Game Test

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    PD game
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    Rock Paper Scissors
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    Stag Hunt
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    • If mixed strategy is needed then solve for p and q
    • p = (d-c)/[(a+d)-(b+c)]
    • q = (d-b)/[(a+d)-(b+c)]
  7. What is a Game of chance? What is an example of such a game? What about in real life?
    • Game of chance: introduction of player called chance, who makes choices using a randomizing device
    • 2+ players
    • 1+ moves with players being allowed to choos
    • outcome is determined by rules and move
    • e.g. poker, gin rummy, bridge
    • peace talks are best treated like game of chance → outcomes can rely on unpredictable variables like storms, supply lines cut, etc.
  8. What is an Information Set?
    Information Set: for particular player, all the possible moves that could have taken place in the game so far given what that player has observed.
  9. What is  the difference between Perfect vs. Imperfect Information? Give examples of each.
    • Perfect Information: every information set contains only one member. i.e. the point actually reached at that stage of the game. e.g. Chess, Checkers, tic-tac-toe
    • Imperfect Information: players with perfect memories cannot know the history of the play before their move. e.g. Monopoly(because of “chance” & “community chest” card), RPS, Card Games where each player’s cards are hidden.   
  10. What assumptions does game theory makes about utility functions?
    • Chance’s role absorbs into outcomes
    • Each player is assumed to have a utility function for outcomes that abide by expected utility theorem
    • the utility of an outcome that happens to be a lottery is equal to its expected utility
    • outcomes, if lotteries or certainties, can be represented by utility numbe
  11. What assumptions does game theory makes about what players know?
    each player knows game table and all other players utilities for the outcome
  12. What assumptions does game theory make about how the players play the game?
    given a choice of strategies by his opponents, each player will choose those strategies that maximize his expected utility
  13. What defines a strict two-person (zero-sum) game?
    • Zero-Sum game: utility function for Col is the negative of that for Row, because Col and Row have strictly opposing preferences
    • if u(A) is row’s utility for outcome of A. Then, Col’s utility for A is -u(A).
    • utilities sum to 0
  14. What is Equilibrium in a game?
    • Equilibrium: neither player can do better by unilaterally changing strategy.
    • n.b. payoff associated with equilibrium  is called equilibrium value
  15. What is the Minimax test for zero sum games?
    • zero-sum payoffs for a pair of strategies in equilibrium if:
    • minimal value of its row
    • maximal value of its column
  16. What is the structure for Rock(RO), Paper(PA), Scissors(SC) (RPS)? How do you solve this game?
    • No pair strategies in equilibrium. i.e. cannot guarantee draw
    • Solution: mixed strategy ( ⅓ SC, ⅓ PA, ⅓ RO) → guarantee utility of 0 even if opponent also plays with same distribution
    • defuse opponent's  power to read your mind
    • useful in war when guessing plays of other side is feasible through means of spies
  17.  What is the Rollback argument?
    • Iterated game: 2 cases
    • (i)know the finite number of iterations
    • (ii)unknown (indefinite) number of iterations
    • Rollback argument: says always defect!
  18. Chicken Game:
    while each player prefers not to yield to the other, the worst possible outcome occurs when both players do not yield
  19. What is a Stag Hunt?
    Stag Hunt: Conflict between safety and social cooperation
  20. Hawk-Dove game
    a situation in which there is a competition for a shared resource and the contestants can choose either conciliation or conflict
  21. How do you solve a zero sum game?
    • (i) check if any act is dominated by another for Row and Col
    • (ii) Run a minimax equilibrium test to see if there are any strategies in equilibrium
    • minimum in its row
    • maximum in its column
    • If mixed strategy is needed then solve for p and q
    • p = (d-c)/[(a+d)-(b+c)]
    • q = (d-b)/[(a+d)-(b+c)]
  22. What is meant by Guthier’s notion of Constrained Maximization?
    • straightforward  maximizer: always defect. i.e. agent  who seeks to maximize utility given the strategies of those he is interacting with  (n.b. fool accepts this rationality)  
    • constrained maximizer: cooperate with other constrained maximizers but defect with straightforward maximizeri.e. disposition to base actions on a joint strategy, without considering if  individual strategy would yield greater utility
  23. How does Guthier try to argue that it is rational to cooperate in P.D.-games?
    • Central Idea: decide before the P.D. if you are going to become a cheater or cooperator. (think of cheater and cooperator as personality types)
    • Short Answer: if it's rational to be moral depends what your chances are that you will be able to exploit or cooperate
  24. What are Axelrod’s collectively stable strategies?
    • All Defect (if invasion is does not occur in clusters), Tit for Tat, and other ‘nice’ strategies that are provocable.
    • ‘nice’ strategy: will cooperate in iterated PD-game however punish those who defect by only defecting after other player defects  
  25. What is an evolutionary stable strategy?
    • Collectively Stable Strategy: A is collectively stable if no other strategy can invade it. i.e. do better than A by employing their strategy
    • B is secure from A’s invasion if:
    • V(A|B) ≤ V(B|B) (n.b. A can invade B if the negation of this is true)
    • If A enters with  clustering: pV(A|A)+(1-p)V(A|B)≤V(B|B)where p is proportions of interactions by player using A with  another player
  26. What is the tit-for-tat strategy?
    An agent using this strategy will first cooperate, then subsequently replicate an opponent's previous action.
  27. computer tournament information
    • tit-for-tat wins
    • if asked this question, you can show what happens when Tit-for-tat plays themselves a lot compared to All Defect.
  28. pareto optimality
     An outcome of a game is Pareto optimal if there is no other outcome that makes every player at least as well off and at least one player strictly better off.
  29. What is fisher’s sex ratio argument?  What does skyrms thinks it has to do with evolution of justice?
    Inherited tendency to produce male or female can affect expected number of grandchildren.Suppose there is more females:Than, males would have more children on average than females and would contribute more genes to the next generationAn individual who carried tendency to produce more males would have higher expected number of grandchildren than population average and this tendency would spread through population.Same reasoning goes if we switch male and female roleThere is an evolutionary feedback that tends to stabilize at equal proportions of males and femalesWhat sex-ratio propensity is optimal for individuals depends on what sex-ratio propensities are used by the other members of the populationtendency to produce mostly males → high fitness in population with  mostly females but low fitness in population with mostly malesTendency to produce both sexes in equal numbers is an equilibrium in the sense that it is optimal relative to a population where everyone has itWe can think of production of males and females as a strategy
Card Set:
Game Test

Game Theory
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