Key Terms

Question 1

continuation

Answer 1

the continuation of a strategy from a (noninitial) node is the remaining part of the plan of action of that strategy, applicable to the subgame that starts at this node

Question 2

credibility

Answer 2

a strategy is credible if its continuation at all nodes, on or off the equilibrium path, is optimal for the subgame that starts at that node

Question 3

information set

Answer 3

a set of nodes among which a player is unable to distinguish when taking an action. Thus his strategies are restricted by the condition that he should choose the same action at all points of an information set. for this, it is essential that all the nodes in an information set have the same player designated to act, with the same number and similarly labeled branches.

Question 4

irreversible

Answer 4

cannot be undone by a later action. in a sequential move game, the first mover’s action must be irreversible and observable before the second mover’s action is irreversible

Question 5

observable

Answer 5

known to other players before they make their responding actions. together with irreversibility, this is an important condition for a game to be sequential-move

Question 6

off-equilibrium path

Answer 6

a path of play that does not result from the players’ choices of strategies in a subgame perfect equilibrium

Question 7

off-equilibrium subgame

Answer 7

a subgame starting at a node that does not lie on the equilibrium path of play

Question 8

subgame

Answer 8

a game comprising a portion or remnant of a larger game, starting at a noninitial node of the larger game

Question 9

subgame-perfect equilibrium (SPE)

Answer 9

a configuration of strategies (complete plans of action) such that their continuation in any subgame remains optimal (part of backward induction), whether that subgame is on- or off-equilibrium. this ensures credibility of all strategies

Question 10

strategic order

Answer 10

the order of moves from a game theoretic point of view, determined by considerations of observability and irreversibility. it may differ from the chronological order of actions and, in turn, determine whether the game has sequential or simultaneous moves

Question 10

best response curve

Answer 10

a graph showing the best strategy of one player as a function of the strategies of the other player(s) over the entire range of those strategies

Question 11

best response rule

Answer 11

a function expressing the strategy that is optimal for one player, for each of the strategy combinations actually played by the other players or the belief of this player about the other players

Question 12

continuous strategy

Answer 12

a choice over a continuous range of real numbers available to a player

Question 13

never a best response

Answer 13

a strategy that is never a best response for a player if, for each list of strategies that the other players choose (or for each list of strategies that this player believes the others are choosing), some other strategy is this player’s best response.

Question 14

quantal response equilibrium (QRE)

Answer 14

solution concept that allows for the possibility that players make errors, with the probability of a given error smaller for more costly mistakes

Question 15

rationalizability

Answer 15

a solution concept to a game. a list of strategies, one for each player, is a rationalizable outcome of the game if each strategy in the list is rationalizable for the player choosing it

Question 16

rationalizable

Answer 16

a strategy is called rationalizable for a player if it is his optimal choice given some belief about what (pure or mixed strategy) the other player(s) would choose, provided this belief is formed recognizing that the other players are making similar calculations and forming beliefs in the same way

Question 17

refinement

Answer 17

a restriction that narrows down possible outcomes when multiple nash equilibria exist

Question 18

assurance game

Answer 18

a game where each player has two strategies, say, cooperate and not, such that the best response of each is to cooperate if the other cooperates, not if not, and the outcome from (cooperate, cooperate) is better for both than the outcome (not, not).

Question 19

battle of the sexes

Answer 19

a game where each player has two strategies, say Hard and Soft, such that [1] (Hard, Soft) and (Soft, Hard) are both Nash equilibria, [2] of the two Nash Equilibria, each player prefers the outcome where he is hard and the other is soft, and [3] both prefer the Nash equilibria to the other two possibilities, (hard, Hard) and (Soft, Soft)

Question 20

belief

Answer 20

the notion held by one player about the strategy choices of the other players and used when choosing his own optimal strategy

Question 21

best response

Answer 21

the strategy that is optimal for one player, given the strategies actually played by the other players, or the belief of this player about the other player’s strategy choices

