game theory midterm

mutual commitments

when two players become tied to each other, separately from the market, their relationship becomes bilateral

private information

when participants in a transaction possess some private info. bearing on the outcome

zero-sum/constant-sum

when there is a winner and loser

opposite: positive sum

imperfect information

when there is uncertainty

• external uncertainty: when a player is uncertain about external circumstances (ex. weekend weather)

• strategic uncertainty: when a player is uncertain about what moves his opponents has made in the past or is making at the same time

asymmetric / incomplete information

when one player knows more than another does

cooperative games

games in which join-action agreements are enforceable

noncooperative games

games in which join-action agreements are not enforceable and individual participants must be allowed to act in their own interests

strategies

choices available to players (complete plans of action)

payoff

number associated with each possible outcome

completeness

between any x and y in a set, x > y (x is preferred to y), y > x, or x ~ y (indifferent)

transivity

if x ≥ y and y ≥ z → z ≥ x

expected payoff

if the player faces a random prospect of outcomes, the number associated w/ this prospect is the avg. of the payoffs associated w/ each component outcome, each weighted by its probability

model

simplification (abstract representation) of a given system, judged by its usefulness

first-mover advantage

ability to commit oneself to an advantageous position and to force the other players to adapt to it

second-mover advantage

flexibility to adapt oneself to the others’ choices

mixed strategies

probabilistic strategies (ex. A player or team may deliberately randomize its choice of action to keep the opponent guessing)

strategy in simultaneous game

only ONE action bc each player has at most one opportunity to act

pure strategies

basic initially specified actions (ex. Always plays rock in rock paper scissors)

nash equilibrium

no player can improve their outcome by unilaterally changing their strategy, assuming other players keep theirs unchanged

• does not require equilibrium choices to be strictly better than other available choices

• does not have to be jointly best for the players

forms of dominance

• superdominance: if the worst possible outcome when playing that strat is better than the best possible outcome when playing any other strat

• weak dominance: outcome when playing a strat is never worse than the outcome when playing any other strat

multiple equilibria in pure strategies

• pure coordination game: equal payoffs in multiple nash (ex. 2 nash of (1,1))

• assurance game: when players can get the preferred equilibrium outcome only if each has enough certainty or assurance that the other is choosing the appropriate action (ex. 2 nash: (1,1) and (2,2))

• battle of sexes: two Nash equilibria but the risk of coordination failure is greater (ex. 2 nash: (2,1) and (1,2))

• chicken game

key factors in changing the order of moves

• irreversible: when does each player’s move become irreversible?

• observable: when does each player’s move become observable to the other player?

can lead to first move and second mover advantage

changing the order of move: game changing tactics

• transparency vs secrecy:

  • transparent: simultaneous → sequential game and first mover advantage

  • secret: sequential → simultaneous

• nimbleness: ability to wait some pd. of time or not wait before making a move irreversible

information set

• consists of more than one node indicating the presence of imperfect info for the player. if no information sets with two or more nodes → perfect info

• when representing simultaenous game in a game tree, an information set represents the imperfect information.

nash eq. and rollback eq.

rollback requires a move to be optimal when the opportunity to move arises → more restrictive than nash