We investigate optimal strategies to defend valuable goods against the attacks of a thief. Given the value of the goods and the probability of success for the thief, we look for the strategy that assures the largest benefit to each player irrespective of the strategy of his opponent. Two...

We study the spatial prisoner’s dilemma game where the players are located on the nodes of a random scale-free network. The prisoner’s dilemma game is a powerful tool and has been used for the study of mutual trust and cooperation among individuals in structured populations. We vary the...

We introduce a “gradient” to find out the defectors, and further a “topology potential” to characterize the individual’s strategy preference in the prisoner’s dilemma on scale-free networks. It is shown that the cooperators typically locate on the nodes with high topology potential...