Cheap talk
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In game theory, cheap talk is communication between players which does not directly affect the payoffs of the game. This is in contrast to signaling in which sending certain messages may be costly for the sender depending on the state of the world. The classic example is of an expert (say, ecological) trying to explain the state of the world to an uninformed decision maker (say, politician voting on a deforestation bill). The decision maker, after hearing the report from the expert, must then make a decision which affects the payoffs of both players.
Cheap talk can, in general, be added to any game and has the potential to enhance the set of possible equilibrium payoffs. For example, one can add a round of cheap talk in the beginning of the Battle of the Sexes. Each player announces whether they intend to go to the football game, or the opera. Because the Battle of the Sexes is a coordination game, this initial round of communication may enable the players to randomize among equilibria yielding payoffs [2.5,2.5] which cannot be achieved with any pure or mixed strategy without cheap talk. The messages and strategies which yield this outcome are symmetric for each player. They are: 1) announce opera or football with even probability 2) if both players announce football or both players announce opera, play opera. if both players announce different entertainment options, play football.
It is not guaranteed, however, that cheap talk will have an effect on equilibrium payoffs. Another game, the Prisoner's Dilemma, is a game whose only equilibrium is in dominant strategies. Any pre-play cheap talk will be ignored and players will play their dominant strategies (Defect,Defect) regardless of the messages sent.
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[edit] Necessary conditions for cheap talk to affect the outcome of a game
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This section may require cleanup to meet Wikipedia's quality standards. Please improve this article if you can (December 2006). |
Consider a game comprising two players, a sender and a receiver. The sender has a non-singleton type space. Nature chooses the sender's type at the start of the game, but this choice is unobserved by the receiver. The order of play is an action taken by the sender (a message) and then an action taken by the receiver. Crucially in a cheap talk game, the sender's action does not affect the payoff per se, insofar as for a given sender type and a given receiver action, payoffs will be the same regardless of the sender's message. However, the action of the sender might affect the payoff for both parties by changing the action taken by the receiver.
The receiver must care about the type of the sender. If this is not the case, only the receiver's action affects his payoff. He maximises his payoff by simply selecting the action that does just that. The fact that he does not observe the sender's type is irrelevant to him and no message sent to him by the sender can affect which action maximises his payoff. This is exemplified by a modified Prisoners' dilemma game in which prisoner 1 is one of two types (not known to the second prisoner). He either has the 'standard' preferences of a prisoner in Prisoners' dilemma or he has a strong aversion to defecting. Prisoner 2 has standard preferences. Prisoner 1 can send a message to prisoner 2 before they choose to cooperate or defect. However, since prisoner 2's best response to any strategy played by prisoner 1 is to defect, the message sent by prisoner 1 cannot affect the outcome of the game (assuming common knowledge and rationality, etc.)
Different sender types must have different preferences. Or rather, not all types have the same preferences. If this is not the case, the receiver cannot differentiate between types because all sender types will take an action that maximises their payoff, which will be the same action since they all have identical preferences. In this pooling case, however, the receiver knows (assuming common knowledge and rationality, etc.) that all types send the same message and so that message cannot be used to discriminate amongst types - the message will not tell the receiver which type the sender is. The best response of the receiver is to maximise his ex ante expected payoff (irrespectively of the message sent). However, the message of the sender cannot determine the sender's payoff either.
The sender and receiver must not have opposite preferences. If the sender wants the receiver to take the opposite action that the receiver would take if he knew the sender's type, cheap talk is useless because the sender's message can be at most an attempt to induce the receiver to take the opposite action to the action he wants to take and be at least completely uninformative. If the sender knows that the receiver knows he is being deceived by any message, the latter is more likely. Suppose that the receiver can only take two actions, A and B, and the sender can be of two types, a and b. The receiver's payoff is maximised if he plays A when the sender is type a and plays B if the sender is type b. The sender's payoff is maximised if the receiver plays A when the sender is type b and the receiver plays B when the sender is type a. If the sender sends 'I am a' to the receiver, the receiver might think that the sender is being truthful, in which case he should play A, but if he plays A, the sender maximises his payoff if he is type b, so perhaps the sender is actually type b. In this case, the receiver should play B, but then the sender maximises his payoff if he is a, so perhaps it is a double bluff, etc.
[edit] Biological applications
It has been commonly argued that cheap talk will have no effect on the underlying structure of the game. In biology authors have often argued that costly signalling best explains signalling between animals (see Handicap principle, Signalling theory). This general belief has been receiving some challenges (see work by Carl Bergstrom and Brian Skyrms 2002, 2004). In particular, several models using evolutionary game theory indicate that cheap talk can have effect on the evolutionary dynamics of particular games.
[edit] See also
[edit] References
- Crawford, VP, J Sobel (1982) "Strategic Information Transmission." Econometrica, Vol 50, No. 6, pp. 1431-1451 (the seminal paper)
- Farrell, J., Rabin M. (1996) “Cheap Talk.” The Journal of Economic Perspectives, Vol. 10, No. 3. (Summer, 1996) pp. 103-118.
- Robson, A.J. (1990) “Efficiency in Evolutionary Games: Darwin, Nash, and the Secret Handshake.” Journal of Theoretical Biology 144: 379-396.
- Skyrms, B. (2002) “Signals, Evolution and the Explanatory Power of Transient Information.” Philosophy of Science 69: 407-228.
- Skyrms, B. (2004) The Stag Hunt and the Evolution of Social Structure. New York: Cambridge University Press.
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