Wednesday, June 27, 2007

The Greatest Game

Ah, Luger. The move of a few more Republicans to the side of sanity and light seems to have sent everyone into palpitations that we've – finally – reached the mythical tipping point. And normally I'd be right there along with them hoping against hope that morning might actually have broken. But maybe it's the unbearably sunny weather outside my window or maybe it's the 3rd degree burns lingering from the last time I bought into the optimistic view but I don't buy it. I've learned, the hard way, September never ends. This isn't signaling the end of the great wall of Republican opposition. It's a few opportunistic politicians trying to rearrange the deck chairs of their own, personal Titanics.

However, someone said the magic words. And made the mistake of invoking the specter of my beloved game theory. Not that I'm an expert or anything. Just someone who plays a lot of games and has long taken an interest in finding any and every advantage to be had. So, I find having some passing familiarity with game theory helpful. Being able to reduce decisions to a series of logical outcomes or to match them to framework templates can be a tremendous advantage. So, allow me to take a crack at Mr. Marshall's paradoxical phalanx of Republican support for the President's policies. Not because I'm particularly well suited to it but because the problem – and the solution – intrigues me.

The game we're playing here is, in fact, Chicken. Not between the President and Republican officials. But the board laid out in Congress itself is a big, iterative, multiplayer version of Chicken. But in this game of Hawks and Doves, votes cast are the moves and the stakes are influence, political capitol, and, incidentally, the fate of the nation.

Now, Chicken is a game the simple version of which probably everyone knows. If not, well, imagine two cars speeding towards each other. The only plays are to stay on course or swerve away. And the only way to win – beyond, you know, not playing – is to be the car that never deviates from a straight line while your opponent wimps out and clears your way. There are, then, four different pay out states. The one where you win – you go straight and your opponent doesn't. The one where you tie – both players swerve. And two where you lose. The first where you swerve and your opponent doesn't. And the second where both cars go straight and crash headlong into each other resulting in catastrophic failure for both players.

But what I mean when I say we're playing Chicken here is that we have a game with mutually exclusive winning states. In the case of this legislative showdown (And, yeah, be warned because I'm going to vastly oversimplify here.) you can either vote to end the war or to continue it – there's no middle ground. And strategies of mutual cooperation – both cars electing to swerve – are undesirable. The maximum payoff in a game of Chicken comes from getting your opponent to defer but that runs the risk of the mutually catastrophic failure. To me and, I'd think, a lot of others, this is a game of Chicken because we're playing with the future viability of our ship of state. Conservatives believe we're in an existential conflict and cannot veer from our course or risk, you know, dhimitude. Liberals, like myself, believe we're engaged in a foolhardy and wasteful conflict and will throw away whatever remains of our international prestige and reputation if we continue on our current course of pissing our country away. Neither side can accomplish anything unless the other side relents. One has to bend but if neither side does then ruination follows for both.

It's multiplayer because the classic version features only a pair of players. Here, we have all 535 members of Congress involved. That's a problem because game theory isn't very advanced (or accurate) when it comes to dealing with multi-agent problems. Especially ones where rational actions and the resulting perfect plays aren't quite assured. It gets messy quickly. But one way it's dealt with is the idea of teams – known as coalitions in game theory – or groups of players that act with coordinated interests. And that translates nicely to the various political parties and voting blocks at play here.

And it's iterative because there's more than one round being played. Which sounds odd if you're thinking of the classical game of chicken where if the two cars crash it's all over. But, if instead of catastrophic failure we represent the situation where both sides elect to maintain their current course as a penalty rather than the game ending, that might make more sense. Hence, we get a game where each round being played affects the overall score. If, say, we assign a value of 1 point for winning and a penalty of -10 for “crashing” we'd have a payout matrix for each round that looks like this:

Player B
Swerves Aside

Player B
Goes Straight

Player A
Swerves Aside


0, +1

Player A
Goes Straight



These values are, of course, arbitrary and could easily be something else. But the point is that “winning” provides only a slight gain while “crashing” is extremely costly (Here, one round where you risk going straight and your opponent doesn't defer and you've set yourself back ten rounds worth of wins. Of course, so has your opponent but that's not your concern if you're playing entirely rationally.) and a state to be avoided. But a state that's hard to avoid because the only way to gain a winning score is to risk that penalty.

And, again, we're simplifying here because that's how we can apply logic and decision making gates to the swirling chaos of real life. If you extend the game out, add in different point payoffs and penalties to go along with providing different options – the same way you can extend Rock, Paper, Scissors by adding new signs to throw – then you get something more closely approaching reality.

Here's how I picture the abstract. There are two vehicle that have been built in the Congress – one for the war, one against it – on opposite sides of a very narrow track. And all the players in this little drama line up behind one car or the other and push it. The sum total of all those vectors is the direction of the car. Each side can either crash their cars into each other or work to shift their car to avoid their opponents. But swerving out of the way on the narrow track lands them in the ditch along side of it. While, of course, running into each other means they have to pick up the shattered pieces, rebuild, and try again. Winning is a matter not just of making your opponent swerve first but also of having more momentum than your opponent (Letting them bowl over and through the other car. Read: Public opinion here.) or of having more undamaged pieces to continually rebuild with (Letting them win the slow and steady war of attrition. Read: political capitol here.). And it's also conceivable that it's possible to squeeze each car past each other (Read: bipartisan compromise) though extremely unlikely. Like a game of staring into the sun, the best way to get ahead is to get your opponent to blink first.

