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Mechanism design for a risk averse seller
 In WINE
, 2012
"... Abstract. We develop efficient algorithms to construct approximately utility maximizing mechanisms for a risk averse seller in the presence of potentially riskaverse buyers in Bayesian single parameter and multiparameter settings. We model risk aversion by concave utility function. Bayesian mechani ..."
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Abstract. We develop efficient algorithms to construct approximately utility maximizing mechanisms for a risk averse seller in the presence of potentially riskaverse buyers in Bayesian single parameter and multiparameter settings. We model risk aversion by concave utility function. Bayesian mechanism design has usually focused on maximizing expected revenue in a riskneutral environment, i.e. where all the buyers and the seller have linear utility. While some work has regarded buyers ’ risk aversion, very little of past work addresses the seller’s risk aversion. We first consider the problem of designing a dominant strategy incentive compatible (DSIC) mechanism for a riskaverse seller in the case of multiunit auctions. We give a polytime computable pricing mechanism that is a (1 − 1/e − ɛ)approximation to an optimal DSIC mechanism, for any ɛ> 0. Our result is based on a novel application of correlation gap bound, that involves splitting and merging of random variables to redistribute probability mass across buyers. This allows us to reduce our problem to
A Simple and Approximately Optimal Mechanism for an Additive Buyer
"... In this letter we briefly survey our main result from [Babaioff el al. 2014]: a simple and approximately revenueoptimal mechanism for a monopolist who wants to sell a variety of items to a single buyer with an additive valuation. ..."
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Cited by 5 (1 self)
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In this letter we briefly survey our main result from [Babaioff el al. 2014]: a simple and approximately revenueoptimal mechanism for a monopolist who wants to sell a variety of items to a single buyer with an additive valuation.
Algorithms for Strategic Agents
, 2014
"... In traditional algorithm design, no incentives come into play: the input is given, and your algorithm must produce a correct output. How much harder is it to solve the same problem when the input is not given directly, but instead reported by strategic agents with interests of their own? The unique ..."
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Cited by 1 (0 self)
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In traditional algorithm design, no incentives come into play: the input is given, and your algorithm must produce a correct output. How much harder is it to solve the same problem when the input is not given directly, but instead reported by strategic agents with interests of their own? The unique challenge stems from the fact that the agents may choose to lie about the input in order to manipulate the behavior of the algorithm for their own interests, and tools from Game Theory are therefore required in order to predict how these agents will behave. We develop a new algorithmic framework with which to study such problems. Specifically, we provide a computationally efficient blackbox reduction from solving any optimization problem on "strategic input, " often called algorithmic mechanism design to solving a perturbed version of that same optimization problem when the input is directly given, traditionally called algorithm design. We further demonstrate the power of our framework by making significant progress on several longstanding open problems. First, we extend Myerson's celebrated characterization of single item auctions [Mye8l] to multiple items, providing also a computationally efficient implementation of optimal auctions. Next, we design a computationally efficient 2approximate mechanism
MultiItem Auctions Defying Intuition?
, 2013
"... The best way to sell n items to a buyer who values each of them independently and uniformly randomly in [c, c+ 1] is to bundle them together, as long as c is large enough. Still, for any c, the grand bundling mechanism is never optimal for large enough n, despite the sharp concentration of the buyer ..."
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The best way to sell n items to a buyer who values each of them independently and uniformly randomly in [c, c+ 1] is to bundle them together, as long as c is large enough. Still, for any c, the grand bundling mechanism is never optimal for large enough n, despite the sharp concentration of the buyer’s total value for the items as n grows. Optimal multiitem mechanisms are rife with unintuitive properties, making multiitem generalizations of Myerson’s celebrated mechanism a daunting task. We survey recent work on the structure and computational complexity of revenueoptimal multiitem mechanisms, providing structural as well as algorithmic generalizations of Myerson’s result to multiitem settings.
Optimal Multiparameter Auction Design
, 2014
"... This thesis studies the design of Bayesian revenueoptimal auctions for a class of problems in which buyers have general (nonlinear and multiparameter) preferences. This class includes the classical linear singleparameter problem considered by Myerson (1981), for which he provided a simple chara ..."
