Abstract: Aiming at the question of number of strategies were chosen by participants in real world when the rational cryptographic protocols running, a model and the algorithm of solving this problem is designed, which simulated the rational actions on the Swarm platform of intelligent agents. Firstly, payoff matrix was defined in this article, and then, the state-copy formulation of participants is listed up; 3 Nash Equilibrium values discovered by solving the formulation, i.e., the different value which all the participants were used to honest strategy, tactics and non honesty mixed strategy, and game algorithm is designed according to the different values; at last, each object is defined in the main game needed on the Swarm, however, the basic object function can not fully meet rational cryptographic protocols on the Swarm, so the transformation of the Swarm platform part of the main object function given the key code transformation, the game of interaction in the whole swarm is implemented on the Swarm. As the result shows, rational participants will be difficult to reach Nash Equilibrium through rounds of game when the pay off function is constant. However, by using incentives to encourage the profits of honest participants, rational participants will be easy to Nash Equilibrium with less rounds of game, and the proportion of the honest participants is at least half the list. There are some reference values by using the algorithmic game theory that presents the methods which simulated on the Swarm platform for researching rational cryptographic protocols in this article.

Key words: network security, rational cryptographic protocols, Swarm, algorithmic game theory