Tax Lawyer Game

• Content map: SMU H3 Game Theory Map

Setup

Definition:

Tax Lawyer Game

• Players: Two representative citizens (Player 1 and Player 2)
• Strategies: Hire a lawyer (L); Do not hire a lawyer (N).

Rules

• Start with two citizens deciding whether to reduce individual tax burden; Players simultaneously choose Hire a lawyer (L) or Do not hire a lawyer (N).
• The player who hires while the other does not gains the individual advantage; Hiring a lawyer helps an individual reduce tax burden.
• If many citizens hire lawyers: \begin{itemize} \item Government raises taxes to compensate \item Society incurs inefficiency (lawyers do not create value) \end{itemize}; If no one hires lawyers: \begin{itemize} \item Lower taxes overall \item Higher social welfare \end{itemize}.

Payoff Matrix

Derivation (Best Response Analysis)

• If opponent chooses $N$, the best response is $L$.
• If opponent chooses $L$, the best response is $L$.
• Thus hiring a lawyer is a dominant strategy.

Nash Equilibrium

Result:

Social Optimum

• The socially optimal outcome is

• This avoids wasteful legal spending and gives total payoff $6$.

Insights

Insight:

• Individually rational behaviour leads to socially inefficient outcome
• Hiring lawyers is a dominant strategy

Insight:

The tax lawyer problem illustrates how individually optimal actions can generate collective inefficiency due to negative externalities.