Frankly speaking, Messr. Bernard 'Bernie' Lawrence Madoff doesn't have an incentive to co-operate with the investigators.
Firstly, he is a septuagenarian, thus, he is edging closer towards the end of his Earthly existence. (This assertion is underpinned by the assumption that he is not immortal). To him, a 25 year sentence is equivalent to a 50 year sentence, and a 150 year sentence: they are all life sentences. Therefore, it is unrealistic for anyone to expect him to co-operate, as he'll be spending the rest of his life behind bars, irrespective of whether he co-operates or not. (It is asinine to try to bargain with Bernie on the basis of a lesser sentence.)
Another related point: Let us postulate a best case scenario, where Bernie's normal life expectancy is 120 years. This means, given Mr. Bernie's current age, that he would have, ceteris paribus, close to 50 years left to live. However, according to The Christian Party, each two years in prison shortens a man's life expectancy by one year. Thus, this implies, based on a 120 year life-span, that Bernie can expect to live another 25 years in prison, in a best case scenario. Therefore, to encourage Bernie to negotiate, they'd have to offer him a prison sentence of less than 25 years, which they can not afford to do, as this would contradict their key goal to use Bernie's sentencing to set a loud and clear example to all would-be Bernies. Simply put: they have nothing tangible to offer Bernie, and since Bernie is evidently an astute person, he already knows this.
Furthermore, Bernie Madoff's epic grift scheme aggrieved a lot of powerful and 'well-connected' people. By now, he should know that he is not safe roaming the streets; in the 'free world', some vigilante-mercenary-type dude/dudette might be contracted to deal with him. Or, to state it explicitly, Bernie knows that he is safer in prison than in the free world.
Clearly, Bernie has no incentive to co-operate.
As my grandfather used to say, "A man who has lost everything has got nothing more to lose; he is bolder, irreverent and pays no attention to right or wrong."
A recommendation: They should put him in the most notorious penitentiary, where the most hardened, die-hard criminals are kept. Trust me, if they do that, he'll opt to co-operate, with the expectation of being placed in a 'better' prison.
