ECON 459 - Game Theory Exam 1 Terms

Strategic Choice

Any time you make a choice where your outcome depends on others’ actions.

Payoffs

Number assigned to an outcome for a player

Strategies

Possible actions for players

Complete/Defined Strategy

Specifies an action for every player in every possible scenario

Need to define an action at every node

Simultaneous Game

Everyone chooses an action at the same time

Players make their choices without knowing what other players will do

All players only move once  

Sequential Game

Some players will be able to observe others’ actions before making their own

Equilibrium

Every player is using the strategy that best responds to everyone else’s strategies

Rationality

Each player assumes all other players are trying to maximize their payoffs

Common Knowledge of Rules

Everyone perfectly understands the game

Uncertainty

When you aren’t sure whats going to happen, but you do know the probability of each outcome 

When you have uncertainty you can calculate an expected outcome 

Node

Where a move is made

Move

Which branch to follow

Terminal Node

The nodes at end of the tree, where payoffs are determined 

Nature’s Move

Represents uncertainty, made at random

Equilibrium Strategy

Every player has a fully defined strategy that satisfies the definition of an equilibrium

Everyone is playing the best response to each other and no one wants to change their strategy

First-Mover Advantage

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

Second-Mover Advantage

Flexibility to adapt to other’s choices

Pure Strategy

Choose an action with 100% probability

Mixed Strategy

A random selection from originally specified strategies made with specified probabilities 

Play multiple actions probabilistically

Mathematically similar to continuous strategies

Discrete Actions

Finite number of possible actions

Continuous Actions

Infinite number of possible actions

Nash Equilibrium

A configuration of strategies where all players are playing a best response to each player’s strategies

In a Nash Equilibrium, no player has a profitable deviation

Best Reponse

Given the other players’ actions, the move that gives the highest payoff

Profitable Deviation

Assuming nothing else changes, making a different decision will increase payoff

Dominant Strategy

A strategy that always outperforms other options no matter what other players play

Dominated Strategy

A strategy that is always worse than at least 1 other option no matter what other players play

Strong Dominance

One option has payoffs that are all greater than other options

Weak Dominance

One option has payoffs that are all greater than or equal to other options

Best Response Analysis

Finding the Nash Equilibrium of a game by calculating the best response for each strategy, simultaneously for all players 

Coordination Game

Games where players have common interests and multiple equilibria

Pure Coordination Game

Games where coordination is all that matters

Focal Points

A configuration of strategies that emerges as the natural outcome to a game because of the convergence of player strategies

Coordination games need thes to have consistent equilibrium

Continuous Strategy Games

Games in which a player has a continuous range of real numbers available as strategies

Best Response Rule

A function expressing a player’s optimal strategy, given the strategies played by the other players

Payoff Function

A function that gives the numerical payoff for a player, based on his or her strategy and the strategies of other players

Exploitation Proof

If one player knew another player’s strategy, she couldn’t gain an advantage by playing a pure strategy 

To find one, you have to find where one player’s payoffs are the same no matter what he/she defends 

Nash Equilibrium in Mixed Strategies

When both players are playing exploitation-proof strategies

Both sides are playing a best response to a correct expectation of mixing; they do not know what actions will be played each time 

Opponent’s Indifference Property

The condition that each player’s strategy in a Nash equilibrium of mixed strategies has the opponent indifferent about choosing either pure strategy