Browsing by Subject "Mechanism design"

Now showing 1 - 10 of 10

Open Access
Design and analysis of mechanisms for decentralized joint replenishment
(Elsevier B.V., 2017) Güler, K.; Körpeoğlu, E.; Şen, A.
We consider jointly replenishing multiple firms that operate under an EOQ like environment in a decentralized, non-cooperative setting. Each firm's demand rate and inventory holding cost rate are private information. We are interested in finding a mechanism that would determine the joint replenishment frequency and allocate the joint ordering costs to these firms based on their reported stand-alone replenishment frequencies (if they were to order independently). We first provide an impossibility result showing that there is no direct mechanism that simultaneously achieves efficiency, incentive compatibility, individual rationality and budget-balance. We then propose a general, two-parameter mechanism in which one parameter is used to determine the joint replenishment frequency, another is used to allocate the order costs based on firms’ reports. We show that efficiency cannot be achieved in this two-parameter mechanism unless the parameter governing the cost allocation is zero. When the two parameters are same (a single parameter mechanism), we find the equilibrium share levels and corresponding total cost. We finally investigate the effect of this parameter on equilibrium behavior. We show that properly adjusting this parameter leads to mechanisms that are better than other mechanisms suggested earlier in the literature in terms of fairness and efficiency. © 2016 Elsevier B.V.
Open Access
Essays on bilateral trade with discrete types
(2019-10) Mohammadinezhad, Kamyar Kargar
Bilateral trade is probably the most common market interaction problem and can be considered as the simplest form of two sided markets where a seller and a buyer bargain over an indivisible object subject to incomplete information on the reservation values of participants. We treat this problem as a combinatorial optimization problem and re-establish some results of economic theory that are well-known under continuous valuations assumptions for the case of discrete valuations using linear programming techniques. First, we propose mathematical formulation for the problem under dominant strategy incentive compatibility (DIC) and ex-post individual rationality (EIR) properties. Then we derive necessary and sufficient conditions under which ex-post efficiency can be obtained together with DIC and EIR. We also define a new property called Allocation Maximality and prove that the Posted Price mechanism is the only mechanism that satisfies DIC, EIR and allocation maximality. In the final part we consider ambiguity in the problem framework originating from different sets of priors for agents types and derive robust counterparts. Next, we study the bilateral trade problem with an intermediary who wants to maximize her expected gains. Using network programming we transform the initial linear program into one from which the structure of mechanism is transparent. We then relax the risk-neutrality assumption of the intermediary and consider the problem from the perspective of risk-averse intermediary. The effects of risk-averse approach are presented using computational experiments. Finally, we broaden the scope of the problem and discuss the case in which the seller is also a producer at the same time and consider benefit and cost functions for the respective parties. Starting by a non-convex optimization problem, we obtain an equivalent convex optimization problem from which the problem is solved easily. We also reconsider the same problem under dominant strategy incentive compatibility and ex-post individual rationality constraints to preserve the practicality of all obtained solutions.
Open Access
Essays on non-cooperative inventory games
(2012) Körpeoğlu, Evren
In this thesis we study different non–cooperative inventory games. In particular, we focus on joint replenishment games and newsvendor duopoly under asymmetric information. Chapter 1 contains introduction and motivation behind the research. Chapter 2 is a preliminary chapter which introduce basic concepts used in the thesis such as Nash equilibrium, Bayesian Nash equilibrium and mechanism design. In Chapter 3, we study a non-cooperative game for joint replenishment of multiple firms that operate under an EOQ–like setting. Each firm decides whether to replenish independently or to participate in joint replenishment, and how much to contribute to joint ordering costs in case of participation. Joint replenishment cycle time is set by an intermediary as the lowest cycle time that can be financed with the private contributions of participating firms. We consider two variants of the participation-contribution game: in the single–stage variant, participation and contribution decisions are made simultaneously, and, in the two-stage variant, participating firms become common knowledge at the contribution stage. We characterize the behavior and outcomes under undominated Nash equilibria for the one-stage game and subgame-perfect equilibrium for the two-stage game. In Chapter 4, we extend the private contributions game to an asymmetric information counterpart. We assume each firm only knows the probability distribution of the other firms’ adjusted demand rates (demand rate multiplied by inventory holding cost rate). We show the existence of a pure strategy Bayesian Nash equilibrium for the asymmetric information game and provide its characterization. Finally, we conduct some numerical study to examine the impact of information asymmetry on expected and interim values of total contributions, cycle times and total costs. quantities for all firm types except the type that has the highest possible unit cost, who orders the same quantity as he would as a monopolist newsboy. Consequently, competition leads to higher total inventory in the industry. A firm’s equilibrium order quantity increases with a stochastic increase in the total industry demand or with an increase in his initial allocation of the total industry demand. Finally, we provide full characterization of the equilibrium, corresponding payoffs and comparative statics for a parametric special case with uniform demand and linear market shares.
