Round-robin tournaments with limited resources

We propose a theoretical model of round-robin tournament with limited resources motivated by the fact that in real-world sport tournaments, participating teams are sometimes forced to distribute their effort over multiple matches. assume have amount must be distributed between all matches tournament. outcome each match as first-price all-pay auction. The prizes awarded according ranking at end tournament, based on number wins. three is solved. In case identical budgets and low first prize, we find two types equilibria—‘effort-saving’ ‘burning-out’—both leading unequal payoffs; when prize large, families equilibria both equal non-equal payoffs. non-identical budgets, show there exist where team lower budget gets higher payoff than larger budget.