The Riddled Auction

All three bid their true valuations: Raj ₹5,000, Simi ₹8,000, Tanu ₹6,000. Simi wins and pays the second-highest bid of ₹6,000 (Tanu's bid), earning a profit of ₹2,000. Truthful bidding is the dominant strategy in any second-price auction.

The Vickrey auction has the remarkable property of making truthful bidding a dominant strategy — optimal regardless of what others do. This incentive-compatibility is why second-price auctions are used in practice. Step 1: Consider Simi's decision (valuation ₹8,000). Should she bid her true value? Step 2: If Simi bids below ₹8,000 (say ₹7,000): she might lose to someone bidding ₹7,500 — a loss she could have prevented by bidding higher. The price she pays is still determined by others' bids, not her bid. No benefit from underbidding. Step 3: If Simi bids above ₹8,000 (say ₹9,000): she wins more often, but if the second-highest bid is ₹8,500, she pays ₹8,500 — more than her valuation. She gets negative profit. No benefit from overbidding. Step 4: Bidding exactly ₹8,000 is weakly dominant: if she wins, the price she pays is determined by others and is always ≤ second-highest bid ≤ her valuation. Same logic applies to Raj and Tanu. Step 5: Result: Raj bids ₹5,000, Simi bids ₹8,000, Tanu bids ₹6,000. Highest bidder = Simi. Second-highest = Tanu's ₹6,000. Simi pays ₹6,000. Profit = ₹2,000. Step 6: Social outcome: the painting goes to the person who values it most (Simi at ₹8,000) — this is allocative efficiency. The Vickrey auction achieves efficiency and truthfulness simultaneously. Key Insight: The second-price auction is one of economics' most elegant mechanisms: by separating the bid from the payment, it removes the incentive to shade bids downward. The payment you make is never affected by your own bid (as long as you win) — it is always someone else's bid. This makes honesty the uniquely rational strategy.