Secure computation against convert adversaries based on game theory

Punish game in game theory models a situation in which players try to cheat, but not to be caught, i.e., the case in secure computation involving convert adversaries. Based on the computational game model for cryptography, the problem proposed by Halpern and Rafael is solved. The result suggests that secure computation with deterrent 1/2 is a universal implementation of the mediator with negligible error in the computational game theory.