- actors hold preferences over outcomes, not over actions or ÔstrategiesŐ
- actors preferences are transitive
o if x is preferred over y (x>y) and y>z, then x>z
- an actor with the preference ranking x>y>z is rational if when faced with a choice between x or z , the actor picks x.
- an actor with preferences ranking x>y>z is irrational if when faced with the choice of x or z , the actor picks z.
- Actors A and B are in condition y.
- To deter actor A with preferences ranked x>y>z from taking some action X to produce outcome x, actor B with preferences ranked z>y>x must threaten some action Z that will produce outcome z iff actor A takes action X.
- actor BŐs intention to produce outcome z iff actor A takes action X must be communicated to actor A
- actor A must believe that actor B is capable of performing action Z iff actor A takes action X
o actor A must hold the correlative belief that actor B will not produce outcome z iff actor B refrains from action X
- actor A must believe that action Z will produce outcome z
Irrationality and Credible Threats
- actors A and B are in condition y
- actor A has preferences ranked x>y>z; actor B y>x>z
- is actor A deterrable?
o why should actor A believe that actor B would take some action Z to produce outcome z if actor B ranks x>y?
o for actor B to seek outcome z would be irrational
o if successful deterrence depends on actor A behaving rationally, how can successful deterrence depend on actor B behaving irrationally
Rationality of Irrationality
- actor B could threaten to perform action Z˘ which will produce outcome z with some probability pz iff actor A perform action X.
- if actor A values a certainty of y more than the expected value of seeking outcome x with the risk of z, then actor A will be deterred
- but formalizations still find BŐs commitment to be irrational (in the technical sense)
o rationality of irrationality
- Schelling argued that by using threats that leave something to chance, a defender can force a challenger into a competition in risk-taking.