An anonymous reader writes: *Now that the airlines are done with it, your suitcase looks like a gorilla stomped on it. The antique vase you'd packed so carefully is smashed. *

Never fear, the airline representative reassures you. The airline will reimburse you for the value of the vase. You just have to agree on what it's worth, and the representative has a scheme to figure it out. One of your fellow passengers, it turns out, had an identical vase, which is now identically smashed. Each of you will say what you think the vase is worth, between $2 and $100. If the two prices are the same, the representative will assume you're telling the truth. If the values differ, he'll figure the lower value is accurate and reimburse each of you that amount — with a $2 bonus for "honesty" for the lower bidder and a $2 penalty for the higher one.

What will you say the vase is worth?

Believe it or not, according to game theory, you're best off bidding $2. But of course, no one is dumb enough to do that. The question is, how does game theory need to be patched up to make it give the right predictions? Someone has a new proposal. Instead of assuming our opponents are selfish and rational (as game theory traditionally does), we assume that different people behave with different personae. The approach has the potential to solve many other game theory paradoxes, too.