THE WORKLOAD GAME:
———————–
Dear Y,
I hope you had a nice trip.
So what is your decision?
Best,
L.
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Hi L,
I would like to have a conversation with you about this. When do you have time today?
Y.
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Dear Y,
It was nice talking to you. Thank you for letting me know your decision.
Given you insist a different interpretation of my contract, I may have to ask others for resolution.
Best,
L.
[ROUTINE]
RUN: 2.1MILES, 9.5MPH, 13MIN;
SWIM: 0;
LEARN: TADELIS, 1 HR (DAYLIGHT SAVING TIME CHANGE, ONE HOUR SHORT FOR SLEEP);
[LIFE: CATALINA TRIP]
WITH KEVIN, J, AND C.
DRIVE TO THE NEWPORT PAVILLION FOR BOAT, PARKING $18, 7:50-8:10AM;
TAKE THE CATALINA FLYER TO CATALINA ISLAND: 8:30-9:15AM, TICKET $75, SEASICK;
RENT GOLF CAR AND DRIVE AROUND, 10AM-12PM;
LUNCH AT BLUE(?), FOR FISH, $20, 12PM-1PM;
ZIP LINE, WITH C, $125, 1PM-3:15PM;
WALK AROUND THE CITY, 3:15-4:15PM;
RETURN ON 4:30PM-5:45PM;
[HAPPY MOMENT]
THE CATALINA TRIP 
[ROUTINE]
RUN: 1.6MILES, 9.5MPH, 10MIN;
SWIM: 1KM;
LEARN: TADELIS, 2HRS;
[WORK]
AO: WRITE UP, 5 HRS;
AO: EMAIL L.G. FOR FEEDBACK;
[SCHOOL]
EMAIL YZW FOR MEETING NEXT WEEK, SMILE BUT NO YIELD ON MY TERMS;
THIS IS A SIMPLE MATTER. HE HAS THE POSITION OF ADMINISTRATIN, BUT NO MORAL GROUND TO LECTURE YOU ANYTHNG. SO FOR THE MEETING, SMILE, LILSTEN TO WHAT HE HAS TO SAY. BUT HOLD YOUR GROUND ON THIS ISSUE. YOU DO NOT YIELD. WITH A SIMLE.
[LIFE]
GROCERY SHOPPING AT COSTCO, \$440, 12:30PM-3:30PM, 3HRS;
[HAPPY MOMENT]
RECEIVED GC APPROVAL;
[15MIN]
When type is private information, the games become more complicated. This is because, for an equilibrium to exist, each player must be able to correctly predict others’ actions.
In a Bayesian game, player 1 can be of different types (assigned by mother Nature). He can observe his type, but player 2 knows only the type distribution. The issue becomes trickier when player 2 has to move in the ensuring information set: even after observing player 1’s action, player 2 is still uncertain about player 1’s type. Without further information, player 2 cannot decide his best response.
This technical difficulty is resolved by introducing the notion of belief. Specifically, for a given Bayesian Nash equilibrium (BNE), at each information set, each player must hold the correct belief that is consistent with the BNE; he then plays the best response to the belief. At the information set reached with positive probability, the belief is updated according to the Bayes’ rule. Off of the equilibrium path, however, the belief can take arbitrary form.
Formally, a Bayesian Nash equilibrium and a consistent belief constitute a perfect Bayesian equilibrium (PBE). Hence, PBE has four requirements: 1) every player holds a belief, 2) on the equilibrium path, the belief follows Bayes’ rule; 3) off the equilibrium path, the belief is arbitrary; 4) the BNE is each player’s best response to that belief.
In a sense, the belief is an intermediate concept that ensures the sequential rationality of BNE (Bayes’ rule and best response). The idea is similar to that of mean field theory.
[ROUTINE]
RUN, 2.3MILES, 9MPH, 15MIN;
SWIM: 1K;
LEARN: LUENBERGER;
[WORK]
AO: WRITE, PELICAN, 3HRS;
TQ2: READ, 1HR;
[DISCIPLINE]
CALL COX TO FIX THE TV ONLINE PROBLEM (WI-FI WIRELESS CONNECTION IN TV’S NETWORK SETTING), 15MIN;
CLEAN UP MAILS, PAY BILLS, 30MIN;
[UNHAPPY MOMENT]
BIG FIGHT WITH DAD; BUT I WON’T BUDGE.
[ROUTINE]
RUN: 2.3MILES, 15MIN;
SWIM: 1KM;
LEARN: LUENBERGER;
[WORK]
AO: WRITE THE POOLING EQUILIBRIUM;
TQ2: WRITE THE EMPIRICAL PART;
[HAPPY MOMENT]
BUILD MY ROUTINE; FIND MY RHYTHM.
A MAN OF ACTION 