Term 2 Week 6: Introduction to Game Theory and Nash Equilibrium Flashcards

1
Q

What is the difference between a strategic and non-strategic action (2)

A

-A strategic action is one where other peoples actions impact you (an auction)
-A non strategic action is one where other peoples actions don’t impact you (what to buy at a supermarket)

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2
Q

What must we define for game theory (3)

A

-Parties with decisions to make (Players = N)
-Different choices to make (Actions, Ai)
-Outcomes for each combination of choices (Payoffs, π:A1 x A2)

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3
Q

What does a payoff matrix look like (3)

A

-You have a table with Player 1’s actions on the rows, Player 2’s actions on the columns
-Within the table, each square represents the payoffs for the 2 players
-The number on the left represents the row players payoff, the player on the right represents the column players payoff

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4
Q

What are the 3 problems for players in game theory, and the assumption made about payoffs (3,1)

A

Players must:
-Understand the game
-Form expectations on what the other placer will do
-Find the best response to what you anticipate the other players doing

-It is assumed payoffs must encode everything (long run, risk appetite) the players care about, and thus players are modelled to maximise their payoff

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5
Q

What is a solution concept (1,2)

A

-A solution concept narrows down the set of outcomes to reasonable ones

-A solution concept is a way to make better predictions about how people will play (positive)
-A solution concept is a way to give better advice about how to play the game (normative)

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6
Q

what is a best response (4)

A

-An action a(i) is a best response if it yields the highest payoff, given the opponents action profile a(-i)
-Formally, a(I) is a best response to profile a(-i) if: a(I) = arg max π(a(I), a(-i))
-To form a best response, players must predict what other players do, and decide what their best action is in response
-This is the basis behind Nash Equilibrium

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7
Q

What is a dominant strategy + example (4,2)

A

-If there is an action which is always the best response, this is the dominant strategy
-This is strongly dominant if its always the best (π(a(I), a(j)) > π(a’(i), a(j)) for all a(j))
-This is weakly dominant if it is the best response for at least one profile, and at least the same for the others (π(a(I), a(j)) ≥ π(a’(i), a(j)) for all a(j), (π(a(I), a(j)) > π(a’(i), a(j)) for some a(j))
-With dominant strategies, we can also say what not to pick, and a’ is dominated if it always gives a lower payoff for any a(j)

-Imagine the prisoners dilemma (Confess vs Quiet), where (C,C) = 1,1, (C,Q) = 10, 0, (Q,C) = 0, 10, (Q,Q) = 5,5
-The dominant strategy is to confess, no matter what (look at if row player C or Q then col players best choice)

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8
Q

What is the Iterated Elimination of Dominated Strategies (2,2,4)

A

-With multiple options, you can have a dominated strategy w/o a dominant one
-You could then assume players should never expect others to play dominated strategies, or even never ones which are never best responses

-Repeatedly removing all dominated actions to see which remain is called IEDS
-After this process we are left with rationalizable strategies

-Imagine a 3x3 payoff matrix where 2 students can put no effort, some effort or high effort into a test
-(N,N) = 0,0, (N,S) = -100, 300, (N,H) = -100, 150, (S,N) = 300, -100, (S,S) = 100,100, (S,H) = -50, 150, (H,N) = 150, -100, (H,S) = 150, -50, (H,H) = 50,50
-In this case you can eliminate No Effort as a strategy, as it is dominated
-Even if you changed (S,N) to 300, 0 so that it was no longer dominant, it is still not rationalizable as it is never the best outcome

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9
Q

Do rationalizable outcomes have to be rational (2)

A

-Rationalizable outcomes include those where players miscoordinate (both go or stop at a stop light)
-Players select the best response to the expected action, but not the actual action, and they’d want to go back and change their strategies

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10
Q

What is Nash Equilibrium (2)

A

-An action profile is a Nash Equilibrium if all players are playing best responses
-Formally, a profile (a(I), a(-i) is a Nash equilibrium if a(I) ε arg max π(a(i), a(-i)) for all i ε N

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11
Q

What are the 3 different interpretations of Nash Equilibrium (3,1)

A

-One way to think of Nash Equilibrium is a self-enforcing outcome, where no individual has an incentive to change their actions
-Another way of interpreting Nash Equilibrium is the resting point of a dynamic process of adjustment, where we update our best response over time in trial and error fashion
-A third way of interpreting Nash equilibrium is as an outcome arrived at by rational introspection, with other outcomes being hard to justify if all players are rational

-Interpretations 2 and 3 don’t apply to all games, only ones with dominated strategies (imagine rock paper scissors)

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12
Q

Why should peoples beliefs be correct, and why is this important for Nash Equilibrium (3,1)

A

Peoples beliefs should be correct since:
-Expectations get updated over time
-Players will have reputations to take certain actions
-Tacit coordination (focal points)

-It is important for peoples beliefs to be important, as players best responding to these beliefs thus means Nash Equilibria are stable

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13
Q

How do we solve games with multiple pure strategy nash equilibria (1,3)

A

-Games with multiple NE present a problem, as we don’t know which one will actually happen, and people could get stuck in bad equilibria

We can solve this via:
-Mediation (have a third party control the game)
-Conventions (unspoken/spoken rules)
-Focal points (out of many NE which will happen naturally)

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14
Q

What is Thomas Schnelling’s idea of focal points (2,1)

A

-Thomas Schnelling’s idea of focal points suggest that some NE are more natural than others
-They are culturally more salient/focal than others, and crucially this must be common knowledge

-This is different from conventions, that are rules/norms that evolve over time

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15
Q
A
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