Budget-balanced Mechanisms Research Articles

Worst-case efficient and budget-balanced mechanism for single-object allocation with interdependent values

Worst-case efficient and budget-balanced mechanism for single-object allocation with interdependent values

Incentive-compatible and budget balanced AGV mechanism for peer-to-peer energy trading in smart grids

Peer-to-peer (P2P) energy trading refers to a type of decentralized transaction, where the energy from distributed energy resources is directly traded between peers. A key challenge in peer-to-peer energy trading is designing a safe, efficient, and transparent trading model and operating mechanism. In this study, we consider a P2P trading environment based on blockchain technology, where prosumers can submit bids or offers without knowing the reports of others. We propose an Arrow-d’Aspremont-Gerard-Varet (AGV)-based mechanism to encourage prosumers to submit their real reserve price and determine the P2P transaction price. We demonstrate that the AGV mechanism can achieve Bayesian incentive compatibility and budget balance. Kernel density estimation (KDE) is used to derive the prior distribution from the historical bid/offer information of the agents. Case studies are carried out to analyze and evaluate the proposed mechanism. Simulation results verify the effectiveness of the proposed mechanism in guiding agents to report the true reserve price while maximizing social welfare. Moreover, we discuss the advantages of budget balance for decentralized trading by comparing the Vickrey-Clarke-Groves (VCG) and AGV mechanisms.

Mechanism design for decentralized peer-to-peer energy trading considering heterogeneous preferences

The bottom-up evolution of power systems demonstrates that the integrated decentralized grid is a compelling vision of the future distribution grid. Hence, the concept of fully decentralized peer-to-peer (P2P) energy markets allows the prosumers to directly trade electricity among each other and makes them one step closer to be independent from upstream generation. To this end, an appropriate market mechanism should be designed to not only the prosumers get encouraged to participate in the market but prosumers’ preferences get taken into consideration. In this paper, a fully decentralized market mechanism is designed in which the preferences of prosumers including willingness to trade green energy, trading partner’s reputation and location in the network are taken into account. Prosumers check other peers’ attributes and select the one who satisfies their preferences the most. The designed market mechanism satisfies market properties involving balanced budget, individual rationality, and Bayesian-Nash incentive compatibility. Prosumers with excess/shortage of power are motivated to individually participate in the market while preserving their privacy. Simulation results verify the effectiveness of the proposed mechanism and premiums in the matching pattern and achieving the desired outcome for prosumers over the course of a day. • A decentralized P2P energy trading considering heterogeneous preferences of prosumers. • Introducing premium coefficients to include prosumers preferences in energy trading. • Designing a budget balanced, individually rational and incentive compatible mechanism.

The river sharing problem with incomplete information

This paper considers the river sharing problem with incomplete information. We ask whether the efficient allocation of water in a river network is possible when agents have private information on their satiation levels. First, we introduce a trading model on a tree network with incomplete information. Then, we focus on the river sharing problem for a three-agent river network in which water flows from two upstream agents to one downstream agent. We assume that each agent has a satiation point and this satiation point is his private information. We are interested in allocation mechanisms that map each profile of the satiation points to an allocation of water and a list of monetary transfers between the agents. We show that, if each upstream agent’s endowment of water is sufficiently larger than the downstream agent’s endowment, then there exists an incentive compatible, individually rational, and budget balanced mechanism that allocates the water efficiently.

Undominated mechanisms and the provision of a pure public good in two agent economies.

We revisit the problem of providing a pure public good in economies involving two agents, under the assumption that preferences are quasilinear. We characterize the class of strategy-proof, anonymous and feasible mechanisms that are not dominated by another strategy-proof, anonymous and feasible mechanism. Mechanisms that decide, at some profiles of preferences, against the alternative that is preferred by all agents are members of this class. On the contrary, Groves mechanisms, with the sole exception of the Pivotal mechanism, are not. Finally, the only budget-balanced mechanism that belongs to this class is the Unanimity mechanism.

