Golem in the Gears (33 page)

Then the timeless minute was done, and Grundy was a golem again. His insignificant little mind was reeling. Truly, the Demon did have a problem! He would never have understood it, had he not been in the Demon's sit- uation for that minute, for status was not a thing he had ever approached as a golem. Now he saw that the Demon was suffering in a manner that was, in its permutated

essence, similar to his. Among omnipotent entities, the Demon X(A/N)th was insignificant, and he didn't like it. Yes—now Grundy could understand. All that differed was the scale.

Meanwhile, the huge Demon face looked thoughtful. "I grasp your concern now, Golem," he said. "Your com- pass is infinitesmal, but your relative challenge is as great. Unlike me, you have a mechanism for solution."

"I do?" Grundy asked, surprised.

"All you require is the respect of a good woman—and you have that if you emerge from this situation."

Grundy realized that it was true. If he survived this, it would mean that he was victor in the trial—and he could lay claim to Rapunzel, who was eager to be claimed. The rapport with the elves had been hopelessly soured;

she would never voluntarily join that society now. With her respect, he needed that of no other person.

If he survived. But that remained unlikely. The Demon had taken up his challenge to exchange places for a min- ute, for the Demon was a creature of challenge, but that did not signify any further commitment.

Unless—

"Let me make you another challenge!" Grundy cried. "You give me my ambition if I show you how to get yours!"

The Demon, being almost omniscient, was not slow to catch on. "Done, Golem!"

So he had the deal that would solve his problem. There was only one flaw. He had no idea how to solve the Demon's problem.

"Urn, I'll need a little time to work it out..."

"I thought you might," the Demon agreed. "You shall have all the time you need, eternity if you wish. But one hour from now, if the deal has not been consummated, I

will confine you to the storage of the Brain Coral, and send the Sea Hag back to the surface."

Ouch! That would mean that the elves and Rapunzel would believe the Hag had won the trial, and by the time Grundy returned, if ever, it would be too late; Rapunzel would be the Hag. The Demon certainly knew how to generate incentive!

The Hag caught on. It was obvious that the Demon was fully aware of her nature and didn't care. "Maybe I can make a deal, too—" she started.

"Better quit while you're ahead," the Demon advised her.

She shut up. Obviously she was ahead; all she had to do was wait one hour, and Gmndy's default would send her to her victory.

Now the Demon's face became still, again resembling stone. But Grundy knew it would click back into ani- mation in exactly one hour. He had to come up with his solution to the Demon's problem in that time. Had to!

His mind, naturally, was blank. How could he think of anything that the Demon had not thought of long before? His intellect was the merest fraction of the Demon's! He was really just a prisoner, as was the Hag, with a chance to gain an advantage if he proved useful to the captor. If he failed, the other prisoner would have the advantage. Should he not have tried at all, so that neither of them returned to the surface? Prisoner's dilemma!

Prisoner's dilemma... that reminded him of some- thing. Bink had spent a lot of time in Mundania and brought back tidbits, and one of them was a riddle of two pris- oners, very like this one. One prisoner could get better treatment if he gave evidence against the other—but if the other did the same, both would be treated more harshly

than before. Both knew this. What, then, were they to do?

But enough of this distraction! He had a problem to work out. How could he help the Demon gain stature in the Demon society?

His mind went blank again. Then, idly, it returned to the prisoner's dilemma. If one prisoner knew the other would not give evidence, then he could afford to do it himself, and get better treatment without actually hurting the other. Still, if the other reasoned the same way—

Of course in this case the other prisoner was the Sea Hag, and he knew she would always do the most treach- erous thing. He could safely assume that she would give evidence against him. So his choice would be whether to keep quiet, and let her have the advantage, or to give evidence, so as to bring her down with him, as he had during the Lines and Boxes Trial.

The trouble with that was, it didn't bring him a victory. What he really wanted was to leave her here, while he returned to Rapunzel. So he had to solve the Demon's problem.

Then it came to him: could there be a prisoner's dilemma type of solution that would help the Demon? For the Demon's situation was in its fashion similar to Grundy's:

the Demon had to gain an advantage over his rival Demons, while they were trying to gain advantage over him. If there were a solution to the prisoner problem, it just might apply also to the Demon problem.

Well, suppose there were a strategy of play that would prevail, no matter what the other party did. One that the other party could catch on to and still not beat.

Suppose the moon weren't made of green cheese! He was dreaming of the impossible.

Yet, almost, he thought there could be something. After

all, there had been a winning strategy in the original lines and boxes game with the ant lion. That had required a
   
i surprise move, a sort of sacrifice, that changed the com- plex of the configuration. Something that seemed non- sensical, yet in retrospect made absolute sense.

Look at it this way, he told himself: if there was such a strategy, Grundy Golem could achieve his heart's desire. If not, he couldn't. So—there had to be such a strategy. All he needed to do was work it out.

He got to it, scratching lines and boxes and figures on the cavern floor. But no matter how he figured it, he couldn't see how he could get ahead of the Hag, who would never give him the slightest break. It simply wasn't there; the best he could do was to bring her down with him, so that both of them lost. Except that they wouldn't;

she would be granted the victory by default.

But then he realized that the Demon's situation differed from his in one important respect: there were more than two participants. Was it possible that the dynamics of several differed from the dynamics of two? So that what might be a losing strategy when going one-on-one could be a winning one when going one-on-several?

But each deal the Demon X(A/N)th made, Grundy remembered from his minute in the Demon's place, was one-on-one. First he interacted with one other Demon, then with another. Sometimes he gained a little against
  
| one, but then he lost more against another. So it reduced to one-on-one, and the loss continued, for it seemed that the other Demons were more cynical and rapacious than X(A/N)th, and nice guys finished last.

