Confession Is Good For Soul And Equilibrium But Maybe Not Justice

Recently, I read this article about how the Department of Labor, the Internal Revenue Service and states are targeting pay practices of home builders.  This got me thinking about how industry enforcement sweeps can be a very effective enforcement tool.

Suppose, for example, an enforcement sweep involves only two firms that do not communicate with each other.  If both firms concede the regulator’s position, they will be given some credit for cooperation and fined only $10,000.  If one resists and the other concedes, then the resistor is punished with a more hefty penalty of $25,000 while the other firm receives a very modest slap on the wrist of $1,000.  If both firms resist, they each receive a penalty of $3,000.  This is the classic “prisoners’ dilemma” and is summarized by the following table:


Firm A




Firm B


$10K; $10K

$1K; $25K


$25K; $1K

$3K; $3K

Each firm will do better if it concedes regardless of what the other firm does.  In game theory, this is referred to as the firm’s dominant strategy.  The solution to the game therefore is for both firms to concede.  Consequently, an equilibrium is achieved with each firm conceding.  This obviously a good result for the regulator and explains why sweep examinations can be an effective enforcement tool.  However, the question remains whether justice is attained when concessions are achieved via the prisoners’ dilemma.

The name for the equilibrium is the “Nash equilibrium”.  It is named for the Nobel prize winning mathematician, John Nash.  A Beautiful Mind by Sylvia Nasar and a movie by the same name tell the story of Professor Nash’s struggle with mental illness.

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