Manga Merits and Flaws
I'm going to start it off by agreeing that it has almost nothing in common with Death Note. I love both, but I still see very few similarities.
The one similarity is that they're quite intelligent. Liar Game is an intelligent manga, in that it gives you the same feeling as reading a mystery novel or trying to solve a puzzle. The characters are all exceedingly clever, the plots are well-thought out and it keeps you reading. I would compare it to Indiana Jones in that the action is constant enough that you have difficulty finding a stopping place.
Keep in mind that I prefer works like this. I couldn't get more than five pages into Fairy Tail because the characters and their actions annoyed me so much. So if you are looking for a manga with intelligent characters and plots, read Liar Game.
At the same time, I will acknowledge its flaws. Namely, characterization. Yes, the characterization is getting better. But by focusing so much on the awesome gambits and games, it often chooses to forego character development. That doesn't mean they are all flat and terrible—on the contrary, you do form an attachment. But they don't have the diverse traits that you'll find in other mangas. And that is the cost of a genius, tightly-paced plot.
If you want to read something reminiscent of a mystery novel, read Liar Game. If you'd rather read something with a lot of swords and screaming...go read something with swords and screaming.
Manga Liar Game Theory
I'll second the statement: Liar Game has almost nothing in common with Death Note. Forget that there was ever such a comparison.
Liar Game is pure and simple a popular treatment of game theoretic concepts. What's perhaps most impressive is that it does it accurately with rational conclusions. The plot is almost a bonus, but worthwhile for its own sake as well.
It should be noted that the series takes a little while to really get going. In particular I found the first 'game' to be a bit dull and perplexing, but beginning with the solution of the first game, the series really begins to take off. Where the series really shines is when it can present solid, logical proofs for the puzzle solutions rather than the vague and frankly hand-wave 'psychological' explanations one unfortunately sees too often in certain other 'intellectual' dramas.
Being familiar with game theory will definitely help in understanding and in enjoying the series. It might be worth learning about 'Tit-for-tat' and Axelrod's Prisoner's Dilemma game before getting too far into the series. The main thrust of the series is that acting in a 'good'/nice manner is not simply a moral imperative (or rather, morality is unnecessary) but simply the optimal, rational solution, even in counter-intuitive situations.
While it's true that there's not much crazy interpersonal drama in the series, it should not be confused with the series lacking characterization or character development. The characters are quite believable, especially the other, more normal participants of the games, and behave pretty much like real people. Many of them go through the more obvious development during the course of the series, in particular realizing the surprising benefits of not always being greedy. But regarding the long term character arcs, the intent is clearly to show Nao progressing from blind idealism to a rational one - not just being a good, nice person, but choosing to do so for intelligent, thoughtful reasons. Admittedly Akiyama is a bit flat as a character, but he's more of a bad-ass exposition fairy than anything else.
Manga Liar Game is Liar Game
So stop with the comparisons.
Death Note is a shonen supernatural action series with the mind games being based more on a OMG cool factor than anything connected with actual human behavior.
Liar Game is a seinen series that has no supernatural elements at all, no physical action, and a bunch of mental action. The mind games are based on both game theory and social psychology.
While some people will like both for the mind games, and there will always be Liar Game vs. Death Note comparisons. Xanatos Gambits and a genius character are all these manga have in common.
On it's own terms: I'm kind of in love with it.
I tend to dislike series that have a lot of violence in it. Especially when that violence doesn't seem to impact any of the characters. So it's nice to see Liar Game, which has very little violence but remains very intense with its consequences (imagine being $1 million U.S. in debt) and has its characters feel it.
I also really tend to like the main characters. Sure we don't get a ton of backstory about them because that's not the focus of the story, but they are distinctive. Akiyama's a genius, he's introverted without hating people or even necessarily being shy, and he doesn't have a God Complex nor does he lack conscience or emotions. Nao's hugely naive, but she proves that she's neither stupid nor helpless just because of that naivety and her abilities actually make her relevant to the story. Though I have some issues with the way Fukunaga's gender identity gets portrayed (it's inconsistent to say the least) zie's also a fully developed character whose identity isn't used to titillate the audience.
Plus it has all the puzzles and mind games ((and maybe a moral dilemma or two)) worth thinking about. The lack of physical action means that both mental and social intelligence count in these games. Plus most of the players who oppose Akiyama and Nao aren't evil, they just want to find a way out.