A Dynamic Budget-balanced Integration Mechanism for LQG Power Networks with Individual Preferences

A Dynamic Budget-balanced Integration Mechanism for LQG Power Networks with Individual Preferences

Approximately Efficient Two-Sided Combinatorial Auctions

We develop and extend a line of recent work on the design of mechanisms for two-sided markets. The markets we consider consist of buyers and sellers of a number of items, and the aim of a mechanism is to improve the social welfare by arranging purchases and sales of the items. A mechanism is given prior distributions on the agents’ valuations of the items, but not the actual valuations; thus, the aim is to maximise the expected social welfare over these distributions. As in previous work, we are interested in the worst-case ratio between the social welfare achieved by a truthful mechanism and the best social welfare possible. Our main result is an incentive compatible and budget balanced constant-factor approximation mechanism in a setting where buyers have XOS valuations and sellers’ valuations are additive. This is the first such approximation mechanism for a two-sided market setting where the agents have combinatorial valuation functions. To achieve this result, we introduce a more general kind of demand query that seems to be needed in this situation. In the simpler case that sellers have unit supply (each having just one item to sell), we give a new mechanism whose welfare guarantee improves on a recent one in the literature. We also introduce a more demanding version of the strong budget balance (SBB) criterion, aimed at ruling out certain “unnatural” transactions satisfied by SBB. We show that the stronger version is satisfied by our mechanisms.

Optimal budget-balanced ranking mechanisms to assign identical objects

Strategy-proof and budget-balanced ranking mechanisms assign q units of an object to n agents. The efficiency loss is the largest ratio of surplus loss to efficient surplus, over all profiles of nonnegative valuations. The smallest efficiency loss is achieved by the following allocation rule: for $$q\le \lfloor \frac{n}{2}\rfloor $$ , assign one object to each of the $$q-1$$ top ranked agents, a substantial probability of one object to the qth ranked agent, and distribute the remaining probability equally to a group of agents ranked behind the qth agent; for $$q>\lfloor \frac{n}{2}\rfloor $$ , assign a small probability to the $$(q+1)$$ th ranked agent, an equally substantial probability to a group of agents ranked immediately before the $$(q+1)$$ th agent, and one object to each of the agent ranked before the group. In both cases, the size of the “equal group” depends on q and n. Suppose $$\frac{q}{n}$$ is fixed and $$\frac{q}{n}\ne \frac{1}{2}$$ , then as q and n increase, the smallest efficiency loss tends to zero exponentially. Participation is voluntary in the above mechanisms only when q is smaller than a threshold that depends on n.

Mechanism design with ambiguous transfers: An analysis in finite dimensional naive type spaces

This paper introduces ambiguous transfers to the problems of full surplus extraction and implementation in finite dimensional naive type spaces. The mechanism designer commits to one transfer rule but informs agents of a set of potential ones. Without knowing the adopted transfer rule, agents are assumed to make decisions based on the worst-case expected payoffs. A key condition in this paper is the Beliefs Determine Preferences (BDP) property, which requires an agent to hold distinct beliefs about others' information under different types. We show that full surplus extraction can be guaranteed via ambiguous transfers if and only if the BDP property is satisfied by all agents. When agents' beliefs can be generated by a common prior, all efficient allocations are implementable via individually rational and budget-balanced mechanisms with ambiguous transfers if and only if the BDP property holds for all agents. This necessary and sufficient condition is weaker than those for full surplus extraction and implementation via Bayesian mechanisms. Therefore, ambiguous transfers may achieve first-best outcomes that are impossible under the standard approach. In particular, with ambiguous transfers, efficient allocations become implementable generically in two-agent problems, a result that does not hold under a Bayesian framework.

Efficiency and budget balance in general quasi-linear domains

We consider efficiency and budget balance in general quasi-linear domains. Green and Laffont (1979) proved that one cannot generically achieve both. We consider strategyproof budget-balanced mechanisms with bounded valuations that are approximately efficient. We show that a deterministic, strategyproof, and budget-balanced mechanism must have a sink whose valuation is ignored in the decision, and is compensated with all the leftover money. We find a tight lower bound on the inefficiencies of strategyproof, budget-balanced mechanisms using this result. The bound shows that the inefficiency asymptotically disappears when the number of agents is large—we provide worst-case bounds and the best possible rate of convergence.We provide results for convex combination of inefficiency and budget imbalance and for randomized mechanisms. Experiments with real data from two applications show that the inefficiency for a simple randomized mechanism is 5–100 times smaller than the worst case.

