Composite transposons are key vehicles for the worldwide spreading of genes that allow bacteria to survive toxic compounds. Composite transposons consist of two smaller transposable elements called insertion sequences (ISs), which flank the genes that permit such survival. Each IS in a composite transposon can either transpose alone, selfishly, or it can transpose cooperatively, jointly with the other IS. Cooperative transposition can enhance an ISs chance of survival, but it also carries the risk of transposon destruction. I use game theory to show that the conditions under which cooperative transposition is an evolutionarily stable strategy (ESS) are not biologically realistic. I then analyze the distribution of thousands of ISs in more than 200 bacterial genomes to test the following prediction of the game-theoretical model: if cooperative transposition was an ESS, then the closely spaced ISs that characterize composite transposons should be more abundant in genomes than expected by chance. The data show that this is not the case. Cooperativity can only be maintained in a transitional, far-from-equilibrium state shortly after a selection pressure first arises. This is the case in the spreading of antibiotic resistance, where we are witnessing a fleeting moment in evolution, a moment in which cooperation among selfish DNA molecules has provided a means of survival. Because such cooperation does not pay in the long run, the vehicles of such survival will eventually disappear again. My analysis demonstrates that game theory can help explain behavioral strategies even for mobile DNA.