Efficient Allocation via Sequential Scrip Auctions

We study the problem of allocating items to two agents with arbitrary valuation functions. Instead of actual money, we use sequential auctions with “scrip money”, i.e. money that has no value outside the auction. By considering such scrip auctions as a special case of more general bidding games, we show that there exists a natural pure subgame perfect Nash equilibrium (PSPE) with the following desirable properties: (a) agents’ utility is weakly monotone in their budget; (b) a Paretoefficient outcome is reached for any initial budget; and (c) for any Pareto-efficient outcome there is an initial budget s.t. this outcome is attained. In particular, we can assign the budget so as to implement the outcome with maximum social welfare, maximum Egalitarian welfare, etc. We provide an efficient algorithm to compute a PSPE in bidding games, and draw implications of the above result for various games and mechanism design problems.