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Games and Economic Behaviour > Games > Flashcards

Games Flashcards

1
Q

Q

A

A

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2
Q

What is rationality (pt1)?

A

A player has beliefs about the other players’ decisions

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3
Q

What is rationality (pt2)?

A

A player maximises utility based on those assumptions

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4
Q

What is a strict dominating strategy?

A

A strategy that always outperforms another strategy, no matter my beliefs about other players’ decisions.

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5
Q

Common knowledge

A

Every player knows that every one knows what everyone knows….

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6
Q

What is a mixed strategy?

A

A lottery over your pure strategies

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7
Q

Why is Nash Equilibrium problematic (assumption)

A

We need to know our opponent has a correct belief about our strategy

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8
Q

Indifference curves in the three lottery space

A

Parallel and straight

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9
Q

How is indifference presented in expected utility notation

A

Weak preference in both directions

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10
Q

How is strong preference presented in expected utility notation

A

Weak preference one way, and not the other way

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11
Q

What is completeness (Axiom 1 of expected utility)?

A

Agents can give you a preference between two lotteries (or be indifferent) for every lottery

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12
Q

What is Transitivity (Axiom 2 of expected utility)?

A

If A is better than B, and B is better than C, A must be better than C

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13
Q

Theorem of expected utility

A

If we have a finite number of transitive and complete ranks of lotteries, we can build a utility function

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14
Q

What is Independence (Axiom 3 of expected utility)?

A

Where lotteries split into multiple lotteries, giving identical probabilities of outcomes, we should be indifferent between this setup in the original

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15
Q

What is Continuity? (Axiom 4 of expected utility)

A

If we have three lotteries, we can make an indifference condition through a lottery between the higher and lower preference utilities

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16
Q

What is the use of an extensive form game

A

When decisions happen over different periods of time, and people have dynamic information

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17
Q

What is the history of a game?

A

The sequence of decisions made to get to a certain point

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18
Q

What are the two types of histories

A

Terminal and Subhistories

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19
Q

How do you present a normal form (non table)

A

All strategies possible for each player listed

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20
Q

Compromise between NE and backwards induction

A

Subgame perfect NE

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21
Q

What is Zermelo’s theorem

A

In a two-player, finite game, with strict preferences win > draw > lose, there is a subgame perfect Nash equilibria

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22
Q

Rubenstein Bargaining model

A

Infinite bargaining setup where payoffs are discounted at a consistent rate each period

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23
Q

Critique of Independence of Irrelevant Alternatives

A

In bargaining situations, removing threats can lead to changes in solution

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24
Q

What is the Jury setup

A

Actions (acquit/convict), Types (looks innocent, looks guilty), State (Innocent, guilty), Payoffs (correct result gets 1, incorrect is 0)

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25
Q

What is Bayes rule?

A

The probability of A given B is the probability of A and B, divided by the probability of B

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26
Q

What is a bayesian nash equilibrium?

A

Everyone is maximising their own utility given what the other player’s actions are and their beliefs about other player’s types

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27
Q

In what scenario does my vote matter in the voting problem?

A

When the vote numbers are equal

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28
Q

What is the word for a voter who casts the deciding vote?

A

Pivotal

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29
Q

What is the strategy in the voting game

A

Voting when their cost is low enough and the probability of being pivotal is high enough

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30
Q

As n increases, what happens to the probability of being pivotal?

A

Decreases

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31
Q

What do people vote if they get the guilty signal?

A

Vote to convict

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32
Q

What do people vote if they get the innocent signal?

A

Some randomisation over innocent and guilty

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33
Q

What is a Weak Perfect Bayesian Equillibrium?

A

Players estimate probabilities of the “nature” at each information set, which we have defined using bayes rule, and then maximise utility with these beliefs

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34
Q

What are the types of equillibria in the signalling game?

A

Pooling and seperating

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35
Q

In the pooling equilibrium, what are the beliefs about information sets?

A

Just nature

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36
Q

Stage 1 - Pooling Equilibrium Checklist

A

Make a hypothesis on the sender equilibrium strategies

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37
Q

Stage 2 - Pooling Equilibrium Checklist

A

Given the hypothesised strategies, work out the receiver’s beliefs on the equilibrium path

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38
Q

Stage 3 - Pooling Equilibrium Checklist

A

Compute the receivers best reply on the equilibrium path

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39
Q

Stage 4 - Pooling Equilibrium Checklist

A

Make sure that our original equilibrium strategies are the best reply for each type of sender

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40
Q

Stage 5 - Pooling Equilibrium Checklist

A

Find the restrictions that step 4 imposes and the receiver’s off-equilibrium beliefs.

