Best Response Game Example

• Content map: SMU H3 Game Theory Map

Setup

Definition:

Best Response Game Example

• Players: Two players, Player 1 and Player 2.
• Strategies: Player 1 chooses $U$ or $D$; Player 2 chooses $L$ or $R$.
• Rules: Players choose simultaneously; each player chooses a best response to the other’s action.

Payoff Matrix

Derivation (Best Response Analysis)

• If Player 2 chooses $L$, Player 1 compares $2$ from $U$ with $1$ from $D$, so Player 1’s best response is $U$.
• If Player 2 chooses $R$, Player 1 compares $0$ from $U$ with $1$ from $D$, so Player 1’s best response is $D$.
• If Player 1 chooses $U$, Player 2 compares $1$ from $L$ with $0$ from $R$, so Player 2’s best response is $L$.
• If Player 1 chooses $D$, Player 2 compares $0$ from $L$ with $2$ from $R$, so Player 2’s best response is $R$.

Nash Equilibrium

Result:

The pure-strategy Nash equilibria are

Insights

Insight:

• A Nash equilibrium is an intersection of best responses.
• Dominance is not required for Nash equilibrium.
• Multiple equilibria can arise when more than one profile is mutually optimal.