Game Theory in Economics and Finance

The Nash equilibrium is the set of strategies for each player that results in the highest payoff for each player, given the strategies of the other players.

The Prisoner's Dilemma is a game in which two players are better off cooperating with each other, but each player has an incentive to defect. This is because each player can get a higher payoff by defecting, regardless of what the other player does.

The Tragedy of the Commons is a situation in which a shared resource is overused because each individual has an incentive to use it as much as possible. This is because each individual can benefit from using the resource, but the costs of overuse are shared by all.

The Coase Theorem states that if property rights are well-defined and transaction costs are zero, then the allocation of resources will be efficient, regardless of the initial distribution of property rights. This is because the parties involved in a transaction will be able to bargain with each other until they reach an agreement that is mutually beneficial.

The principal-agent problem arises when the principal and the agent have different objectives. This can lead to a conflict of interest, in which the agent may take actions that are in their own best interest, but not in the best interest of the principal.

Adverse selection is a situation in which one party to a transaction has more information than the other party. This can lead to a situation in which the party with more information is able to take advantage of the party with less information.

Moral hazard is a situation in which one party to a transaction can take actions that affect the other party, but the other party cannot observe those actions. This can lead to a situation in which the party with the ability to take hidden actions takes actions that are in their own best interest, but not in the best interest of the other party.

The signaling game is a game in which one player sends a signal to another player, and the other player must decide whether or not to believe the signal. The sender of the signal has private information that the receiver of the signal does not have, and the sender can use the signal to try to convince the receiver of something that is not true.

The bargaining game is a game in which two players negotiate over the division of a pie. The pie is a fixed amount of resources, and the players must decide how to divide it between themselves. The players can either agree to a division of the pie, or they can disagree and walk away with nothing.

The ultimatum game is a game in which one player proposes a division of a pie to another player, and the other player can either accept or reject the proposal. If the other player accepts the proposal, then the pie is divided according to the proposal. If the other player rejects the proposal, then neither player gets any of the pie.

The centipede game is a game in which two players take turns alternating between two actions, and the player who takes the last action wins the game. The game is played on a centipede, which is a long, thin board with a number of spaces on it. The players start at one end of the centipede, and they take turns moving their pieces one space at a time. The player who reaches the end of the centipede first wins the game.

The battle of the sexes is a game in which two players have different preferences over two outcomes, and each player prefers the outcome that the other player does not prefer. For example, one player might prefer to go to the movies, while the other player might prefer to go to a concert. If the players cannot communicate with each other, then they may end up going to different places, even though they would both prefer to go to the same place.

The stag hunt is a game in which two players have different preferences over two outcomes, and each player prefers the outcome that the other player also prefers. For example, one player might prefer to hunt a stag, while the other player might prefer to hunt a rabbit. If the players can communicate with each other, then they can agree to hunt the stag, which is the outcome that both players prefer. However, if the players cannot communicate with each other, then they may end up hunting different animals, even though they would both prefer to hunt the stag.

The prisoner's dilemma is a game in which two players have different preferences over two outcomes, and each player prefers the outcome that the other player does not prefer. For example, one player might prefer to confess to a crime, while the other player might prefer to remain silent. If both players confess, then they will both receive a long prison sentence. If both players remain silent, then they will both receive a short prison sentence. However, if one player confesses and the other player remains silent, then the player who confesses will receive a short prison sentence and the player who remains silent will receive a long prison sentence. Therefore, each player has an incentive to confess, even though they would both prefer to remain silent.