Open Access
Joint design and fabrication for multi-material soft/hybrid robots
(IEEE, 2019-04) Aygül, Cern; Kwiczak-Yiğitbaşı, Joanna; Baytekin, Bilge; Özcan, Onur
The premises of safer interactions with surroundings and the higher adaptability to its environment make soft robotics a very interesting research field. Some robots try to achieve these feats using soft materials in their designs whereas some achieve behavioral softness through compliant use of hard materials. In this work, we present soft/hybrid robot leg designs that utilize elastomers as leg materials but hard DC motors as actuators. Two different leg designs that would convert the rotational motion of the DC motors to a foot trajectory are proposed. The different leg designs are kinematically identical; however, the hourglass design utilizes geometrical modifications to differentiate joint locations, whereas the composite design uses materials with different Young's Moduli without geometrical effects to create joints. In order to fabricate the composite design, a new method is developed involving 3D printed molds with removable joint pieces and a two-step molding process. Both of the legs are fabricated and simulations and experiments are run to compare their performances. Both mechanisms achieve a good foot trajectory, however the hourglass joint experiences higher mechanical stress during operation, which might lead to earlier failure especially under high loads. Such multi-material structures made out of elastomers can be utilized in miniature robots or mechanisms of similar size in which absolute joint locations are needed and continuum robotic limbs are not preferred.
Open Access
MinIAQ-II: a miniature foldable quadruped with an improved leg mechanism
(IEEE, 2018) Askari, Mohammad; Karakadıoǧlu, Cem; Ayhan, Furkan; Özcan, Onur
Origami has long been renowned as a simple yet creative form of art and its folding techniques have recently inspired advances in design and fabrication of miniature robots. In this work, we present the design and fabrication novelties, enhancements, and performance improvements on MinIAQ (Miniature Independently Actuated-legged Quadruped), an origami-inspired, foldable, miniature quadruped robot with individually actuated legs. The resulting robot, MinIAQ-II, has a trajectory-optimized leg actuation mechanism with longer stride, improved traction, less flexure joint bending, and smaller leg lift resulting in faster and smoother walking, better maneuverability, and higher durability and joint life. In order to maximize the joint fatigue life while keeping the leg design simple, the initial four-bar mechanism is optimized by manipulating the joint locations and changing the leg link into a non-straight knee shape with a fixed-angle lock. Despite having a 1 cm longer frame to embed its new actuation mechanism, the overall weight and dimensions are similar to its first version as its legs are no longer extended beyond its frame. As a result, MinIAQ-II is 12-cm-long, 6-cm-wide, 4.5-cm-high and weighs 23 grams. The test results demonstrate the improvement in speed over its predecessor from 0.65 to more than 0.8 bodylengths/s at 3 Hz, and an approximate decrease in body's roll ±21° to ±9° and pitch from 0°-11° to 0°-7°. The independent actuation and control over each leg enables such a robot to be used for gait studies in miniature scale, as is the next direction in our research.
Open Access
Non-linear pricing by convex duality
(Elsevier, 2015) Pınar, M. Ç.
We consider the pricing problem of a risk-neutral monopolist who produces (at a cost) and offers an infinitely divisible good to a single potential buyer that can be of a finite number of (single dimensional) types. The buyer has a non-linear utility function that is differentiable, strictly concave and strictly increasing. Using a simple reformulation and shortest path problem duality as in Vohra (2011) we transform the initial non-convex pricing problem of the monopolist into an equivalent optimization problem yielding a closed-form pricing formula under a regularity assumption on the probability distribution of buyer types. We examine the solution of the problem when the regularity condition is relaxed in different ways, or when the production function is non-linear and convex. For arbitrary type distributions, we offer a complete solution procedure.