Question 22

best response analysis

Answer 22

finding the nash equilibrium of a game by calculating the best response functions or curves of each player and solving them simultaneously for the strategies of all the players

Question 23

chicken

Answer 23

a game where each player has two strategies, say Tough and Weak, such that [1] both (Tough, Weak) and (Weak, Tough) are Nash equilibria, [2] of the two , each prefers the outcome where she plays tough and the other plays Weak, and [3] the outcome (Tough, Tough) is the worst for both

Question 24

convergence of expectations

Answer 24

a situation where the players in a noncooperative game can develop a common understanding of the strategies they expect will be chosen

Question 25

coordination game

Answer 25

a game with multiple Nash equilibria, where the players are unanimous about the relative merits of the equilibria, and prefer any equilibrium to any of the nonequilibrium possibilities. Their actions must somehow be coordinated to achieve the preferred equilibrium as the outcome

Question 26

dominance solvable

Answer 26

a game where iterated elimination of dominated strategies leaves a unique outcome, or just one strategy for each player

Question 27

dominant strategy

Answer 27

a strategy X is dominant for a player if the outcome when playing X is always better than the outcome when playing any other strategy, no matter what strategies other players adopt

Question 28

dominated strategy

Answer 28

a strategy X is dominated by another strategy Y for a player is the outcome when playing X is always worse than the outcome when playing Y, no matter what strategies other players adopt

Question 29

game table

Answer 29

a spreadsheet like table whose dimension equals the number of players in the game; the strategies available to each player are arranged along one of the dimensions and each cell shows the payoffs of all the players in a specified order, corresponding to the configuration of strategies that yield that cell, also called a payoff table

Question 30

focal point

Answer 30

a configuration of strategies for the players in a game, which emerges as the outcome because of the convergence of the players’ expectations on it

Question 31

iterated elimination of dominated strategies

Answer 31

considering the players in turns and repeating the process in rotation, eliminating all strategies that are dominated for one at a time, and continuing to do so until on such further elimination is possible. Also called successive elimination of dominated strategies

Question 32

mixed strategies

Answer 32

a mixed strategy for a player consists of random choice, to be made with specified probabilities, from his originally specified pure strategies

Question 33

nash equilibrium

Answer 33

a configuration of strategies (one for each player) such that each player’s strategy is best for him, given those of the other players

Question 34

normal form

Answer 34

representation of a game in a game matrix, showing the strategies (which may be numerous and complicated if the game has several moves) available to each player along a separate dimension of the matrix and the outcomes and payoffs in the multidimensional cells, also called strategic form

Question 35

ordinal payoffs

Answer 35

each player’s ranking of the possible outcomes in a game

Question 36

payoff matrix

Answer 36

same as payoff table and game table

Question 37

prisoners’ dilemma

Answer 37

a game where each player has two strategies, say cooperate and defect, such that [1] for each player defect dominates cooperate, and [2] the outcome (defect, defect) is worse for both than the outcome (cooperate, cooperate)

Question 38

pure coordination game

Answer 38

a coordination game where the payoffs of each player are the same in all nash equilibira. thus all players are indifferent among all the nash equilibria and coordination is needed only to ensure avoidance of a nonequilibrium outcome

Question 39

pure strategy

Answer 39

a rule or plan of action for a player that specifies without any ambiguity or randomness the action to take in each contingency or at each node where it is that player’s turn to act

Question 40

successive elimination of dominated strategies

Answer 40

same a s iterated elimination of dominated strategies

Question 41

superdominant

Answer 41

a strategy is superdominant for a player if the worst possible outcome when playing that strategy is better than the best possible outcome when playing any other strategy

Question 42

weakly dominant

Answer 42

a strategy is weakly dominant for a player if the outcome when playing that strategy is never worse than the outcome when playing any other strategy no matter what other strategies players adopt