Week 3 - Game Theory - The basics Flashcards Preview

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Flashcards in Week 3 - Game Theory - The basics Deck (15)
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1
Q

What are the 4 different games with different levels of information?

A
  1. Static games of complete information
  2. Dynamic games of complete information
  3. Static games of incomplete information
  4. Dynamic games of incomplete information
2
Q

What are the 5 rules every game is played by?

A
  1. Who is playing (which players)
  2. What they are playing with (alternative actions or choices)
  3. When each player gets to play (or in what order)
  4. How much they stand to gain
  5. What each player knows when they act
3
Q

What are the Cartesian products of 2 sets?

A

The Cartesian product of 2 sets AXB is the set of all possible ordered pairs

4
Q

What are the 4 essential concepts of game theory?

A
  1. Best Response
  2. Dominance
  3. Nash Equilibrium
  4. Pareto efficiency
5
Q

What is the definition of the best response concept?

A

The best response is the strategy or strategies which produce the most favorable outcome for a given player, taking as given the strategies of other players.

6
Q

What is a dominance strategy and a dominated strategy?

A
  • Dominance occurs when one strategy is better than another regardless of the other player’s strategies.
  • A dominated strategy is one in which you are better off not playing at all because you will be worse off and would not rather play.
7
Q

What is the Nash equilibrium?

A
  • A Nash equilibrium occurs when a player is best responding given the actions of the other players
8
Q

What is a pure strategy and a mixed strategy?

A
  • Pure strategy is a strategy you play with 100% certainty e.g confess
  • Mixed strategy is when you are randomized across several pure strategies e.g playing confess with 50% and not confess with 50%
9
Q

Explain the rock paper scissors game in terms of best response, dominant strategy, and Nash equilibrium

A
  • No unique best response as it all depends on the other person
  • No dominant strategy as we don’t know what the other person picks which could make whatever we potentially pick bad.
  • No Nash equilibrium, because there is no unique best response so individuals cannot choose a strategy in which they are best responding
10
Q

Define Pareto Efficiency

A
  • An outcome is said to be Pareto efficient if its impossible to so that one person is better off and the others are no worse off
  • Therefore Pareto efficiency is the point where changing one thing will make someone else happier and the others less happy.
11
Q

In a prisoners dilemma explain which is the dominated strategy and if there is a Pareto efficiency

A
  • Imagine Player X → and player y downwards. With confess first then not confess
  • Confess is a dominant strategy for Y as whatever X picks the best response for Y would confess. For example, if X picks confess the best option is confess, and if X picks not confess the best option is confess.
  • Y not confessing and X confessing 1,-2, is Pareto efficient as moving from this point will make someone better off but at the same time someone worse off.
12
Q

What is the Nash equilibrium for mixed strategies?

A
  • Let J denote the number of pure strategies in S1, and let K denote the number in S2.
  • We have S1 = {s11,…….s1} and S2 = {s21,…..,s2k]
  • If player 1 believes that player 2 will play the strategies {S21,….,S2K} with probabilities (P21,…..,P2K) then players 1’s expected pay off from playing the pure strategy s1j is: Sum(k=1,K) P2kU1(s1j,s2k)
13
Q

What is the expected Pay off to player 1 for playing the mixed strategy p1=(p11,…,p1j)?

A

V1(p1,p2) = Sum (J,j=1) P1j [ Sum (K,K=1) p2kU1(s1j,s2k)]

14
Q

If player 2 believes that player 1 plays the strategies {s11,….,s1j} with probabilities (p11,…,p1j) the expected Pay off to player 2 is from playing the mixed strategy is (p2,1…..,p2k) is?

A

v2(P1,P2) = Sum (K,k=1) p2k [Sum J(j=1) p1ju2(s1j,s2k)]

15
Q

Define the Nash equilibrium with mixed strategies.

A
  • In a 2 player normal-form game, the mixed strategies (p1,p2) are a Nash equilibrium if each player’s mixed strategy is the best response to the other player’s mixed strategy. The 2 conditions below must hold
  • V1(P1,P2) ≥ V1(P1,P*1)
  • V2(P1,P2)≥V2(P*1,P2)