Mechanism Design for Resource Allocation in Networks With Intergroup Competition and Intragroup Sharing

We consider a network where strategic agents, who are contesting for allocation of resources, are divided into fixed groups. The network control protocol is such that within each group agents get to share the resource and across groups they contest for it. A prototypical example is the allocation of data rate on a network with the multicast/multirate architecture. Compared to the unicast architecture (which is a special case), the multicast/multirate architecture can result in substantial bandwidth savings. However, design of a market mechanism in such a scenario requires dealing with both private and public good problems as opposed to just private goods in unicast. The mechanism proposed in this paper ensures that social welfare maximizing allocation on such a network is realized at all Nash equilibria (NE), i.e., full implementation in NE. In addition it is individually rational, i.e., agents have an incentive to participate in the mechanism. The mechanism, which is constructed in a quasi-systematic way starting from the dual of the centralized problem, has a number of useful properties. Specifically, due to a novel allocation scheme, namely “radial projection,” the proposed mechanism results in feasible allocation even off equilibrium. This is a practical necessity for any realistic mechanism since agents have to “learn” the NE through a dynamic process. Finally, it is shown how strong budget balance at equilibrium can be achieved with a minimal increase in message space as an add-on to a weakly budget balanced mechanism.

Robust trading mechanisms with budget surplus and partial trade

In a bilateral bargaining problem with private values, Hagerty and Rogerson (J Econ Theory 42(1):94–107, 1987) showed that essentially all dominant strategy incentive compatible, ex post individually rational, and budget balanced mechanisms are posted-price mechanisms, where a price is drawn from a distribution, and trade occurs if both players benefit from trading at this price. In this paper, we demonstrate a feasible bargaining mechanism that yields more ex ante gains from trade than any posted-price (budget balanced) mechanism.

Envy-free and budget-balanced assignment of identical objects

Strategy-proof, budget-balanced, and envy-free rank mechanisms assign q identical objects to n agents. The efficiency loss is the largest ratio of surplus loss to efficient surplus, over all profiles of non-zero valuations. The smallest efficiency loss $$\frac{n-q}{n^{2}-n}$$ is uniquely achieved by the following simple allocation rule: assign one object to each of the $$q-1$$ agents with the highest valuations, a large probability to the agent with the qth highest valuation, and the remaining probability to the agent with the $$(q+1)$$ th highest valuation.

A simple budget-balanced mechanism

In the private values single object auction model, we construct a satisfactory mechanism—a dominant strategy incentive compatible and budget-balanced mechanism satisfying equal treatment of equals. Our mechanism allocates the object with positive probability to only those agents who have the highest value and satisfies ex-post individual rationality. This probability is at least $$(1-\frac{2}{n})$$ , where n is the number of agents. Hence, our mechanism converges to efficiency at a linear rate as the number of agents grow. Our mechanism has a simple interpretation: a fixed allocation probability is allocated using a second-price Vickrey auction whose revenue is redistributed among all the agents in a simple way. We show that our mechanism maximizes utilitarian welfare among all satisfactory mechanisms that allocate the object only to the highest-valued agents.

Balanced ranking mechanisms

In the private values single object auction model, we construct a satisfactory mechanism – a symmetric, dominant strategy incentive compatible, and budget-balanced mechanism. The mechanism converges to efficiency at an exponential rate. It allocates the object to the highest valued agent with more than 99% probability provided there are at least 14 agents. It is also ex-post individually rational. We show that our mechanism is optimal in a restricted class of satisfactory ranking mechanisms. Since achieving efficiency through a dominant strategy incentive compatible and budget-balanced mechanism is impossible in this model, our results illustrate the limits of this impossibility.

