Maximizing social welfare in congestion games via redistribution

It is well-known that efficient use of congestible resources can be achieved via marginal pricing; however, payments collected from the agents generate a budget surplus, which reduces social welfare. We show that an asymptotically first-best solution in the number of agents can be achieved by the appropriate redistribution of the budget surplus back to the agents

Task Assignment with Autonomous and Controlled Agents

We analyse assignment problems in which not all agents are controlled by the central planner. The autonomous agents search for vacant tasks guided by their own preference orders defined over subsets of the available tasks. The goal of the central planner is to maximise the total value of the assignment, taking into account the behaviour of the uncontrolled agents. This setting can be found in numerous real-world situations, ranging from organisational economics to "crowdsourcing" and disaster response. We introduce the Disjunctively Constrained Knapsack Game and show that its unique Nash equilibrium reveals the optimal assignment for the controlled agents. This result allows us to find the solution of the problem using mathematical programming techniques.

Redistribution in Online Mechanisms

Following previous work on payment redistribution in static mechanisms, we develop the theory of redistribution in online mechanisms (e.g., [2, 10, 8]). In static mechanisms, redistribution is important as it increases social welfare in scenarios with no residual claimant. Many online scenarios also do not have a natural residual claimant, and redistribution there is equally important. In this work, we adopt a fundamental online mechanism design model where a single expiring item is allocated in each of T periods. Agents with unit demand are present in the market between their arrival and departure periods, which are private information along with the value an agent attributes to the item. For this model, we derive a number of properties characterizing redistribution in online mechanisms (including revenue monotonicity properties, and quantifying the effect an agent can have on the total revenue). We then design two redistribution functions. The first one generalizes the static redistribution proposed by Cavallo [2] making redistribution after the departure of the last agent. For this redistribution function we provide theoretical worst-case guarantees. The second function is truly online making redistribution to each agent on her departure. The performance of both functions is evaluated using numerical simulations. Copyright © 2013, International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved

Destroy to save

We study the problem of allocating m identical items among n > m agents with unit demand and private value for consuming the good. We allow payments and focus on dominant-strategy implementation. In the absence of an auctioneer who can absorb payments collected from the agents, the payments must be burnt to support dominant-strategy implementation. Recent work modified the classic VCG mechanism by redistributing as much of the payments as possible back to the agents while still satisfying incentive constraints. This approach guarantees allocative efficiency, but in some cases a large percentage of social welfare is lost. In this paper, we provide a mechanism that is not allocatively efficient but is instead guaranteed to achieve at least 80% of the social welfare as n -> [...] Moreover, in the extreme case of m = n - 1 where VCG-based mechanisms provide zero welfare, the percentage of social welfare maintained by our mechanism asymptotically approaches 100%

Efficient regret bounds for online bid optimisation in budget-limited sponsored search auctions

We study the problem of an advertising agent who needs to intelligently distribute her budget across a sequence of online keyword bidding auctions. We assume the closing price of each auction is governed by the same unknown distribution, and study the problem of making provably optimal bidding decisions. Learning the distribution is done under censored observations, i.e. the closing price of an auction is revealed only if the bid we place is above it. We consider three algorithms, namely ε—First, Greedy Product-Limit (GPL) and LuekerLearn, respectively, and we show that these algorithms provably achieve Hannan-consistency. In particular, we show that the regret bound of ε—First is at most O(T⅔) with high probability. For the other two algorithms, we first prove that, by using a censored data distribution estimator proposed by Zeng [19], the empirical distribution of the closing market price converges in probability to its true distribution with a O(1/√t) rate, where t is the number of updates. Based on this result, we prove that both GPL and LuekerLearn achieve O(√T) regret bound with high probability. This in fact provides an affirmative answer to the research question raised in [1]. We also evaluate the abovementioned algorithms using real bidding data, and show that although GPL achieves the best performance on average (up to 90% of the optimal solution), its long running time may limit its suitability in practice. By contrast, LuekerLearn and ε— First proposed in this paper achieve up to 85% of the optimal, but with an exponential reduction in computational complexity (a saving up to 95%, compared to GPL)

Optimal payments in dominant-strategy mechanisms for single-parameter domains

We study dominant-strategy mechanisms in allocation domains where agents have one-dimensional types and quasilinear utilities. Taking an allocation function as an input, we present an algorithmic technique for finding optimal payments in a class of mechanism design problems, including utilitarian and egalitarian allocation of homogeneous items with nondecreasing marginal costs. Our results link optimality of payment functions to a geometric condition involving triangulations of polytopes. When this condition is satisfied, we constructively show the existence of an optimal payment function that is piecewise linear in agent types

Optimizing payments in dominant-strategy mechanisms for multi-parameter domains

In AI research, mechanism design is typically used to allocate tasks and resources to agents holding private information about their values for possible allocations. In this context, optimizing payments within the Groves class has recently received much attention, mostly under the assumption that agent’s private information is single-dimensional. Our work tackles this problem in multi-parameter domains. Specifically, we develop a generic technique to look for a best Groves mechanism for any given mechanism design problem. Our method is based on partitioning the spaces of agent values and payment functions into regions, on each of which we are able to define a feasible linear payment function. Under certain geometric conditions on partitions of the two spaces this function is optimal. We illustrate our method by applyingit to the problem of allocating heterogeneous items

Select problems at the intersection of computer science and economics

We apply computer science techniques to try to solve a selection of problems that arise in economics and electronic commerce. The problems we address and our results are summarized below. The first problem is from the field of Mechanism Design. The goal is to find a procedure for allocating identical items among agents with private values in the manner that maximizes the total utility of the agents. We approach this problem computationally: solutions are found algorithmically rather than through mathematical derivations. Our computational approach yields a nearly optimal solution greatly improving prior results. In the case with 3 agents and 2 items, we were able to find a provably optimal solution. Next, we address a game-theoretic problem of finding Nash Equilibria in auctions. We investigate when a computational procedure finds an equilibrium in first and second price auctions with discrete bids and values. The rest of the thesis is devoted to automated decision making in electronic commerce domains. Three domains are considered: sponsored search, supply chain management, and simultaneous auctions. The last two domains are studied in the context of the SCM and Travel divisions of the Trading Agent Competition (TAC). Our contributions to automated decision making are both practical and theoretical. On the practical side, the bidding strategy we designed for sponsored search auctions is currently being used by a large advertiser. Our work on TAC Travel culminated in winning the competition in 2006. In the TAC SCM competition, the agent we built was among the top 5 out of over 20 agents almost every year of the competition. For theoretical contributions, we characterized optimal strategies for bidding in simultaneous auctions when prices are known and complemented this analysis with an empirical comparison of different strategies. We identified that bidding decisions in TAC SCM can be modeled as a non-linear knapsack problem and proved the asymptotic optimality of a greedy algorithm for solving a class of non-linear knapsack problems