Best responses
Game Theory // Fall 2025
marcio.santetti@emerson.edu
Applying rationality
Applying rationality
People refrain from using dominated strategies.
- Dominance as a good descriptive and prescriptive concept.
Applying rationality
If a player wishes to maximize their payoff (i.e., be rational),
- Select the strategy that yields the greatest expected payoff given their belief.
Such a strategy is called a best response.
A player’s strategy is a best response if it yields a higher (or the same) payoff as another strategy.
Applying rationality
An alternative definition:
Given what the other player(s) is(are) doing, a strategy is a best response if and only if a player cannot obtain a higher payoff from switching to a different strategy.
Isolate!
Isolate!
Rationalizability
Rationalizability
When a player has a dominated strategy, it is irrational to play it.
- Therefore, a dominated strategy can be deleted from a matrix-form game.
Rationalizability
Rationalizability
Rationalizability
Rationalizability
Rationalizability
Rationalizability
The procedure of eliminating dominating strategies is called Iterated Elimination of Strictly Dominated Strategies (IESDS).
- Order of elimination does not matter!
- As long as one applies the concept of strict dominance correctly.
Rationalizability
Rationalizability refers to strategies that remain after one iteratively removes those that are never best responses (NABR).
This process is equivalent to applying dominance.