The Efficiency of Resource Allocation Mechanisms for Budget-Constrained Users

We study the efficiency of mechanisms for allocating a divisible resource. Given scalar signals submitted by all users, such mechanism decides fraction resource that each user will receive and payment be collected from her. Users are self-interested aim to maximize their utility (defined as value they minus payment). Starting with seminal work Johari Tsitsiklis, long list papers studied price anarchy (in terms social welfare—the total users’ value) allocation variety rules. Here, we further assume has budget constraint invalidates strategies yield is higher than user’s budget. This subtle assumption, which arguably more realistic, constitutes traditional analysis meaningless set equilibria may change drastically welfare can arbitrarily far optimal. Instead, using liquid benchmark measures taking constraints into account. show tight bound 2 on well-known Kelly prove this result essentially best possible among multiuser mechanisms. comes in sharp contrast no-budget setting where there considerably outperform even achieve full efficiency. In our proofs, exploit particular structure worst-case games equilibria, also allows us design (nearly) optimal two-player solving simple differential equations.