A Prize Worth Ten and Six
One prize is auctioned in a sealed-bid all-pay auction (both bidders pay their own bid; the higher bid wins; a tie is broken by a fair coin). Bidder 1 values the prize at 10 and bidder 2 values it at 6, and these values are common knowledge. Bids are real numbers at least 0. In the unique Nash equilibrium, what is the seller's expected total revenue? Give a reduced fraction.
Related problems & prerequisites
Worth solving first
- The Gap Between the Top Two 5.0/10
- Matching Pennies 5.0/10
- The Reserve That Reshapes Bids 5.0/10
Source: Complete-information all-pay auction analysed by Baye, Kovenock and de Vries (1996). Statement written for AxiomIQ.