An AIG bankruptcy filing did not hinge on the resolution of these contracts, thus there could not have been a game of chicken.
Details (greatly simplied but still quite wordy): This story is set in November of 2008, but to understand it we have to go back two months earlier - to September. In September 2008 the clearing price of mortgage-backed securities implied a high rate of mortgage default with low recovery on foreclosed property - a decline in real estate values such as never seen before. Observers were still debating whether prices were correctly forecasting widespread defaults or whether prices were merely depressed due to illiquidity. For institutions levered to real estate the distinction was very important because it meant the difference between short-term liquidity problems and long run insolvency which would force bankruptcy
To understand liquidity problems, we need to understand collateral. In order to minimize credit risk to each other, financial institutions ask for collateral from each other. As trades slowly move up or down in value, cash and securities flow between institutions so that everyone owes each other approximately nothing and the effects of a sudden bankruptcy are much smaller than they otherwise would be. Having collateral in hand means not having to worry about why your counterparty's trades are marking down so low - you are 100% insured by the collateral and if prices rebound you'll just give it back. And if your counterparty goes bankrupt you won't take a loss. Lehman was long real estate and, due to falling prices and having to post collateral, come September they ran out of cash. Regulators shopped them to other banks whose traders pored over Lehman's books and concluded "the company is insolvent, not just illiquid" so "goodnight Lehman Bros".
AIG was in the same boat as Lehman however AIG is an insurance company - this opened up three problems. (1) Banks are usually regulated by federal entities like the Fed and the SEC, so they all fit into similar frameworks nationwide. However insurance companies are only regulated by states. States are not particularly great at regulating because they are small and every state does things differently. (As a side note for fans of health care reform, regulating insurance companies at the federal level and creating national competition is the single most important reform needed. Lack of this in the so-called reform bills is proof that the legislation is all about creating health care entitlement without any real reform.) You can't just call in JP Morgan or Goldman Sachs to tell you what to do here because a bank can't really analyze an insurance company over a weekend. (2) Next, the ratings agencies had assigned AIG their highest rating, AAA, meaning that people who didn't want to do a lot of their own credit analysis, but didn't want to take any risk of default, were the sort of people who bought AIG bonds - that is to say, AIG bonds were largely being held in accounts that were presumed to be taking no risk by their owners. If you go back to news stories from September 2008 you will find many shrill voices invoking the spectre of systemic melt-down, but those voices tend to come from holders of AIG bonds, not random investors worried about "the system". (3) As an insurance company the general public was very broadly exposed to AIG in pensions, annuities, home insurance, etc... and these people aren't holding any collateral at all, but would account for a lot of votes at the polls come November. So, because of these three complications, the same politicians who let Lehman go under decided, at about the same time, to bail out AIG.
Now, there are lots of ways to do a bailout. This very same month, the largest financial entities in the world, Fannie and Freddie, were bailed out - and basically by the federal government saying "we simply guarantee all the debts and obligations of Fannie and Freddie". (Note that, in the end, the agency bailout is where the "taxpayer" will take almost all his lumps. But the politicians don't talk about this too much because Washington spent decades exempting Fannie and Freddie from any meaningful regulation and encouraging them, via various acts of congress, to facilitate mortgage loans to people who probably couldn't afford homes, but would make U.S. home ownership "more diverse".) In the case of AIG the bailout took the form of an billion loan. It is important to remember at this point the debate over whether real estate securities were down because a bunch of mortage defaults were coming or just because nobody wanted to own the bonds. The politicians were still hoping for the latter and hoping that a loan would tide AIG through its illiquid period and into a time when the securities recovered. The TARP legislation was debated this same month, and the original intent of TARP was to buy these securities, thus creating a market for them, and a recovery in their prices. (In the end, however, TARP was not used in this way. It was used to invest in banks, for which no legislation was required anyway, and auto companies - which was probably illegal.) The TARP debate informs us that in September the politicians were not believing the market-implied rate of mortgage default. So, AIG used its bailout money to keep collateral flowing on its real estate positions. The thinking on this was that it stopped the counterparties from closing out the trades and thus "locking in the loss".
Now let's move forward to November 2008, the subject of this post. By November those debating that real estate securities were down due to illiquidity rather than coming defaults had given up their argument. A wave of defaults was coming and everyone finally realized that a lot of people who took out sub-prime mortgages always had the intention of defaulting because they didn't want to own a home so much as speculate on real estate going up. Back at AIG, their positions had continued to go against them and it became pretty obvious that AIG was insolvent, not just illiquid, and a more aggressive bailout was going to be needed if they were not to declare bankruptcy. But now if AIG goes bankrupt the government is in for a loss too since it has made all these loans. So "in for a penny in for a pound" the feds decide to up the bailout. Among many issues to be sorted out in the fresh bailout is that AIG still has all these real estate positions which keep bleeding money and, since AIG made the wrong calls on this all along, the feds decide to close out all of these positions.
At this point, the "unlimited bailout" decision has been made, and the discussion over mopping up these positions is a sidebar, not super important at the time (but it will become very politically sensitive a year later). The feds would like to save a few bucks by negotiating the close-out on these trades with the banks. However, because all the banks are holding lots of collateral, and some of them are even insured against AIG defaulting, they expect to be paid in full just like everyone else exposed to AIG. The feds aren't calling PIMCO and asking them to take 80 cents for their AIG bonds, they are calling retirees and asking them to take 80 cents for their pension annuities, and the aren't calling up auto insurance holders and asking them to take 80 cents for fender-bender repairs. Further, the insured banks wouldn't take a loss even if AIG went bankrupt unless you buy the end-of-the-world systemic melt-down scenario. But, even if you believe that, why aren't all of AIG's creditors being asked to contribute? Indeed, why not everyone in the world, since all benefit from there being no global melt-down. The banks are not the primary beneficiaries of the bailout, the bondholders are - bondholders have no collateral. In essence, there is nothing for the fed to negotiate, so they abandon the effort.
So, back to Steve's question. AIG was going to go bankrupt without a bailout, and negotiating 80 cents on the dollar for its real estate positions would not have changed that either way - so no game of chicken. For political reasons, the decision was made to bail them out. The banks were not asked to pay a disproportionate amount towards that bailout, and intelligent minds can debate whether or not they should have, but the case is far from clear. Lastly, I will add that I am unconvinced that letting AIG go bankrupt would have created a systemic meltdown, but it is clear why those involved in the bailout would say that. It is human nature that when you make a convenient but unpopular choice, your first defense is likely to be that you didn't really have a choice. The choice to bailout AIG was convenient and unpopular, but I don't agree that it would have led to systemic meltdown, and the historical arguments on my side are quite strong. Panics happen every 10 to 20 years and it is never the end of the world.
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