Hydrogen enrichment does work for lean engine operation. This is a condition when there is more air than at stoichiometric. Hydrogen makes the air/fuel mixture more homogeneous, which permits a more efficient combustion of gasoline during such conditions and smooths out the large temperature gradients associated with localized fuel charges. By having more air in the combustion cylinder, more work on the piston can be done, especially at higher compression ratios, because less heat from combustion is transferred to cylinder walls.
As for hydrogen enrichment at stoichiometric conditions, this is extremely questionable. I haven't seen any peer-reviewed studies that address this specific question, so this suggests that it is not a viable option. A while ago, I remember reading an article that looked at this aspect during a combustion simulation. If I recall correctly, the thermal efficiency increased by 2% but I forget what the assumed hydrogen flow rate was during the simulation. This efficiency improvement does not appear to compensate for the energy needs to produce hydrogen. If I find the article, I will post the data.
Although your argument makes sense Ivan Seeking, I am not fully convinced. The reason why is because hydrogen addition will likely change the combustion products, which could affect sensor data. If sensor data is affected is such a way, then it may be possible to "trick" your car into running lean, which may increase fuel economy but yet could be damaging in the long-term to your engine. For example, if hydrogen addition causes more gasoline to be combusted, which would be no more than 1% since most fuel is combusted anyways, then there is a reduction of free oxygen in the exhaust products. As a consequence, the O2 sensor would measure that the car is running "rich" for some throttle position, which could cause the ECU to shorten the fuel pulse-width to obtain the required free-oxygen products. Thus the car is now operating lean, and it could be possible to obtain an improvement in fuel economy. This is a hypothesis that I plan to test in the upcoming months by using an OBD-II interface and laptop computer to measure sensor data.
In regards to the hydrogen economy, I see that it will not be feasible for a long time, since many breakthroughs are needed, like storage, production, infrastructure, etc. What does make sense to me is that gasoline-hydrogen automobile hybrids, with the appropriate engine modifications for lean operation and machinery for producing sufficient quantities of hydrogen on-board, could become common in the near future. Such vehicles would have improved fuel economy and reduced emissions.