The really basic premise:

Game Theory is, essentially, a mathematical abstraction of social behaviors and an explanation of how / why certain behaviors are common / persistent. Basically, Game Theory finds that every animal species known plots their decisions based on maximizing personal reward while minimizing penalties they might face. This is why it's called 'Game Theory'. It proposes that life is, essentially, lived as though it's a big game, with every organism trying to achieve the best 'score' they can (...But be careful! 'Cuz you only get 1 mann!)

The Prisoner's Dilemma is the classic example most people will refer you to. I tend to illustrate it like this:

You and I are squaring-off in a pistol duel. Once the clock chimes noon, the duel starts. Until then, our pistols remained holstered (and, presumably, our hand readied)

Noon arrives. What's the best choice I can make?

I could opt to not draw my gun (Cooperation). If you do the same thing, we'll both walk away unharmed. If you draw your gun when I don't, however, I'll most assuredly get cut down on the spot without a chance to defend myself.

I could opt to draw my gun and defend myself (Defection). If you don't draw your gun, I win the duel and kill you with no trouble. If you do draw your gun, I might still die or get hurt - but I also might successfully defend myself and kill you instead, so at least I have a fighting chance.

Drawing my gun is my best option (Defection) when I have no idea what your action is going to be. It's the one action of the two that offers me the best likelyhood of surviving (or being rewarded).

This is, of course, a slight problem for evolutionary theory. If defection is always the best option (and we go through this Prisoner's Dilemma in every single interaction we have with another organism - choosing to either cooperate with them or defect in favor of self-interest), how does cooperation (and thus species-wide survival) occur?

The solution to the conundrum is that defection also always carries with it the penalty of punishment. So while the short-term benefit may be greater, once the experiment starts being repeated, cooperation becomes the superior choice. Let's go back to the gunfighter example:

So, I drew my gun and won the duel. But let's say you didn't die (you drew your own gun and defended yourself, afterall) - you're just injured. Now, I'm in a worse position. People know I'm an effective gunfighter now, and that experience can  (and will) be used against me the next time I get into a gun duel. Someone might cheat. Or someone might start practicing so they can draw and shoot faster and more accurately than me. I'm recieving the negative, punitive, results of my short-term benefit decision - and if I keep repeatedly defecting, I'll pay a very hefty cost for it. Learning from my example, it becomes logcial to start cooperating, to avoid the sort of punishment I'm recieving - so more and more duels are likely to end with nobody drawing a gun.

(I'm fond of that example because, historically, that's more or less exactly what we see - both in the literal 'wild west' sense and in a more global sense regarding international conflict).

Now, that's just the basic, layman's 'nutshell' of it. There a LOT more to it, and it's a highly mathematical field (frankly, I suck at math, so there's some parts that are way over my head).

If you are a mathematician you need to understand it so your buddies won't laugh at you. Problem there is damn little human matters it applies to. So there is no way to handle anything but a zero sum game. This is one where there are a fixed number of, say dollars, in the game and only the fraction of the total each player has can change. That leaves out just about every human activity except contrived games. Played correctly trading with other people increases the wealth of both. If you are buying food from farmers you can make money from selling them fertilizer and get a lower food price. Farmers will be able to diversify into more profitable foods. I know there are people who do not like the idea and it is not expected to be perfect at all times but if it is not true, how come we can afford more than stone axes and hides? The value of what is in the game has not remained zero. In theory marriage makes two people happier than they were. It is not that they trade back and forth the fixed amount of happiness they each brought to the marriage. I may be wrong. Investigate it yourself. But do so before you start to be sure you are not wasting your time learning something the tool cannot address.

Economic models of human behaviour all tend towards the same mistake: they assume that humans are rational actors, who will make decisions based on a long view of the best outcome.  We aren't, and we don't.

Has anyone tried to rejig these models so the motivations aren't the best possible acquisition of resources; but the avoidance of fear?  I think this would make a much more accurate model for practically all human behaviour.

yes. Expirimental economics condouct labrotory studys, where students are paid acondenly to how they perform in simulations of games. and the results are maped in behaveial Economics. there are numorus biases found in those fields and some of them are somewhat robust.

forinstance if you take the dictator game:

goes like this "god" gives player A 100 dollars and player A says a % beetween 0 and 100, if he (or she) says 75 %

then player B have to deside Either that B gets 25% or 25 dollars ,and A gets 75% or 75 dollars- or both gets nothing

if both players are rational in economic sence the sulution would be for player A to take 99.99e % since it would be irational for B to turn down even 1c.

Expirimental economics have shown allmost the same distribution of when B desides to the nothing sulotion worldwide.

as I recall dont offer below 30%

Hmm... actually, the solution to the prisoner's dilemma in evolution is the realization that the game is (1) open-ended and (2) played between many individuals simultaneously, forming a web, not a linear progression.

Memory is also part of the solution.  Because we remember individuals who defect, we choose not to play with them again.  Reputation is everything.

Ah... fair enough.