Deterrence, Rationality and Game Theory

 

Rationality in the Theory of Games

 

-      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.

 

Rational Deterrence

 

-      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.