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41
Q

Stage 1 - Separating Equilibrium Checklist

A

Make a hypothesis on the sender equilibrium strategy

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42
Q

Stage 2 - Separating Equilibrium Checklist

A

Identify the receivers beliefs at every point on the equilibrium paths (all are in this case)

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43
Q

Stage 3 - Separating Equilibrium Checklist

A

Compute the receiver’s best reply in each of these cases

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44
Q

Stage 4 - Separating Equilibrium Checklist

A

Verify that the sender is acting rationally to nature

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45
Q

What is herding?

A

When your signal is dominated by external signals, so everyone goes with the same outcome in social learning

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46
Q

What is the payoff in the cheap talk game?

A

Negative deviation squared

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47
Q

How does Bayesian Persuasion differ from cheap talk

A

The sender commits to a communication strategy

48
Q

What structure does the solution to Bayesian persuasion come in

A

The sender maximises the chance of sending the “2” signal while keeping his signals believable enough to be trustworthy

49
Q

Stable pairing

A

When there is no alternative that both parties would prefer

50
Q

Deferred acceptance procedure

A

All A propose to their favourite B, all B reject everyone except favourite A, continued until all gone

51
Q

What is an auction - theory definition

A

Allocation mechanism of a scarce good with transfers

52
Q

Structure of an auction - setup

A

The auctioneer communicated how the “messages” will be translated into an allocation and a transfer

53
Q

Structure of an auction - messages

A

All players send a message into the message space

54
Q

When are auctions a bad idea

A

Low commitment, low number of bidders, high bidding costs

55
Q

Structure of an auction - solution concept

A

All individuals’ bidding strategies

56
Q

What are the impacts of transfers on total utility?

A

Nothing - transfers are irrelevant

57
Q

What is Ex-ante

A

No one knows their type

58
Q

What is interim

A

You know your own type but not everyone’s

59
Q

What is ex-post

A

You know everyone’s type

60
Q

What is a direct mechanism?

A

A bidding mechanism that bidders truthfully report their types

61
Q

What is the revelation principle

A

We can assume every mechanism can be presented as a direct mechanism

62
Q

Reasoning behind the revelation principle

A

You are always able to avoid the intermediate step of message mapping by going directly from types to transfer and allocations

63
Q

What is the goal of VCG?

A

Internalising everyone’s utility into the transfers of the individual

64
Q

Benefit of VCG

A

Bidders maximise their own utility by bidding truthfully

65
Q

What is the pivot mechanism?

A

The payment is set at the externality inflicted on the other bidders

66
Q

What is an example of a pivot mechanism?

A

Second price auction

67
Q

What is shading?

A

The difference between your personal value and the bid

68
Q

Assumption about type distribution

A

Everyone has identical type distribution ex-ante, which gives us symmetric strategies in the interim (as no bayesian update based on type)

69
Q

How does the level of shading change as number of bidders changes?

A

Shading falls

70
Q

On the uniform distribution, how much shading do we do?

A

1/N

71
Q

Which gets more revenue - first or second price auction?

A

Same

72
Q

What is the formula for integration by parts?

A

UV - INT(UV’) = INT(U’V)

73
Q

Structure of the advertising market

A

Advertisers bid on ad exchanges, second highest bid is submitted to the ad network, who choose the highest of those bids

74
Q

Is the advertising market ex-post efficient?

A

No, as someone could have a higher value but lose because of their second-highest bid, which they can’t control

75
Q

What did google do that messed up the advertising market?

A

Had both an ad exchange and ad network, and then allowed the exchange a “last look advantage.

76
Q

Result of the google case

A

Anti-trust case ended the second price auctions

77
Q

Stages of solving the differential equation

A

Homogenous problem, varying the constant, verifying the constant (requires the initial)

78
Q

Indirect utility approach

A

Using our type, what is the maximum utility we can get - our willingness to pay to get into the auction

79
Q

Rule from indirect utility

A

Value of higher type is equal to the value of the increased interim probability of winning the auction

80
Q

How to set up indirect utility solution

A

Utility is both equal to the classic description of winning utility, as well as the integral of the marginal probability of winning over price, integrated in the range - set them in a fraction

81
Q

How do we find the Kth highest bid?

