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AREC 688 > Lecture 1 > Flashcards

Lecture 1 Flashcards

1
Q

What’s the difference between Nash Equilibrium and Dominant Strategy?

A

Dominant Strategy is one type of Nash Equilibrium.

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2
Q

Who started Game Theory?

A

John von Neumann and Oskar Morgenstern 1944

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3
Q

When did Nash’s paper come out

A

1950s

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4
Q

What are the two types of approach for the players in Game Theory?

A
  • Strategic & non-cooperative
  • Cooperative
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5
Q

What is another name for Game Theory?

A

Multi-agent decision theory

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6
Q

What are the key assumptions for Game Theory?

A
  • People interact in a rational manner, even when being altruistic.
  • Common Knowledge: players know the rules, and know that each other know the rules, and that each other know that each other know the rules.
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7
Q

What is Game Theory?

A

The study of rational behaviour in situations involving interdependence.

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8
Q

What are the essential elements of the game?

A

Who: players
What: strategies
Information sets
When: when players learn the information
When: timing
Payoffs: how much

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9
Q

What are the two principal representations of the game?

A
  • Normal / strategic form
  • Extensive (tree) form
    *both forms should yield the same results.
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10
Q

What do A and a represent?

A

A = all the strategies (actions)
a= a particular strategy/ action for a particular player
*“Feasible Set”

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11
Q

What does p stand for?

A

p = payoff for a particular strategy profile

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12
Q

What is a strategy?

A

A complete plan of action that specifies for the player a feasible action in every contingency in which the player might be called on to act.

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13
Q

What is a Pure Strategy?

A

A pure strategy is the choice by a player of a given
action with certainty. A pure strategy is a special case of a mixed strategy.

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14
Q

What is a Mixed Strategy?

A

A mixed strategy is when one player plays randomly
between different strategies. Imperfect information does not automatically mean it’s a mixed strategy.

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15
Q

What is Complete Pre-order?

A

Complete pre-order: When presented with any pair of actions, the agent knows which action she prefers or equivalently she knows that she regards both action as equally desirable.

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16
Q

What is Preference Transitivity?

A

Preference transitivity: If an agent prefers action a to b, and action
b to c, then she prefers action a to c.

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17
Q

What is a payoff function?

A

A practical way to represent preferences:
u (a) > u (b) if and only if a is preferred to b.

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18
Q

What is a preference indicator function?

A

What game theorists call a payoff function.

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19
Q

What is a Utility Function?

A

The name economists use for a Payoff Function.

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20
Q

What is Ordinal Information?

A

Using numbers to represent </>, but their value is kind of meaningless - can’t add/subtract/divide.

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21
Q

What is Cardinal Information?

A

When numbers have their regular mathematical meaning.

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22
Q

What is the normal-form representation of an n-player game?

A
23
Q

What is a payoff matrix?

A
24
Q

What brings about the possibility of the prisoner’s dilemma?

A

When free-riding is possible.

25
Q

What is a zero-sum game?

A

When the overall utility at the end equals zero. The matching pennies game is an example. Remember that this means one of the utilities will go to negative sometimes.

26
Q

What is the natural outcome of this game?

A

Outcome: (A 2/1, A 3/2)

27
Q

What does IESDS stand for?

A

Iterated elimination of strictly dominated strategies

28
Q

If a set of strategies is not eliminated using IESDS, then what are those strategies?

A

The unique Nash Equilibrium of the game.

29
Q

What is a Vickrey auction?

A

Highest bidder gets the item but only pays the second highest price that anyone bid.

30
Q

What does this mean?

A

This indicates that si is single strategy within the greater set of strategies, Si.

31
Q

What does (a+b)^2 expand to?

A

a^2+2ab+b^2

32
Q

What does (a-b)^2 expand to?

A

a^2-2ab+b^2

33
Q

What does (a+b)(a-b) expand to?

A

a^2-b^2

34
Q

simplify a^2+2ab+b^2

A

(a+b)^2

35
Q

simplify a^2-2ab+b^2

A

(a-b)^2

36
Q

Simplify a^2-b^2

A

(a+b)(a-b)

37
Q

Simplify 1-b^2

A

(1+b)(1-b)

38
Q

What is the definition of a Cournot game?

A
  • oligopoly
  • identical products
  • compete in quantities
39
Q

What is a Nash Equilibrium?

A

When all decisions are such that no player wishes to change their decision given the decisions of the other players.

40
Q

How do we solve a maximization equation?

A

1) expand
2) First Order Condition (FOC)
3) substitute one equation into the next
4) expand
5) collect like terms and simplify
6) plug everything back into the original payoff function

41
Q

What is the Bertrand Paradox?

A

Bertrand paradox:
The mathematical proof that all prices go towards marginal cost is quite strong, but we know in a duopoly there’s a great deal of profit made.

42
Q

How do we escape the Bertrand Paradox?

A
  • Capacity constraints
  • Temporal dimensions
  • Product differentiation
43
Q

How do we show product differentiation with the Bertrand Paradox?

A

Gamma (weird y or r symbol)
- If gamma is close to 1 then the goods are quite similar, if gamma close to zero the goods are independent.
- If gamma is negative, then our products are compliments
- The unit cost should be such that cj < 1 (where 1 is the maximum)

44
Q

When can we use this formula?

A
  • After the First Order Condition (where we set the derivative equal to zero).
  • When all q are equal
45
Q

Is this formula used before or after FOC?

A

Before the FOC.

46
Q

How do we find q*?

A

a) Production function into profit equation
b) Q = Q-1+q1
c) FOC
d) Q-1=(n-1)q *as long as all q are equal
f) Isolate q

47
Q

How do we find the socially optimal level of production?

A

Maximize total (group) utility or profit.

48
Q

How do we find the Nash Equilibrium level of production?

A

Maximize the individual utility or profit function.

49
Q

In a Cournot competition, what is price equal to?

A

P=alpha - Q

50
Q

What is a Cournot competition?

A
  • n firms
  • identical goods
  • identical costs
  • Firms are competing on quantities (not price)
  • P = (alpha-Q if Q</= alpha) or (0 if Q > alpha)
  • when the number of firms in the market (n) becomes high, unit price converges towards marginal cost.
51
Q

What is the difference between a Bertrand competition and a Cournot competition?

A

Cournot: firms compete on quantity, no accounting for differentiation
Bertrand: firms compete on price, can show differentiation

52
Q

How do we solve for Cournot NE when we have two q’s?

A

q1=q2=q*

53
Q

How do we move from n=2 firms to n= unknown # of firms?

A
  • Q now is Q-i + qi before the FOC
  • after FOC Q-i becomes (n-1)q
  • once we find q, then Q is just q^n

AREC 688 (4 decks)

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