CARL BERGSTROM intro’d it…

You want the strangest games from algorithmic game theory? Fine. Here’s a guided safari through the zoo where adding a road makes traffic worse, everyone pays even if they lose, and the “move” is emailing a lie with just enough math to make it incentive-compatible.

1) Selfish routing & paradox factories

• Pigou/Braess games: Each player routes on a network; latency depends on congestion. Add a zero-latency shortcut and everyone gets slower. Because humanity.
• Strange bit: Equilibria can be uniquely terrible. This is where the Price of Anarchy was born and raised.
• Tooling: Smoothness bounds and no-regret dynamics guarantee welfare ≥ 1/PoA under a buffet of behaviors, not just Nash.

2) Network creation games (a.k.a. pay-to-friend graphs)

• Setup: Nodes buy edges at cost α; distances then determine their cost.
• Weirdness: Equilibria flip between spindly trees and near-cliques as α changes. Everybody wants to be connected; nobody wants to pay.

3) Virus inoculation on graphs

• Setup: Each node pays C to inoculate or risks loss L if an infection percolates.
• Weirdness: Herd immunity becomes a selfish coordination mess with sharp thresholds. One cheapskate can make the whole component cry.

4) All-pay contests (war of attrition, Tullock)

• Setup: Everyone bids effort; everyone pays; only the top effort wins.
• Weirdness: Burning resources is rational. Equilibria are mixed and beautifully wasteful. Perfect for modeling, say, grant applications.