Sad-Loser Lottery

We consider lotteries with reimbursements. It turns out that without loss of generality it is enough analyze lotteries where the winner gets her expenses reimbursed. We find that such a lottery (Sad-Loser) has multiple pure-strategy equilibria. We describe all equilibria and discuss their properties. In particular, we find (1) a sufficient condition for the net total spending to be higher in the Sad-Loser lottery than in the standard lottery, (2) that the Exclusion Principle holds.