Almost budget balanced mechanisms with scalar bids for allocation of a divisible good

This paper is about allocation of an infinitely divisible good to several rational and strategic agents. The allocation is done by a social planner who has limited information because the agents’ valuation functions are taken to be private information known only to the respective agents. We allow only a scalar signal, called a bid, from each agent to the social planner. Yang and Hajek [Yang, S., Hajek, B., 2007. “VCG-Kelly mechanisms for allocation of divisible goods: Adapting VCG mechanisms to one-dimensional signals”, IEEE Journal on Selected Areas in Communications 25 (6), 1237–1243.] and Johari and Tsitsiklis [Johari, R., Tsitsiklis, J. N., 2009. “Efficiency of scalar-parameterized mechanisms”, Operations Research 57 (4), 823–839.] proposed a scalar strategy Vickrey–Clarke–Groves (SSVCG) mechanism with efficient Nash equilibria. We consider a setting where the social planner desires minimal budget surplus. Example situations include fair sharing of Internet resources and auctioning of certain public goods where revenue maximization is not a consideration. Under the SSVCG framework, we propose a mechanism that is efficient and comes close to budget balance by returning much of the payments back to the agents in the form of rebates. We identify a design criterion for almost budget balance, impose feasibility and voluntary participation constraints, simplify the constraints, and arrive at a convex optimization problem to identify the parameters of the rebate functions. The convex optimization problem has a linear objective function and a continuum of linear constraints. We propose a solution method that involves a finite number of constraints, and identify the number of samples sufficient for a good approximation.

Mechanism Design with Ambiguous Transfers

This paper introduces ambiguous transfers to study the (partial) implementation problem. We show that under all profiles of utility functions, any efficient allocation rule is implementable via an individually rational and budget-balanced mechanism with ambiguous transfers, if and only if the Beliefs Determine Preferences (BDP) property is satisfied by all agents. This property holds generically when there are at least two agents. It is weaker than the necessary and sufficient conditions for implementation via a Bayesian mechanism. Therefore, ambiguous transfers may provide a solution for situations where Bayesian mechanism design is impossible. In particular, efficiency becomes achievable generically in two-agent problems, which contrasts the impossibility results in the literature.

Is Shapley cost sharing optimal?

A general approach to the design of budget-balanced cost-sharing mechanisms is to use the Shapley value, applied to the given cost function, to define payments from the players to the mechanism. Is the corresponding Shapley value mechanism “optimal” in some sense? We consider the objective of minimizing worst-case inefficiency subject to a revenue constraint, and prove results in three different regimes. First, for the public excludable good problem, the Shapley value mechanism minimizes the worst-case efficiency loss over all truthful, deterministic, and budget-balanced mechanisms that satisfy equal treatment. Second, even with randomization and approximate budget-balance allowed and dropping equal treatment, the worst-case efficiency loss of the Shapley value mechanism is within a constant factor of the minimum possible. Third, for no-deficit mechanisms, we prove a general positive result: for every monotone cost function, a suitable blend of the VCG and Shapley value mechanisms is no-deficit and enjoys good approximate efficiency guarantees.

Optimal allocation of an indivisible good

In this paper, we consider the problem of allocating an indivisible good efficiently between two agents with monetary transfers. We focus on allocation mechanisms that are dominant-strategy incentive compatible when agents' types are private information. Inefficiency of an allocation mechanism may come from two sources: misallocation of the indivisible good and an imbalanced budget. Unfortunately, as Green and Laffont (1979) demonstrate, no allocation mechanism can always overcome both kinds of inefficiency. We identify allocation mechanisms that maximize the expected total utilities of agents, and characterize optimal mechanisms for a large class of agents' type distributions. For strongly regular type distributions, we show that the optimal mechanisms must be budget-balanced: they are either fixed-price mechanisms or option mechanisms. The result may not hold for other type distributions. For certain type distributions, we show that optimal mechanisms are hybrids of Vickrey–Clarke–Groves mechanisms and budget-balanced mechanisms.

Search costs and the severity of adverse selection

In view of some recent empirical evidence, I suggest a relationship between the magnitude of search costs and the severity of adverse selection in the context of a dynamic model with asymmetric information. In markets with small search costs sellers with low quality products misrepresent their quality and demand a high price. If search costs are not negligible, sellers׳ price offers are truthful and all product qualities are traded over time. In markets with small search costs, a budget balanced mechanism can mitigate adverse selection: sellers should pay a per period market participation tax and receive a rebate after trading.