A Game Theory Analysis of the Final Five Laps of the 2008 Formula 1 Brazilian Grand Prix Jordan Diekema.

A Game Theory Analysis of the Final Five Laps of the 2008 Formula 1 Brazilian Grand Prix

Jordan Diekema

Analyze the pit strategies of three key drivers for the final five laps of Brazilian GPFelipe Massa (Ferrari)Lewis Hamilton (McLaren-Mercedes)Timo Glock (Toyota)

Goal:Show that the reason Glock chose not to pit

was out of self-interestShow that what would normally be viewed as

an irrational strategy was, in fact, rational

Rain started with 5 laps to go

Massa running in 1st, Hamilton running in 4th

If Massa won, Hamilton needed 5th or better

Massa and Hamilton pitChange to intermediate

wet tiresSensible strategy

Glock does not pitStays on dry tires

despite rainPasses Hamilton while

in pitsHamilton drops from

5th to 6th, out of contention

Massa wonHamilton passes Glock

on final corner of final lap to take 5th

Two basic strategies:Make a pit stop (P)Don’t make a pit stop

(D)Reasons to pit:

Wet trackChange to wet tires for

better tractionMinimize risks

Reasons not to pit:Very fewDon’t waste time by

pitting

Championship pointsPoints based on

finishing place10, 8, 6, 5, 4, 3, 2, 1

Monetary rewardsComparative payoffs(+), (-)

ReputationComparative payoffs(+), (~), (-)

Risk discount factor multiplied by D payoffs0 < r < 1

Helps to differentiate payoffs for P and D

Example:Massa gets 10 pts if PMassa gets 10r pts if DD is far riskier

strategy, and thus the payoff is discounted by r

P=PitD=Don’t pitRow 1—

Championship points payoffs

Row 2—monetary reward comparative payoffs

Row 3—reputation comparative payoffs

Used:Iterated Elimination of

Dominated StrategiesSub-Perfect Nash

EquilibriaResults:

Massa, Hamilton always choose P

Glock always chooses D

Holds for all three variables

Choosing D was rational for GlockBecause of his

perception of riskD was the strategy

that maximized his payoffs