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Game theory > Definitions lectures 1-11 > Flashcards

Definitions lectures 1-11 Flashcards

1
Q

Strategic interdependence

A

action of one individual or group impact on others, individuals involved are aware of this

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2
Q

Formal study of decision making

A

several players must make choices that potentially affect interests of other players, decision includes the though of how it impacts others

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3
Q

Decision theory vs. Game theory

A

EX1
if everyone pays for their own bill= decision problem
If everyone agrees to split the bill= game problem
EX2
absolute grading system: decision problem to study for self
grading on a curve= this is a game, decision to study impacts others

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4
Q

Best choice/decision to make

A

highest payoff

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5
Q

case studies

A

analyzing situations and learning a recipe of how to play (many different situations, may be able to recognize parallelism)

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6
Q

game theory

A

focuses on general principles to explain why certain outcomes emerge (in a new situation you will recognize which principles to apply)

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7
Q

What is a game?

A

situation where each players actions affect others

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8
Q

Games that do not have strategic interaction

A
  • games of pure chance: lotteries, slot machines
  • games of pure skill: 100m sprint
  • games without strategic interaction bw players: solitaire
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9
Q

Defining the game

A
  1. strategic environment
  2. the rules
  3. the assumptions
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10
Q

Strategic environment (I)

A
  • players= everyone who has an effect on outcomes
  • strategies= actions available to each player + define plan of action for every contingency
  • payoffs= numbers (wins, losses) associated w each outcome + completely reflect interests of other players
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11
Q

The Rules (II)

A
  1. Timing of Moves
  2. Nature of conflict and interaction
  3. Informational conditions
  4. enforceability of agreements
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12
Q

Timing of moves

A

(Part of ‘The rules’ in ‘Defining a game’)

Are moves simultaneous or sequential?

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13
Q

SIMULTANEOUS MOVES

A

players have to figure out what the other is doing right now + you do not need to worry about retaliation

  • analyzed w strategic forms of the game (payoff matrix)
  • retaliation is important to consider: how ppl will react to your action
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14
Q

sequential moves

A

opponent (and/or yourself) reacting to other players (generally known) moves + have to account for future consequences
- analyzed w extensive forms of game trees

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15
Q

Do strategic games involve simultaneous moves or strategic?

A

Many require both!

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16
Q

Nature of Conflict

A

(“rules of game” in “defining a game”

  • interest in conflict? zero sum or constant sum + coordination game
  • will player interact once of many times? one shot games + repeated games
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17
Q

Zero sum (or constant sum)

A

Games where one player’s winning are the others losses

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18
Q

coordination games

A

games w multiple NE

  • players have some common interests
  • players act independently
  • achieve a jointly preferred outcme
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19
Q

one shot games

A

play of the game occurs once– players don’t need to worry about retaliation + also can’t build up reputation or trust

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20
Q

repeated games

A

play of the game is repeated w same players + can build up reputations for toughness + can coordinate
*game can be zero-sum in short run but mutually beneficial in the long run

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21
Q

Informational conditions

A

(“rules of game” in ‘defining a game’)

- are some players better informed?

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22
Q

perfect information

A

if they know what has happened every time decision is made – no external uncertainty or strategic uncertainty

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23
Q

imperfect information

A

when one player knows more than the other

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24
Q

Enforceability of agreements

A

(‘rules of game’ in ‘defining a game’)

- can contracts be enforced (cooperative games)

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25
Q

cooperate games

A

games in which agreements are enforceable

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26
Q

non-cooperative games

A

games in which agreements are non-enforceable

** to understand how to reach cooperative outcome, first understand non-cooperative

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27
Q

The Assumptions (III)

A
  • rationality

- common knowledge

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28
Q

Rationality (subset of assumptions)

A
  • players understand aim to maximize own payoffs

- players flawless in calculating which actions will max. own payoff

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29
Q

common knowledge (subset of assumptions)

A
  • each player knows rules of games
  • knows each player knows the rules
  • continues
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30
Q

Equilibrium concept

A

each player is using the strategy that is best response to strategies of other players
- likely outcome of game when rational strategic agents interact

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31
Q

equilibrium does not mean…

A
  • that things don’t change over time (parameters of model can change)
  • that everything is for the best (doesn’t mean every outcome of game is best)
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32
Q

payoff matrix (normal-form game)

A

table where strategies of one player are listen in rows and those of other players in columns
- helps determine dominant strategy and nash equilibrium if they exist

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33
Q

row

A

horizontal

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34
Q

column

A

vertical

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35
Q

Nash equilibrium

A

a pair of strategy choices (one for each player) that are ‘best responses to each others play’

    • best response given highest payoff of what opponent has chosen
  • no incentive to deviate
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36
Q

Ways to find nash equil.

