) 1. The belief µ ( · | m ′ ) is completely inaccurate given m ′ and θ if P ( θ ) = 0 for all θ such that µ R ( θ | m ′ ) > 0. 2. The belief µ ( · | m ′ ) is inaccurate given m ′ and θ if P ( θ ) = 0 for some θ such that µ R ( θ | m ′ ) > 0. 3. The belief µ ( · | m ′ ) is accurate given m ′ and θ if µ R ( θ | m ′ ) = 1. 4. Given the mixed strategy σ ( · ) of S , the belief µ ( · | m ′ ) is rational given m ′ , θ , and σ ( · ) if it is derived from the prior and Sender’s strategy whenever possible. Lying and Deception Sobel
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