Game theory is the study of interactive strategic decision-making among rational actors. A game has three components: players, strategies, and payoffs. A player is a decision-maker, a strategy is the player’s decision for every possible situation, and a payoff is the player’s reward or loss.
In game theory, pure strategies do not involve randomness; instead they offer a decision for all possible situations. Mixed strategies depend on some element of chance.
Tax systems can be viewed as hosting several different games including taxpayers versus tax authorities, minority versus majority owners, and stewards of the cash position versus the effective tax rate.
Scott P. Stevens, James Madison University professor and author of Games People Play: Game Theory in Life, Business, and Beyond, postulates that taxpayers and tax authorities can be seen as engaging in non-zero-sum games having mixed strategies.
Taxpayers employ strategies like planning and compliance. Tax authorities rely on guidance, audits, and prosecutions. Governments publish regulations that affect taxpayer planning in what appears to be a sequential game — that is, a game that unfolds over time in which players have information about the earlier actions of other players. Taxpayer reporting and government auditing are more akin to spontaneous games, which require players to make decisions without knowing what other players have done. A taxpayer’s payoff is tax savings (and public services), while the government’s payoff is revenue.
Stevens points out that enforcement is also an iterated game. Conducting an audit or catching a violator puts other players on notice. Game theory suggests that publicizing taxpayer prosecutions should be part of the government’s strategy.
"Coopetition" — a portmanteau word combining competition and cooperation — games are statistical models that consider how partnering with potential competitors can create synergy. Players are considered competitors if a customer values one player’s product less when they have the other’s product; players are complementors if the opposite is true.
Stevens questions whether tax avoiders and tax professionals are complementors in a coopetition sense. Does one make the other more attractive?
Coopetition can also occur between taxpayers and tax authorities in settlement negotiations. A mutually settled and closed audit could constitute a Nash equilibrium: Neither player can improve its payoff by unilaterally changing strategies.
Editor’s note: Tax Notes will publish an article on Nash bargaining theory on September 30.