A
  1. cell by cell inspection

2. Dominant strate

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37
Q

Not nash equilibrium if…

A

one of players would like to deviate

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38
Q

incentive to deviate

A

only if you will get something higher for a different choice

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39
Q

Golden Balls Game

A

more than one nash equilibrium

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40
Q

interpretations of Nash equilibrium

A
  • no regret= no player regrets choice after observing other player
  • self-enforcing agreement= both agree on NE strategy profile
  • viable recommendations=
  • transparency of reasons= if players rational, can duplicate strategy
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41
Q

Dominant strategy

A

best strategy for a player no matter what opposing players do
- always play dominant strategy bc expect opponent will use their dominant

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42
Q

strongly dominant strategy

A

no matter what rival does it always does strictly better than other available strategies
*only one strongly dominant strategy

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43
Q

weakly dominant strategy

A

no matter what rival does, it does equally well and sometimes strictly better than other available strategies

  • can have more than one weakly dominant strategy
  • never eliminate bc u can lose a NE
44
Q

dominant strategy equilibrium

A

if both players have dominant strategy, then we have a dominant strategy equilibrium

  • strongly DS: combination of only SDS
  • weakly DS: combination of dominant strategies some weak some not
45
Q

Symmetric games

A

if you have something happen to one player, will happen to other player
- if P1 has weakly dominant strategy one way, P2 will have it the same way

46
Q

Strongly or weakly dominated

A

no dominant strategy equilibrium= remove outcome that gives lowest payoff– reduces size of game

47
Q

iterated dominance equilibrium/elimination

A

an equil. found by removing strongly or weakly dominated strategies until one pair of strategies remains– game is dominance solvable
- careful when deleting weakly dominated strategies

48
Q

Best response analysis

A
  • nash equilibrium and best response means that it yields the player the highest payoff given what opponent has chosen
  • finds all possible NE of a game
49
Q

Nash equilibrium strategy

A

if game is repeated and played by ‘populations’ observations of experiences over time make new players find the nash equilibrium

50
Q

Beliefs (w complete information)

A

each players does not know actual choices of others but has beliefs about other players’ actions, as games played beliefs are updated

51
Q

complete information

A

players know payoffs of other players

52
Q

best response dynamics

A

both players play best response strategies to each other and believe the opponent will play that strategy

53
Q

Nash equilibrium: set of strategies

A
  • each player has correct beliefs about strategies of other

- strategy of each player is best response given beliefs about strategies of others

54
Q

pure coordination games

A

some games have more than one equilibrium

55
Q

No nash equilibrium in pure strategy

A

sometimes best response analysis finds not equil. = no equil in pure strategy, but could have equil. in mixed strategy
EX/ tennis match as simultaneous move

56
Q

pareto efficiency

A

an outcome if it is not possible to improve the payoff of one player without lowering payoff of the other
- one solution is the most efficient way

57
Q

Pareto domination/ pareto superior

A

an outcome pareto dominates or is pareto superior to another if payoffs of one of more players are higher and none is lower

58
Q

Types of simultaneous games

A
  • pure coordination game
  • assurance game
  • battle of the sexes
  • chicken games
59
Q

pure coordination game

A
  • payoffs of NE are better than other payoffs
  • payoffs of each player are same in all NE
  • *coordination is needed but only to ensure avoidance of non-equil.
60
Q

Assurance game

A

both players have higher preference/ higher payoffs for one option= focal point
-coordination is needed to avoid non-equil + to achieve jointly preferred outcome

61
Q

constant sum game

A

one where sum of payoff for any combination of strategies is equal to constant
– conflict of interest among players (higher payoff for one player means lower for other)

62
Q

zero sum game (type of constant sum game)

A

if sum of payoffs for any combo of strategies is = to zero

63
Q

convergence of expectations

A

situation where players in non-cooperative game can develop common understanding of strategies they expect will be chosen

64
Q

focal point equilibrium

A

configuration of strategies for players in a game, emerges as outcome bc of convergence of players expectations on it
- equilibrium where players expectations converge

65
Q

Battle of the sexes games

A
  • players prefer different equilibrium= conflict of preferences
  • highest risk of coordination failure
66
Q

chicken games

A
  • each player has one strategy that is ‘tough’ and one ‘weak’
  • two-pure strategy NE: one weak one strong
  • each player prefers equil. where other player is weak
  • most liekly outcome= non-equil.
  • conflict of interest
67
Q

Prisoners Dilemma Game

A
  1. each player has two strategies: to cooperate or to defect from cooperation
  2. each player has a dominant strategy
  3. dominant strategy equil is worse for both players than non-equil.
67
Q

Prisoners Dilemma Game

A
  1. each player has two strategies: to cooperate or to defect from cooperation
  2. each player has a dominant strategy
  3. dominant strategy equil is worse for both players than non-equil.
68
Q

externalities: tragedy of the commons

A

overexploitation of free resources

- when individuals neglect the wellbeing of society in the pursuit of personal gain