If only nice guys could finish first!

But maybe they could—

Then it burst upon him. Neither the nice-guy nor the nasty-guy strategy was best, because others took advan-

tage of the first and were out to get the second. What was needed was a tough-but-fair strategy that rewarded the nice guys and punished the nasty guys—and that the oth- ers know it.

Grundy scribbled some more. Suppose he tried Tough- But-Fair (TBF) against all other types? The always-nice would wash out quickly and drop out of the game, but how about the always-nasty? Could TBF beat the Nas- ties? It seemed to him that it was possible, if— "Time," the Demon announced. So soon! It had seemed like only a few minutes, but Grundy knew it really had been an hour, not a piece of a second more or less. "I—" "Have you the answer?" "I, uh, think so, but I need to test it—" "Certainly I wouldn't want to use an untested strat- egy," the Demon agreed wryly. "Test it now."

"I, uh, need several people, like me and the Hag—" "How many of each?" the Demon asked. "Well, a minimum of two. You see, the types—" Abruptly there were four people where there had been two. Grundy and the Hag each had a double. That wasn't exactly what Grundy had meant, but he was afraid that if he protested, the Demon would conclude he was stall- ing, and that could finish him. "Uh, yes, thank you. Now the rules—"

"You presume to dictate rules to me?" the Demon demanded.

"There have to be rules, to show how the game works, so that the strategy can operate," Grundy explained.

"Proceed."

"I think it's easiest if we use a point-scoring system. The complexities of Demon status are beyond human understanding, so—"

"True," the Demon agreed.

"So we can use simple-folk-minded numbers. But it will illustrate the underlying strategy—"

"Get on with it!"

"Uh, yes. Now the object is to score points. The one who scores the most points overall is the winner. So if my strategy always produces a winner—"

"You couldn't win anything, Golem!" one of the Prince Gimlet elves put in. "Everybody knows that!"

"Shut your puss. Hag!" the other Grundy snapped. "If everybody were here, they'd see you get your bottom

booted!"

Grundy discovered that he rather liked his double; the golem had a good way of expressing himself. But he wasn't certain whose bottom would get booted. "Uh—"

"Then let everybody see," the Demon decided.

Suddenly everybody was present. It was as if the cave had become a monstrous theater, with themselves in the center. In the front row sat King Dor and Queen Irene and little Ivy and Dolph and King Emeritus Trent and Queen Emeritus Iris and Bink and Chameleon and Ches- ter and Cherie Centaur and Amolde Centaur and every- one else who was anyone in Xanth, and in the rows behind sat Jordan and Threnody and Stanley Steamer and Snor- timer and everyone else who wasn't anyone, and farther back were all the other people and creatures who weren't quite classified yet. At the very most rear floated the glowering cloud Fracto. Most of them looked a bit star- tled, but none protested. All watched what had become the stage, and waited for Grundy's demonstration.

It had never occurred to Grundy to doubt the awesome power of the Demon X(A/N)th. But if it had, that doubt would have been obliterated in this instant. All the Magi- cians and Sorceresses and creatures and things of Xanth,

summoned here in the blink of an eye—and the Demon hadn't even blinked. All watching Grundy. Waiting for him to perform.

Suddenly he suffered a siege of stage fright. His tongue seemed to swell up and fill his mouth, and his jaws crys- tallized. All Xanth was watching!

"Hey, snap out of it!" his double whispered, nudging him. "You've got to show the winning strategy."

But Grundy stood frozen, overwhelmed by the enor- mity of it.

"He has no strategy!" an Elf-Hag said to the Demon. "Dump him in the Brain Coral's pool and send me back to the surface!"

"Send whom to the surface?" the other Elf-Prince demanded.

"Who asked you to butt in?" the first replied. Still Grundy was mute, conscious only of all those eyes upon him. He knew he was about to default his case and cost himself everything, but he just couldn't move or speak while he was the cynosure of this immense and important gathering.

Then a new voice cut through his self-immolation. "Oh, Grundy!"

Rapunzel! She was here too—and when he failed, she would pay the penalty as much as he!

His tongue shrank and his body unfroze. There was no way he could allow her to suffer like that!

"The object of this demonstration contest is to score points," he said. "The points vary according to the com- bination of decisions by the participants. Let's say that each person gives evidence against the other: in that case each will score one point."

"One point," one of the Hags said, suddenly paying

close attention. She wanted to be sure that he had no case that would satisfy the Demon.

"Now let's say that each person does not give evidence against the other," Grundy continued. "In that case each will score three points. They remain even, no advantage to either."

"Three points," the other Hag said.

"But suppose one prisoner gives evidence, and the other does not," Grundy concluded. "Then the one who gives it gets five points—and the other gets no points."

"Definitely!" both Hags agreed, licking their Princely lips. It was obvious that both intended to score five points.

"I have been losing points," the Demon murmured. "But that is merely the situation, not the solution. What is your strategy?"

"Let me show you," Grundy said. "Each of the four of us—two Golems and two Hags—will match off against the others. The Hags will of course give nothing away to anyone—"

"Naturally," the Hags agreed.

"While the other Golem will follow my strategy," he said. He glanced at the other. "You do know it?"

"Oh, sure. I'm your clone; I know everything you do."

"Good. Now let's do this one at a time, so the Demon can see clearly what happens. There will be several rounds to each match, to allow the strategy to manifest as some- thing other than chance. I will start off."

Grundy approached one of the Hags. He paused. "Oh— we'll need pieces of paper, and pencils, for—"