01.16.01

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Game Theory Applications Lecture 2

• Galina Albert Schwartz
• Department of Finance
• University of Michigan
• Business School

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How to find me

• My office D3270A (Davidson Hall)
• My e-mail galka_at_umich.edu
• My office hours
• Mon., 10am - 12pm
• Th., 1pm - 3pm,
• or by appointment

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Lecture 2 Terminology Examples of Basic Games

• Dixit, Chapters 1 2 (mostly 2)
• Definitions
• strategy
• outcome
• equilibrium
• payoff
• expectations
• rationality

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The Major Definition

• Dixit, p. 29 second paragraph from the bottom
• Our definition of the rules of the game
• list of players
• strategies available to each of them
• payoffs of each player for all possible
  combinations of all player strategies
• each player is a rational maximizer

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Definitions

• Strategy is a set of the choices available for
  the players, (Dixit, p. 25)
• Payoff is a number associated with each possible
  outcome of the game (Dixit, p. 26) (and Expected
  payoff)
• Equilibrium - each players strategy is a best
  response to the strategies of others, p. 30

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What Do We Assume about the Game?

• Rationality implies
• consistency in the ranking of the payoffs
• ability to calculate what is in his best interest
• Common knowledge of the rules of the game

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What is Rationality?

• Rationality does not imply
• the same values for everyone
• impossibility of altruismcould be incorporated
  in payoff
• short-term rationality irrational from immediate
  perspective may be valuable as a long-term
  strategy
• example prices introductory prices predatory
  prices. Interaction between the two

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Classification of the Games

• Dixit, Chapters 1 2 (mostly 2)
• constant-sum games ? zero-sum games
• bargaining games
• brinkmanship
• sequential moves games
• simultaneous moves games
• cooperative games (we will not address)
• i.e. games with a possibility of enforceable
  joint-action agreements

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Classification of the Games (cont.)

• Dixit, Chapters 1 2 (mostly 2)
• non-cooperative games
• non-repeated games (one-shot games)
• repeated games
• repeated but with different opponents
• dynamic games (evolutionary games)
• or, are the rules fixed or permit
  manipulation?

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What is more important How or Why?

• How (cases)
• Why (theory)
• Apply game theory to
• explain
• predict
• advise (prescribe)
• Why is needed to advice (prescribe)

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Lewis, Chapter 2 Never Mention Money. Game 1

• Never Mention Money Does it makes any sense?
• Yes, it does. The required answer actually makes
  perfect sense. Emotions matter! I.e.
• the people excitement by the high-caliber
  people
• the challenge
• the thrill of the deal

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Lewis, Chapter 2 Never Mention Money. Game 2

• Why analysts job has super-long hours?
• from a production point inefficient
• Prisoners dilemma? A small part of the
  explanation
• But a cutthroat business competition is a
  Prisoners dilemma
• Major purpose - to deter cheats time constraint
  on physical implementation , and design of the
  cheating mechanism

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Lewis, Chapter 2 Never Mention Money. Game 3

• Interviewing with Solomon Brothers.
• Why intellect is not checked sometimes?
• It is implied to be sufficient
• Why education (the knowledge) is irrelevant, but
  still is required?
• signals interests
• signals ability
• majoring in economics permit direct comparison

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Lewis, Chapter 2 Never Mention Money. Game 3
(cont)

• Why to intimidate?
• Speed (and quality) or responses in unfamiliar
  situation are tested
• Why no explicit offer?
• Nobody could turn it down
• Importantly impossible to state that you turned
  Solomon down
• No explicit salary offer. To underpay?
• No, to screen. A quest for the able ones (who do
  not fear the risk confident in abilities)

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Summary of Today

• Definition of the Game p. 29
• The definition of Nash Equilibrium, p. 30
• Lewis, Chapter 2 examples of the games

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To Do your preparation to 01.18.01

• Read Dixit, chapter 2
• Read Lewis, chapters 2 3
• Next time we will explain what is the absolutely
  necessary component of the Greenspans strategy
  and any other Central Bankers strategy
• Please, prepare your guesses of the
  absolutely necessary component