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This thesis studies the design of Bayesian revenueoptimal auctions for a class of problems in which buyers have general (nonlinear and multiparameter) preferences. This class includes the classical linear singleparameter problem considered by Myerson (1981), for which he provided a simple characterization of the optimal mechanism, leading to numerous applications in theory and practice. However, for fully general preferences no generic and practical solution is known (various negative computational or structural results exist for special cases), even for the problem of designing a mechanism for a single agent. With general preferences, the optimal mechanism can be complex and impractical. This thesis identifies key conditions implying that the optimal mechanism is practical. Our main results are different in that they identify different conditions implying different notions of practicality, but are all similar in adopting a modular view to the problem that separates the task of designing a solution for the singleagent problem as the main module, from the task of combining these modules to form an optimal multiagent mechanism. First, for multiparameter linear settings, we specify a large class of distributions over values that implies that the optimal singleagent mechanism is posted pricing, and the optimal multiagent mechanism maximizes virtual values for players ’ favorite items. When agents are identical, the mechanism becomes the second price 4auction with reserve for favorite items. Second, and more generally, we specify a condition called revenuelinearity, defined beyond multiparameter linear settings, that implies that optimizing agents ’ marginal revenue maximizes revenue. Finally, adopting efficient computability as the notion of practicality, we show that for any setting in which singleagent solutions are efficiently computable, multiagent solutions are also computable.
Multidimensional Virtual Values and Seconddegree Price Discrimination *
"... Abstract We consider a multidimensional screening problem of selling a product with multiple quality levels. We show that only offering the highest quality is the revenue optimal mechanism if high valued customers are relatively less sensitive to quality. For a class of instances where values are ..."
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Abstract We consider a multidimensional screening problem of selling a product with multiple quality levels. We show that only offering the highest quality is the revenue optimal mechanism if high valued customers are relatively less sensitive to quality. For a class of instances where values are perfectly correlated, our condition is also necessary for optimality of only offering the highest quality. Our main methodological contribution is a framework to design multidimensional virtual values. A challenge of designing virtual values for multidimensional agents is that a mechanism that pointwise optimizes virtual values resulting from a general application of integration by parts is not incentive compatible, and no general methodology was previously known for selecting the right paths for integration by parts. We resolve this issue by imposing additional restrictions on the problem until the virtual value for the high quality product is uniquely defined, which pins down the paths and in turn the virtual values for other products. The correlation condition on the distribution implies that the derived virtual values are indeed pointwise optimized by the nondiscrimination mechanism. Our method of solving for virtual values is general, and as a second application we use it to derive conditions of optimality for selling only the grand bundle of items to an agent with additive preferences.
Reverse Mechanism Design
, 2014
"... Myerson’s 1981 characterization of revenueoptimal auctions for singledimensional agents follows from an amortized analysis of the incentives of a single agent. To optimize revenue in expectation, he maps values to virtual values which account for expected revenue gain but can be optimized pointwis ..."
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Myerson’s 1981 characterization of revenueoptimal auctions for singledimensional agents follows from an amortized analysis of the incentives of a single agent. To optimize revenue in expectation, he maps values to virtual values which account for expected revenue gain but can be optimized pointwise. For singledimensional agents the appropriate virtual values are unique and their closed form can be easily derived from revenue equivalence. A main challenge of generalizing the Myersonian approach to multidimensional agents is that the right amortization is not pinned down by revenue equivalence. For multidimensional agents, the optimal mechanism may be very complex. Complex mechanisms are impractical and rarely employed. We give a framework for reverse mechanism design. Instead of solving for the optimal mechanism in general, we assume a (natural) specific form of the mechanism. As an example of the framework, for agents with unitdemand preferences, we restrict attention to mechanisms that sell each agent her favorite item or nothing. From this restricted form, we will derive multidimensional virtual values. These virtual values prove this form of mechanism is optimal for a large class of itemsymmetric distributions over types. As another example of our framework, for bidders with additive preferences, we derive conditions for the optimality of posting a single price for the grand bundle. 1