Game Theory & Information

A zero-sum game is a situation where one player's gain exactly equals another player's loss, so the total is unchanged.

The principal-agent problem arises when one party (the agent) acts on behalf of another (the principal) but has different incentives and better information.

Signaling is when an informed party credibly reveals private information to a less-informed party to overcome asymmetric information.

Screening is when a less-informed party designs choices to get an informed party to reveal hidden information.

The median voter theorem says that under majority rule with single-peaked preferences, the outcome chosen matches the preference of the median voter.

The Condorcet paradox is when majority preferences cycle (A beats B, B beats C, C beats A) even though each individual voter has consistent rankings.

Arrow's impossibility theorem proves no ranked voting system can convert individual preferences into a group ranking while satisfying a few basic fairness conditions and avoiding a dictator.

Logrolling is vote trading in which legislators swap support across bills so each can pass a measure they care intensely about.

Tit-for-tat is a repeated-game strategy that cooperates on the first move, then simply copies whatever the opponent did last round.

A grim trigger strategy cooperates until the opponent defects even once, then punishes by defecting forever after.

The folk theorem states that in an infinitely repeated game with patient players, almost any reasonable (individually rational) outcome can be sustained as an equilibrium.

Backward induction solves a sequential game by reasoning from the last decision backward, choosing each player's best move at every stage.

A dominated strategy is one that pays less than some other strategy of yours no matter what the opponent does, so a rational player never plays it.

A mixed strategy is a plan to randomize over your moves with fixed probabilities, used when always making the same predictable choice would be exploited.

A payoff matrix is a table listing every combination of the players' strategies and the payoff each one earns, written as (row player, column player).

A sequential game is one where players move in turns and later movers see what came before, so it is drawn as a game tree and solved backward from the end.

A repeated game is the same game played again and again by the same players, so cheating today can be punished later and cooperation becomes possible.

A credible threat is one the threatening player would actually want to carry out when the time comes, which is why a rival believes it.

First-mover advantage is the gain a player wins by committing to a move before rivals, so they must take that choice as given and react to it.

A coordination game is one where players do best by making the same choice, so it has two or more Nash equilibria and the problem is agreeing on one.

The market for lemons is George Akerlof's model showing that when only sellers know quality, buyers offer average prices and good goods leave the market.