69
Q

Fiscal Battles

A

multinational decides where to locate based on taxation: want to locate where taxation is lower

70
Q

SEQUENTIAL MOVES

A

ex/ matchsticks

  • players take turns and perfect info implies that players known everything
    • strategic thinking
71
Q

backward induction

A

look forward and reason back

72
Q

representing sequential games

A

who, what, how much

- use game theory or extensive form

73
Q

game tree/extensive form

A

representation of a game in form of nodes, branches, w associated payoffs

74
Q

node

A

point from which branches emerge, or where branch terminates in a decision tree

  • initial node or root of game
  • action node
  • terminal node
75
Q

branch

A

each branch emerging from node in a game tree represent one action that can be taken at that node

76
Q

Strategies vs. moves

A
  • move= single action taken by player at a node

- strategy= complete contingent plan of moves– defines actions at all posible nodes where players could play

77
Q

subgame

A

smaller game embedded in complete game

  • game that develops from all nodes after node 1
  • full game is a subgame of game
78
Q

Path of play and outcome

A

how the game goes and what the payoffs of players are

79
Q

equilibrium found from backward induction

A

subgame perfect nash equilibrium

80
Q

subgame perfect nash equil

A

is combo of strategies that yield NE in every subgame

  • *a sequential game can have more than one SPNE
  • actions that are not sequentially rational are eliminated
81
Q

zermelos theorem

A

in finite, two-player ‘win-lose-draw’ games of perfect info. players can either
- one player has strategy that gurantees a win or both players have a strategy that guarantees draw
(ex/ tic-tac-toe or chess)

82
Q

subgame emphasizes what?

A

that in every subgame, even those that are not being played, players still have to act rationally

83
Q

All SPNE are NE, BUT…

A

not all NE survive backward induction

84
Q

First mover advantage

A

first mover is leader
- player who is leader is not worse off
*leader had ability to commit to advantageous position than P2 has to adapt to it
(ex/ of two firms investing)

85
Q

second-mover advantage

A

second mover has flexibility to dapt to others choices to achieve better outcome (Ex/ when firms are choosing prices and tennis game ex)
*reacting optimally

86
Q

both players have advantage

A

both can do better under one set of rules of play than under another (ex/ IR and ECB–if IR moves first this will result in better outcomes for both players than those of others*whats more beneficial to IR is more beneficial for ECB)

87
Q

both players have advantage

A

both can do better under one set of rules of play than under another (ex/ IR and ECB–if IR moves first this will result in better outcomes for both players than those of others*whats more beneficial to IR is more beneficial for ECB)

88
Q

when will dominant-strategy equilibrium hold in both sim and seq games?

A

when both players have a dominant strategy

89
Q

no change in outcome advantage

A

some games have same outcome in both types regardless of order of moves
- normally when both players have a dominant strategy, equil doesnt change– prisoners dilemma games

90
Q

TWO STAGE GAMES

A

w both simultaneous and sequential games (uses matrices and game trees)
*use backwards induction to solve for first stage

91
Q

pure strategies/ mixed strategy equilibrium

A

each player needs to keep other guessing, act randomly or unsystematically, uncertain

92
Q

mixed strategy

A

random mixture among pure strategies

  • assigns to each action a likelihood/probability of being selected
  • induces lottery over possible outcomes of games
93
Q

expected payoff

A

corresponding probabiity-weighted averages of payoffs from constituent pure strategies

94
Q

NE in mixed strategies

A

list of mixed strategies, one for each player, such that choice of each is best choice=highest expected payoff, given mixed strategies of other players

95
Q

mixed strategy NE in zero-sum or constant-sum games

A
  • mixing is better than playing pure strategy
96
Q

constant sum games

A

sum of players’ payoffs is constant, same for all their strategy combinations

97
Q

opponents indifferent property

A

players needs to find a mixed strategy that other player cannot exploit, so the other player is indifferent bw moves

98
Q

which pure strategy should be played?

A

opponent indifferent between her own strategies

99
Q

if indifferent bw two possibilities

A

you can randomize

100
Q

best mixed strategy

A

one that makes opponent indifferent between his own pure strategies

101
Q

In Harry Sally game (game of sexes), which equilibrium is the best and why?

A

pure strategies equil is higher than mixed strategy BC mixed strategy gives confusion,randomizes on where you are going to go and both players want to end up in same place

102
Q

chicken game mix or pure?

A

there is an advantage for players to mix, pure strategies isnt best response for sure

103
Q

Beliefs and Responses

A

each player forms beleifs about probabiity of mixture that other is choosing and chooses best response to those

104
Q

NE occurs in mixed strategies when…

A

the beliefs are correct

105
Q

difference bw being uncertain and having incorrect beliefs

A
  • incorrect beliefs can be updates

Game theory (3 decks)

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