Abstract
This paper considers the Prisoner's Dilemma Game in which there exists a dilemma that the best response is that both players are to confess, but doing not confess can give a higher gain to the both players in a social perspective. To resolve such a dilemma in the game, an incentive model to encourage to confess and a penalty model for being imposed when not confessing are introduced, respectively. Then, the conditions are characterized under which incentive or penalty involved in the game's payoffs can make the game rational without a dilemma on both the personal and social perspectives, by taking the payoff values as variables with the incentive and penalty factors. Furthermore, it turns out that the resulting values of incentive and penalty are inversely proportional to each other, and thus, obtaining one of these amounts can provide the other. Simple examples are shown to interpret the theoretical verifications of our models, and randomly generated data based simulation results investigate the tendency of incentive and penalty and the resulting game values for a variety of instances. These results can provide a framework on resolving the dilemma by artificially putting incentive or penalty, although it is careful to apply more generalized real world games.
