L1

Question 1

non-cooperative game theory

Answer 1

interacting individuals (players) cannot jointly agree on a course of action, but each of them acts independently, pursues own objectives, and is affected by actions of others.

Question 2

Game is a list of

Answer 2

Players: (actors, agents) consumers, firms (a collection of agents representing a decision-making unit)

Actions and information integrated into strategies: how players interact, what do they know, who can do what

Payoffs: representation of players’ preferences over the economic outcomes (profits, allocation of goods) but also less tangible outcomes (reciprocity, emotions) in terms of utility functions

Question 3

Solution concept

Answer 3

the interacting players have well-defined preferences over all the possible outcomes of the strategic interaction and are rational

Question 4

Strategy is

Answer 4

a complete contingent plan for a player in the game

Question 5

NFG

Answer 5

All players announce simultaneously and independently of each other their strategies. The combination of the strategies leads to payoff outcome for each of the players.

Question 6

EFG

Answer 6

includes richer move structure - order of moves for the players, information available for each of the players each time the player is called to move

Question 7

NFG is given by

Answer 7

1. players N={1,2,..n}
2. strategies for each player
3. payoff function

Question 8

Strategy profile

Answer 8

A strategy profile (strategy combination) is a vector of strategies, one strategy for each player. Often, we denote one strategy profile by s, and it is the case that s=(s1,s2,…,sn) specifies one strategy for each player.

Question 9

Payoff function

Answer 9

is a list of payoff consequences for a particular player for each strategy combination in a game (each possible outcome of a game)

Question 10

Mixed strategy is

Answer 10

a probability distribution over set of own (pure) strategies

Question 11

Mixed strategy can be used to

Answer 11

1. express that a players sometimes randomizes among own actions, or
2. as a description of a whole population of agents, each of whom might be a player in the game. The agents themselves use a pure strategy, but on average, the other player(s) receive a payoff from playing to various representatives of the population - on average given by the mixed strategy
3. capture player’s own uncertainty about actions of other player(s), thus player’s beliefs about behavior of others.

Question 12

coordination problem

Answer 12

both players prefer to choose the same strategy as the other player, rather than to miscoordinate; but they might disagree on what strategy to be the coordinated one

Question 13

utility function

Answer 13

represents preferences of an individual when it holds that alternative x is preferred over alternative y if and only if u(x)>u(y).

Question 14

risk averse and risk loving

Answer 14

An individual is RISK AVERSE if the expected utility of choosing a lottery is lower than the utility of receiving for sure the expected monetary equivalent of the lottery.

A risk averse individual is willing to forego expected monetary profit in order to avoid uncertainty connected to the expected monetary outcome.

Risk loving if the opposite

Question 15

Risk neutral

Answer 15

An individual is RISK NEUTRAL, if he/she is indifferent between playing a lottery or receiving for sure the expected value of the lottery.

Question 16

what distinguishes nooncoperative game theory

Answer 16

the noncooperative framework treats all of the agents’ actions as individual actions. An individual action is something that a person decides on his own, independently of the other people present in the strategic environment. The interacting individuals (players) cannot jointly agree on a course of action, but each of them acts independently, pursues own objectives, and is affected by actions of others.

Question 17

Prisoners dilemma

Answer 17

Game with 2 NE and each player has incentive to deviate

Question 18

Strictly competitive game (matching pennies) or ZERO-SUM game

Answer 18

When one player looses, the other wins

Question 19

Pure coordination

Answer 19

both prefer to choose the same strategy as the other player, rather than to miscoordinate; but they might disagree on what strategy to be the coordinated one.

Each coordination outcome is equally liked by either player

Question 20

Pareto coordination

Answer 20

: both players prefer to choose the same strategy as the other player,
One NE is preferred by both players to the other one.

Question 21

Battle of the sexes

Answer 21

both players prefer to choose the same strategy as the other player, rather than to miscoordinate; but they might disagree on what strategy to be the coordinated one.

Question 22

Chicken game

Answer 22

being tough (Hawk) gives the highest payoff IF the other player is weak (Dove)
“both weak” is better than “both tough” (costly conflict!)
This game has two “ anticoordination” equilibria.

Question 23

Game of dominance

Answer 23

Weak player gets a lower payoff from being active (“pushing”) no matter what the stronger (dominant) player does!
dominant player gets a higher payoff by NOT pushing IF the weak player pushes; BUT gets a higher payoff by pushing IF the weaker player DOES not
weak player is COMMITTED not to push!
and hence, the stronger player
is NOT SO STRONG in the end…

Question 24

Infinitely repeated prisoners dilemma game

Answer 24

if the discount factor is high enough, then both players sustain infinitely cooperation, using trigger strategies.

Question 25

Finitely repeated game with possibility to sustain higher payoff in period 1 which is NOT NE

Answer 25

– if the payoffs of the stage game NE differ sufficiently, then both players can be motivated to stick a payoff outcome that is not NE of the stage game