A

Order statistics

82
Q

Order statstic expression

A

Probability of k-1 higher, n-(k-1) lower, and binomial multiplier

83
Q

Model - multiple mechanism designer

A

Both designers offer some subset of A, B, C, and then the chooser maximises their equillibrium

84
Q

Result from the multiple mechanism design

A

Using out-of-equillibrium messages can allow us to manipulate the equillibrium

85
Q

Requirements for incentive-compatible direct mechanisms

A

Probability of winning is non-decreasing in type, and utility the utility benefit of the higher type is only based on increased probability of winning

86
Q

Proof of incentive compatibility

A

We must benefit by bidding truthfully - assuming this, setup an inequality and rearrange, find that the probability of winning has to be non decreasing, and the marginal gains of in W are equal to the increased prob of winning.

87
Q

Revenue equivalence theorem

A

If two auctions have the same expected payoff from their lowest valuation, and the same probability of winning ex ante (symetric), then the auctions will have the same expected revenue

88
Q

What is another way of saying expected auction revenue

A

The sum of all the expected transfers of the players - revenue equivalence is maximised by setting U=V

89
Q

What is the difference between utility (U), and forced utility (V),

A

V is unoptimised bidding - in a direct mechanism, they are equivalent

90
Q

Structure of the wind energy subsidy

A

Government loans seabed space, signs contracts to pay the extra “strike price” for a certain amount of energy produced (years), the companies build wind power plants

91
Q

What does the auctioneer choose

A

The “q” value - the interim probability of winning

92
Q

Definition of the symmetric revenue maximising auction

A

Assigns the object to the highest bidder, conditional on the “virtual surplus” being positive

93
Q

Finding on reserve price

A

Any standard auction with a common reserve price is revenue maximising

94
Q

Hetrogenous ex ante

A

Bidders have different probabilities of winning

95
Q

Results of “weak and strong bidding”

A

Weak bidders will bid higher with the same valuation

96
Q

Issue with weak bidders bidding more aggressively?

A

Ex-post inefficiency in first-price: weak bidder can win the item with a lower valuation

97
Q

What gives higher revenue in an asymmetric bidding situation

A

First price gives higher than second price, due to its ex-post inefficiency

98
Q

Second-price auction - asymmetric auction bidding strategies

A

Same as always, bid your type (same outcome as symmetric)

99
Q

Why can auctioneer increase revenue in the asymmetric auction

A

Surplus from weak bidder is higher, so the auctioneer can favour them, forcing the strong bidder to bid harder. This is the first price auction

100
Q

True optimum auction for revenue optimisation - asymmetric

A

Asymmetric reserve prices, due to different virtual surplusses

101
Q

Expression for virtual surplus

A

Theta - (1-F(theta)/f(theta))

102
Q

What is a bidding ring?

A

Collusive agreement between bidders before the actual auction

103
Q

Issue with bidding rings

A

Enforcing commitment to not bid in the final auction

104
Q

Issue with transfers in a bidding ring

A

People may participate with no intention of winning to get the money, also easier to trace

105
Q

The result of no commitment or transfers in the bidding ring

A

Cheap talk, result should be the same as no bidding ring

106
Q

Result about bidding rings with commitment

A

The best utility result is randomising the winner - no one reveals anything about their type, and you are best of randomising

107
Q

Informed-uninformed bidder equilibrium - 2nd price

A

Informed bids type, the uninformed either bids maximum and pays value, or bids nothing and the other person wins

108
Q

What is the winner’s curse?

A

When you win an auction, information about other’s assessment of value is revealed to be lower

109
Q

How do we know that the uninformed bidder randomises?

A

To avoid winner’s curse, if they bid a specific number, they only win when they’re taking a loss in the NE

110
Q

Proof that both bidders have the same range of bids in equillbrium

A

Must have same upper bound, as otherwise the other bidder can reduce max at no cost, must have the same lower bound, as if theta is 0, one with the lower minimum gets a negative payoff, or if their minimum is higher than the other, can benefit by reducing

111
Q

Proof of uninformed bidder having 0 indirect utility

A

Indifferent between all bids (as randomised), and one of those bids is 0 at 0, so all must have 0 indirect utility

112
Q

How does the non-neighbour choose their bid in the oil drilling auction

A

“Makes up” a fictitious oil amount, uses other bidders bidding strategy

113
Q

Distribution of bids in the non-symmetric info case

A

Identical from neighbour and non-neighbour

114
Q

Common values

A

All see a signal, but the valuation is derived from everyone’s signal

115
Q

How do you conceive your bid in a common values setting

A

Value of item subject to your bid, and conditional on everyone else having a lower signal

116
Q

What yields a higher revenue - first or second price auction, in a commons value situation

A

Second price - bidders are less worried about being overly optimistic, as would be insured by the second highest bidders. This leads to more optimistic bidding

Games and Economic Behaviour (1 decks)

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