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The liar's dilemma basically implies that a liar is not incentivized to reveal himself as liar. However, there is a twist to this which takes into the time of evaluation, t, of any proposition, x, that a liar would purport. Basically, as t increases a liar is further incentivised to lie. In fact t approaching infinity could be considered a non-sequitur. So if there exists the potential to introduce non-sequiturs, your statement can not be evaluated, and therefore you have a continuing incentive to lie and any cumulative lies thereafter have no impedance to their creation. One non-sequitur based lie provokes another, provokes another, ad infinitum (reflect on thoughts of religion or many political stances). *This is actually represented in first order logic simply as False->False = True.
What a large t also does, is give a liar the ability to evaluate the value of proposition x given to another person and change p(x) - where p(x) is the probability of actually changing the value of x from false to true before evaluation is performed by the other person. In other words, actually doing what you said you would do in proposition x. This is an immense power. For you can actually decide the value of your next move based on the a response to proposition x from the other person without having to actually do x. Also, the value of x that is found (if past the 'doability' threshold) can actually dictate the level of quality (and therefore the amount of time required) in which you perform the acts to turn x from false to true.
This is the basis for selling a product before it's built to evaluate the market demand, 'alias' writing, and many other such things which require value evaluation prior to execution or attribution. So consider this fact the next time you are thinking of lying. If t is considerably small, then don't do it. However if t is fairly large, lie like a rug and use the results to your advantage.