Is Hobbes' state of nature a prisonners' dillema?

 Is Hobbes' state of nature a prisonners' dillema? 

A prisoners' dillema is an economic game wherein two players are faced with the choice to cooperate for a mutually split benefit or betray the other prisoner for a greater individual benefit. The catch is that if both prisoners choose to betray, they will both receive a poorer outcome than if they were to cooperate. The dillema is that the prisoners are unable to reach the mutually beneficial cooperative outcome because they can not trust that the other prisoner will uphold their cooperation and not betray.

Hobbes' describes the creation of a contract as voluntarily giving up ones right of nature, either by renouncing or transferring it. This contract then grants its member parties an obligation to not hinder one another and a duty to not void the contract voluntarily entered, either of which being an injustice to the other person. As explained by Hobbes, the strength of a contract's bond is largely in the consequence of breaking the contract, not in the verbal utterances of the contract creation itself. 

In the context of the prisoners' dillema, the prisoners' right of nature is to make the choice (betray or cooperate) that they believe will lead to their self-preservation and ends. The law of nature is in the mathematics of the game, that the most mutually beneficial outcome is mutual cooperation where neither party hinders the other for advantage. The contract, then, is the voluntary laying down of both prisoners' right to make either choice to instead adopt the golden rule of, "treat the other prisoner the way you would want to be treated." Yet, under Hobbes' conception, the prisoners' dillema is an example of the impossibility of creating a contract bound only by words in the state of nature. In this single-match game, where the betrayal leads to massive gains, the cost of obligation to the contract is too high. Because the betraying prisoner will see no retribution from the prisoner he betrayed, he will choose to betray, and the other prisoner will likely think the same, leading to the outcome of the dillema as described in the first paragraph. So, yes, Hobbes' state of nature is a prisoners' dillema. 

Yet, pulling on Locke slightly, say the prisoners are well-connected with many affiliates both in and out of the prison system who would gladly take revenge on their behalf if one was to be wronged in the process of the economic game (this example takes "prisoners' dillema" quite literally. I found it the best fit to illustrate my point). In this case, the prisoners are much more likely to cooperate out of fear of retribution from the kin of the betrayed. Though this would mean the cooperation contract is built out of fear, this is a valid method under Hobbes' conception. In Locke's state of nature, the prisonners' dillema is solved through retribution.

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