Advanced Game Theory

1
Advanced Game Theory

• Introduction

2
Two Dimensions of Game Theory

• Strategy
• Design

3
Strategy

• Stand in shoes of other players
• Key issues
• Cooperation Realise opportunities to create
  value
• Commitment Ensure you can credibly claim a share
  of that value
• Coordination signal actions to others
• Qualitative/Robustness Focus

4
Design

• Stand in the shoes of agents
• Key Issues
• Incentives aligning agents interests with your
  goals
• Information getting agents to reveal private
  information
• Implementation practicalities of dealing with
  complexity
• Quantitative/Details Focus

5
Housekeeping

• Assessment
• Syndicates
• Project
• Readings
• Problem Sets
• Web Page

6
Concept Review

• Rational Choice
• Statistical Concepts
• Noncooperative Game Theory
• Set-up payoffs, players, actions
• Dominated strategies
• Nash equilibrium
• Backwards induction
• Repeated interactions

7
Incentives

• May desire a particular action
• Engage in effort
• Reveal information
• Design issue is to design a mechanism that makes
  it a dominant strategy to undertake the desired
  action

8
Case

• Corporate Raiding

9
Information

• Have to act with incomplete information
• If rational, recognise own ignorance and
  recognise ignorance of others
• Think about what others know and dont know and
  what they know about what they know and dont
  know (e.g., Holmes and Moriarty)
• Assume agents have common knowledge
• An event is common knowledge among a group of
  players if each one knows it, if each one knows
  that the others know it, if each one knows that
  each other one knows that the others know it, and
  so on.
• Common knowledge of public events, rationality
  etc.

10
Exercise

• Hat Game

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Common Knowledge in Hat Game

• It is common knowledge that
• Everybody can see two hats
• Public pronouncements of ignorance
• Knowledge of others reasoning
• Later common knowledge that at least one hat is
  red (initially it was knowledge but not common
  knowledge)

12
Envelope Game

• Two envelopes, each with money
• Either 5, 10, 20, 40, 80 or 160
• Common knowledge that one has twice as much as
  the other.
• Give one to A and the other to B
• Open private knowledge of contents
• Give opportunity to switch and if both A and B
  want to they are allowed to
• Unless have 160 looks like each is better off
  switching but how can that be?

13
Email Game

• A and B are arranging meeting up in another city.
  They email each other about a location because if
  they fail to meet up they would be better off not
  traveling.
• Suppose A emails B a location but there is a
  probability, p, the email is not received (there
  is no message sent that a message is not
  received). So A cant be sure B knows where to
  go.
• A could ask for confirmation. But that
  acknowledgement may not get through. A and B know
  where to meet but B does not know if A knows that
  B knows.
• Knowledge has increased but what about
  coordination?

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Is Email Useful?

• As choices
• If travels regardless of acknowledgement, is
  ignoring that and are in situation B has sent no
  acknowledgment.
• Should not travel since it was more likely
  original message was lost (p) than
  acknowledgement lost (p(1-p)).
• Therefore, only travel if get acknowledgement
• Bs choice
• Should travel if got message but not otherwise.
• Outcomes
• Coordinate with probability (1-p)2
• B travels alone with probability (1-p)p
• No travel at all with probability p
• Acknowledgement does not and never will help

15
Implementation

• In design, the details are critical.
• Failure to take into account all of the rules can
  lead to
• Embarrassment
• Inefficiency

16
New Zealand UHF License Auction

• A simultaneous sealed-bid second price auction

17
Australian Satellite TV Auction

• A sealed bid auction with no withdrawal penalty

Initial Winning Bid
Final Transaction Price
212,000,000
117,000,000
177,000,000
77,000,000
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From here

• Matching markets
• Mechanism Design
• Nonlinear Pricing
• Auctions and Bidding
• Voting and Institutions