We show an embedded wavelet coder with a prioritization protocol, which provides an acceleration of benefit gain for quantizers of interest at extremely low bit rates. This means that decoded outputs provide better image quality at very low bit rates. By changing its risk attitude within a rational approach, which avoids certain forms of behavioral inconsistency, a quantifier may modify the gain in benefit that results from a particular bitstream candidate to be transmitted at a truncation time. At medium and high bit rates, quantizers exhibit only low risk tolerance, since they are aware that the next truncation time might be the last one. Since at extremely low bit rates the target bit rate may be far away, quantizers are able to exhibit higher risk tolerance, and as a consequence they will have greater possibilities of accelerating their benefit gain. The cooperation among subsets of the quantizers may be needed to increase the risk tolerance at very low bit rates within a rational approach and still prioritize first the more relevant pieces of information at each truncation time. The members of any coalition of quantizers can then negotiate a feasible change in the risk attitudes of the quantizers of the coalition that would benefit them all. The final risk tolerance of different quantizers comes from the balance of power among the coalitions of quantizers. The prioritization protocol chooses to transmit, at each truncation time, a bitstream for the quantizer that receives the highest payment (per coding bit) in a coalitional game, which minimizes the dissatisfaction of coalitions.