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Game Theory Exam Two
ECN 416 Exam Two
| Question | Answer |
|---|---|
| two types of sequential games | Extensive Form Games and Repeated Games |
| Extensive Form Games have three components | 1. Game Tree 2. Information Structure 3. Payoffs (Utility Functions) |
| A non-terminal node is called | decision node |
| At ___________, the player associated with the node chooses a branch | each decision node |
| consists of a finite set of branches connecting two points (or nodes). | The game tree |
| The leftmost node is the ____________ and represents the beginning of the game | initial node |
| The rightmost nodes are the __________ and represent possible endings of the game. | terminal nodes |
| initial node is also called _______ | the root |
| A path from the root (initial node) to a terminal node is known as | a path of play |
| An information set for a player is ___________ | a set of nodes that cannot be distinguished for that player |
| If no information set contains more than one node then the game is said to be of _________ | perfect information |
| Information Structure is also known as _________ | An information set |
| A ______________ for a player in an extensive form game is a rule that tells the player which choice to make depending on which information set the player is at. | strategy |
| Sequential games have a __________ order | definite |
| Is there an advantage for a player that moves earlier in the order than the others? We refer to this concept as _________ | First Mover Advantage |
| Is there always a first mover advantage in a game? | It greatly depends on the structure of the game in question. |
| The pure strategy set for each player in a game with perfect information is ______________ the pure strategy sets for those players in a game with imperfect information that is identical in all other aspects. | larger than or equal to |
| singular decision node is not equal to information set | OK |
| If two games are identical except that one is of perfect information and the other is not, what must be different? | information structure |
| A ___________ is a Nash Equilibrium where __________ players choose a strategy that strictly dominates all other strategies for that player. | Strictly Dominant Nash Equilibrium; all |
| A ___________ is a Nash Equilibrium where _________ players choose a strategy that weakly dominates all other strategies for that player. | Weakly Dominant Nash Equilibrium; each |
| A process of __________ strategies always terminates in the same residual game | sequential elimination of strictly dominated |
| If the process terminates with one pure strategy left for each player then the corresponding outcome is the ____________ Pure Nash Equilibrium (PNE) of the game. | unique, and only in sequential elimination of strictly dominated strategies |
| When the process terminates, all Nash Equilibria of the residual game are Nash Equilibria of the original game and _____________ | vice versa, and only in sequential elimination of strictly dominated strategies |
| The three facts listed above ______________ hold if at any stage of the process we use weak dominance elimination instead of strict dominance elimination. | do not |
| Nash Equilibria of the original game are Nash Equilibria of the residual game, when the process terminates, only in _________ | sequential elimination of strictly dominated strategies |
| An infinite number of MNE can be found in _________ game | sequential elimination of weakly dominated strategies |
| In weakly dominated games, all Nash Equilibria of the residual game are ___________ Nash Equilibria of the original game | the subset |
| every decision node is _______ a subroot of the game | not; only in games with perfect information, |
| In games with perfect or imperfect information, initial node is also a _________ of the game. | subroot |
| a subgame must also be a game, it must have a __________ | unique initial node and contain all information sets |
| A strictly dominant Pure Strategy Nash Equilibrium (PNE) in a game ___________ always be Strongly Pareto Optimal (SPO). | will not |
| In finitely repeated game, usually (but not always), the stage game is _____ game | a normal-form |
| In finitely repeated game, each occurrence of G is called | an iteration or a round. |
| In finitely repeated game, the game consisting of all iterations or rounds is called ________ | the supergame |
| In finitely repeated game, usually each agent knows what all the agents did in the previous iterations, but not what they’re doing in the current iteration. We call this __________ | an imperfect-information game with perfect recall |
| In finitely repeated game, usually each agent’s payoff function is __________ | additive. |
| In finitely repeated game, one iteration or round of a game is played multiple times by the same set of agents is called ______ | the stage game (game G) |
| In prisoner's dilemma, they could make _________ if they could learn to cooperate | a Pareto Optimal Improvement |
| It is ________ to assume that the outcome of a repeated game with the same players and strategies will simply be a repetition of the one-shot static game. | not correct |
| In which game are players more likely to cooperate? | The infinite game |
| If the number of iterations is finite and known, we can use ______ to get a subgame perfect equilibrium. | backward induction |
| always cooperate | The Dove |
| always defect | The Hawk |
| cooperate until the other player defects, then always defect | Grim Trigger Strategy |
| cooperate on the first move. On the nth move, repeat the other agent’s (n–1)th move | Tit-for-Tat |
| defect on move 1. If the other agent retaliates, play TFT. Otherwise, randomly intersperse cooperation and defection | Tester |
| In infinitely repeated game, if the discount rate (r) is not too high, then Player One and Player Two are willing to adopt ___________ and it is _______________ of the repeated Prisoner’s dilemma. | the Grim Trigger Strategy; a subgame perfect Nash Equilibrium |
| if we have finitely many repetitions of the Prisoner’s Dilemma, the subgame perfect PNE is _________ on every round. | (Talk,Talk) |
| the strategy space of the repeated game is _______ than a repetition of the one-shot static game. | much larger |
| In the infinitely repeated Prisoners' Dilemma game Grim Trigger vs. Grim Trigger can yield a result in which two players always ___________ | cooperate |
| T/F, In laboratory experiments the Centipede game always yields the expected result of defection in the first round. | False |
| the discount rate _______ of the players | has impact to the decisions |
| Perfect recall ___________ in a repeated game. | is normally assumed |
| __________________ always exist in finite sequential games of perfect information. | Pure Strategy Subgame Perfect Nash Equilibria |
| If we want subgame perfect | no non-credible (incredible) threat |
| the unique initial node, we call this a ______ of the initial game | subroot |
| A Nash Equilibrium is _____ if on every game its _____ is a Nash Equilibrium. | subgame perfect; restriction |
| game is a new subgame started after every move | chess, checkers, tic-tac-toe |
| which of the following games could you describe to me the subgame perfect strategy | tic-tac-toe |
| In golden ball, steal is a __________ | weekly dominant strategy |
| In prisoner's dilemma, ______ is a strictly dominant strategy | Talk |
| Is every node of a chess game a subroot for a subgame? | Yes |
| Subgame is the _______ of initial game | subroot |
| Subgame is subgame perfect when ___________ | the outcome is Nash equilibrium |
| subgame perfect means | ignore the opponent's action, I will still play the right strategy |
| What game is not subgame perfect? | The cookie game |
| The movie Circle is an example of | backward induction |
| Characteristic of finitely repeated game one | each occurrence of G is called an iteration or a round; the game consisting of all iterations or rounds is called the supergame one iteration or round of a game is played multiple times by the same set of agents is called the stage game (game G) |
| Characteristic of finitely repeated game two | usually each agent knows what all the agents did in the previous iterations, but not what they’re doing in the current iteration. We call this an imperfect-information game with perfect recall; usually each agent’s payoff function is additive |
| Characteristic of finitely repeated game three | Pure Strategy Subgame Perfect Nash Equilibria exist in perfect information; use backward induction to find subgame perfect equilibrium |
| look all possible outcomes and find a way to get to the optimal one | backward induction |
| Subgames must fully contain all information sets and start at an initial node (subroot). | OK |
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