But whatever game it is we're playing, what Mr. Marshall is talking about is a change in the game's equilibrium. A game that has a limited move set only has a certain number of states to be in regardless of how many rounds it's played (There are four, for example, in Chicken – Draw, Player Wins, Opponent Wins, and Both Lose Big.) and among those potential states there are certain positions that are more beneficial than others – for each player, the states where they win more than they lose. In game theory, each round the players make a move, attempting to make the best move possible – known as making a best response – to either move the game into a more advantageous state or keep it in the previous state which they found acceptable. The case where every player sees no reason to shift the game's state is called equilibrium (The - game theory – famous Nash equilibrium is the one this really is true. It's defined as the point where, if everyone plays the same way as they just did, you and every other player gain nothing from changing their own play.). It's a stable state that results in a game being frozen, as it were, as all plays will be the same no matter how many additional rounds are played.

The game state persists to infinity, however, only if it's taken for granted that every play is made rationally. One player randomly changing their move to something less advantageous would be, well, insane, but it alters the evaluation of every other player potentially resulting in a different outcome. As well, outside information can alter the perspective of players. If, for example, in the classic Prisoner's Dilemma game, you know that you're playing the final round of the game against an opponent who retaliates if you attempt to harm them then your best move is to always screw over your opponent – because they won't have any chance for payback in the next round. Or, if for instance, someone passed you your opponent's top secret game plan – the strategy they intended to follow for each and every round – then you'd have a reason to act irrationally and make moves that, logically, might not be in your best interest but will, in reality, both block your opponents move and benefit your own position.

Such moves, though, require a knowledge outside of the game. Of what's known as the metagame. Like bluffing in poker, they require you to not just read what's on the table but your opponents around it. And their past actions. And the game of Chicken is all about the metagame. You want to make your opponent swerve before you lose your own resolve. It's the only way to consistently win.

Interestingly, Chicken is also a game where you're actually better off reducing your options. If your opponent believes you're never going to swerve then they can either suicidally charge into you or they can wisely step out of your way and concede the points. Eliminating any possibility that you're going to swerve yourself means you vastly reduce the chances that your opponent won't (Barring irrational actions, of course. You don't want to run into that stubborn bastard who'll wreck his car just to prove a point, right? However, if we're talking about a game with points – a war of attrition, say – then sometimes the rational action is to charge into your opponent to establish that you won't swerve. It hurts your position in the short term and, thus, isn't a best response, but it helps your position over the long term. And that's where game theory starts to fall apart, at least as I understand it.). This can work against you, though, as it cuts both ways. If your opponent believes you're always going to swerve they've got no reason to divert their own course. They can charge forward and win every single time. Which is why, by the way, the Democrats strategies in the last round of showdowns over the war were so stupid. They shot themselves in the foot by showing, from the start, that they were going to blink first. That left the Republicans free to, in so many words, rip the steering wheel from their car and put the pedal to the metal.

And when, as happens with this reality, you have some factor that upsets the equilibrium what happens is a realignment of the game board. Mr. Marshall is correct when he says there's safety in numbers for the Republicans. As long as their coalition hangs together, as long as they vote the same way, then the game state continues to be in a state of equilibrium that's favorable to them. But as soon as that coalition breaks apart then the game can tip over to a new state. It can either reach a state where one side has won or devolve into a new equilibrium which can be better or worse than the previous one. How? Well, it's all very Pareto.

And this shift in the attitudes of a handful of Republican representatives might, indeed, signal such a phase change. And if enough Republicans think the state of the game has actually changed then, yes, there's going to be a rush to get through the door and play their chips, as it were, in a way that preserves their fading advantages. If it ever looks like there will be a successful vote against the President's policies here then, yeah, game theory says you should see a rats leaving a sinking ship effect here. But until that tipping point is reached, the benefits of staying pat outweigh the risk of shifting states and the game's in equilibrium.

The problem with this game (Beyond the ingrained defensive crouch reducing Democratic strategies before the pieces are even doled out.) is that no one knows exactly what are the rules to this game. It's changing, shifting, and it's eminently possible that the Republicans have convinced themselves they're playing a different game entirely. Some version of Pesky Brother, maybe (Which is a game where, say, you and your little brother both have coins which they flip, heads or tails in secret and then reveal the faces to each other. If they match, your bratty little brother owes you a buck. If they don't, you put a dollar in his grubby little mitts. The proper move in such a game is to just go completely random. There's no best response possible so just flip your coin and take your chances with luck. It's, you know, Morra. In other words, it's a game where there is no good move and the only move is to do the opposite of what your opponent wants.). And that means they're operating under an entirely different set of logical conclusions and imperatives.

And, if we're being really nasty then it's also possible that the liberal view of this as a game of Chicken is wrong as well. That there aren't mutually exclusive winning states but, instead, beneficial states that arise from cooperation. That we're really playing a complicated game of Prisoner's Dilemma and the metamove is to convince everyone playing that reaching a compromise is going to be better off for everyone involved. That way, however, lays the madness of High Broderism. And, thus, I reject it soundly.

No, the stakes here are real. And there's no potential for a compromise to be a viable game state. And the only logical course here is to keep increasing the apparent potential rewards for those players in the opposing coalition to alter their play which strengthens, reinforces our own position and creates an opportunity to tip the game from equilibrium into an advantageous derivative state. To, in short, peel off more Republican votes.

Or, to put it another way, to keep playing the hand we've been dealt.

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