Obviously, this series isn't for everybody and probably has a niche appeal at best, but I found it hit a lot of my particular resonances as far as plot and characterization go.
Manga Like Death Note...but inferior.
Remember all those interesting and carefully defined characters in Death Note? Well Liar Game forgot to add them.
Liar Game's most severe issue is its characterisation. The protagonist, Nao, clearly has a lot of heart, but she is thick, naive and pathologically gullible. This is a problem in a series that relies on huge battles of intellect to carry the story, so the character Akiyama is introduced to provide the brains. Unfortunately that is the only thing he provides. He has no defining characteristics outside of his intelligence. Early on it is shown that he is laconic and has a tragic past, but it isn't explored to its full potential. As it stands, it feels like someone split a main character in two - one with all the personality and one with all the intelligence. This doesn't work because Nao often gets relegated to the sidelines whilst Akiyama is merely a computer. Add to this a one note villain whose soul desire is power, and you have a far less interesting conflict than anything out of Death Note.
There is only one remarkable character in the entire series to date. She is Fukunaga, a secondary antagonist who happens to be a transvestite. She is easily the most fleshed out, and what is more, this series contains one of the few fair treatments I have seen of a trans character in an anime or manga. Usually, "deviant" types tend to get marked out as creepy perverts or comic relief, flamboyant queers. Fukunaga is neither. She is ruthless, selfish and violent, but she is not made to look a weirdo. She is also intelligent, strong willed, and a martial artist to boot, and this is all established in his initial portrayal. Throw in her development and occasional moments of poignancy, and you end up with a really cool character who grew on me. She alone almost makes up for the others.
Liar Game is weaker than Death Note because, beyond the interesting explorations of game theory and logic, Liar Game is lacking in every other respect - the story is less exciting, the stakes are lower, there is less humour (and what little there is, it doesn't translate so well), and the characters are dreadful hams.
Do I recommend it? Not before recommending Death Note. The puzzles are the saving grace of the series and they alone make it worth reading. But really, there is little else there.
EDIT: corrected the pronouns for Fukunaga, who is not a "transvestite" as I had originally wrote, but a trans woman.
Manga Like Death Note, But Actually Good!
When Liar Game was first brought to my attention, it was under the auspice of 'Like Death Note, but with Con Men.' This was a surprising approach, to me, because I may have intimated to a few people in my circle of friends, readers of several blogs, wiki viewers, and anyone who walked past while I bellowed it from the rooftops that I think Death Note was a very bad series. I tried it nonetheless, and was pleased and am pleased to report that Liar Game differs from Death Note, but actually good.
What Spice And Wolf did for economics, Liar Game does for game theory. It's a very information-dense series, currently incomplete, and goes through a large number of game theory problems. If you're prone to analysing your environment and daily dealings with people, it might just be a bit too Paranoia Fuel for you.
Because the story works by building tension and resolving it, rather than by a never-ending series of one-upped gambits, there's no need to keep track of an ever-expanding ring of second-guesses. Bonus? This means that even if the ending does turn out to be an unimpressive bust, it doesn't diminish the cleverness leading up to it. There aren't any rabbit-out-of-a-hat moments in the games; the rules are explicitly stated up front.
So, if you read Death Note, and figured that all it needed to be a good, enjoyable series was the addition of likeable characters, sensible constraints, an interesting moral compass, plot and a transvestite, then Liar Game is for you.
Manga Excellent Survival Game
I am a fan of what I call Survival Game, a "genre" in which you have to play a game to survive (Doubt, Ousama Game, etc...), and Liar Game is one of the best in that genre.
First of all, the manga excels in showing how deep the Meta Game can be, but with one simple thought: Decieving your opponent. The game will usually be extremely simple (Minority Game, Musical Chairs, Russian Roulette...), but with one rule in particular: No violence. And death is replaced with debt, which would also explain why they could afford such playgrounds, as well as being as frightening as being dead.
The characters are a mixed bag: While Akiyama and Yokoya are really cool, and Fukunaga was also kind of cool, I didn't like Nao that much even though she is what the audience would likely be in this situation and gets better, and the other opponents are usually boring.
The other mixed bag is a nitpick, but I thought either some games didn't fit (The first round), or were too complicated (The contraband game), which is really annoying because some rounds can be pretty long.
The biggest Flaw however is the ending, which I won't spoil but really dissapointed me.
Overall, if you like Books or Mangas like those mentionned above, Liar Game is a truly unique approch in that genre.