Open Access
Robust bilateral trade with discrete types
(Springer, 2018) Kargar, Kamyar; Bayrak, Halil İbrahim; Pınar, Mustafa Çelebi
Bilateral trade problem is the most common market interaction in which a seller and a buyer bargain over an indivisible object, and the valuation of each agent about the object is private information. We investigate the cases where mechanisms satisfying Dominant Strategy Incentive Compatibility (DIC) and Ex-post Individual Rationality (EIR) properties can exhibit robust performance in the face of imprecision in prior structure. We start with the general mathematical formulation for the bilateral trade problem with DIC, EIR properties. We derive necessary and sufficient conditions for DIC, EIR mechanisms to be Ex-post efficient at the same time. Then, we define a new property—Allocation Maximality—and prove that the Posted Price mechanisms are the only mechanisms that satisfy DIC, EIR and Allocation Maximal properties. We also show that Posted Price mechanism is not the only mechanism that satisfies DIC and EIR properties. The last part of the paper introduces different sets of priors for agents’ types and consequently allows ambiguity in the problem framework. We derive robust counterparts and solve them numerically for the proposed objective function under box and ϕ-divergence ambiguity specifications. Results suggest that restricting the feasible set to Posted Price mechanisms can decrease the objective value to different extents depending on the uncertainty set.
Open Access
Robust screening under ambiguity
(Springer, 2017) Pınar, M. Ç.; Kızılkale, C.
We consider the problem of screening where a seller puts up for sale an indivisible good, and a buyer with a valuation unknown to the seller wishes to acquire the good. We assume that the buyer valuations are represented as discrete types drawn from some distribution, which is also unknown to the seller. The seller is averse to possible mis-specification of types distribution, and considers the unknown type density as member of an ambiguity set and seeks an optimal pricing mechanism in a worst case sense. We specify four choices for the ambiguity set and derive the optimal mechanism in each case.
Open Access
Robust trading mechanisms over 0/1 polytopes
(Springer New York LLC, 2018) Pınar, Mustafa Çelebi
The problem of designing a trade mechanism (for an indivisible good) between a seller and a buyer is studied in the setting of discrete valuations of both parties using tools of finite-dimensional optimization. A robust trade design is defined as one which allows both traders a dominant strategy implementation independent of other traders’ valuations with participation incentive and no intermediary (i.e., under budget balance). The design problem which is initially formulated as a mixed-integer non-linear non-convex feasibility problem is transformed into a linear integer feasibility problem by duality arguments, and its explicit solution corresponding to posted price optimal mechanisms is derived along with full characterization of the convex hull of integer solutions. A further robustness concept is then introduced for a central planner unsure about the buyer or seller valuation distribution, a corresponding worst-case design problem over a set of possible distributions is formulated as an integer linear programming problem, and a polynomial solution procedure is given. When budget balance requirement is relaxed to feasibility only, i.e., when one allows an intermediary maximizing the expected surplus from trade, a characterization of the optimal robust trade as the solution of a simple linear program is given. A modified VCG mechanism turns out to be optimal.
Open Access
Three essays in the interface of optimization with mechanism design, nonexclusive competition, and prophet inequalities
(2022-09) Bayrak, Halil İbrahim
Mechanism Design. We consider the mechanism design problem of a principal allocating a single good to one of several agents without monetary transfers. Each agent desires the good and uses it to create value for the principal. We designate this value as the agent's private type. Even though the principal does not know the agents' types, she can verify them at a cost. The allocation of the good thus depends on the agents' self-declared types and the results of any verification performed, and the principal's payoff matches her allocation value minus the verification costs. It is known that when the agents' types are independent, a favored-agent mechanism maximizes her expected payoff. However, this result relies on the unrealistic assumptions that the agents' types follow known independent probability distributions. We assume that the agents' types are governed by an ambiguous joint probability distribution belonging to a commonly known ambiguity set and that the principal maximizes her worst-case expected payoff. We consider three types of ambiguity sets: (i) support-only ambiguity sets, which contain all distributions supported on a rectangle, (ii) Markov ambiguity sets, characterized through first-order moment bounds, and (iii) Markov with independence ambiguity sets. For each of these ambiguity sets, we show that a favored-agent mechanism, which we characterize implicitly, is optimal and also Pareto-robustly optimal. The optimal choices of the favored agent and the threshold do not depend on the verification costs in all three cases. Nonexclusive Competition. A freelancer with a time constraint faces offers from multiple identical parties. The quality of the service provided by the freelancer can be high or low and is only known by the freelancer. The freelancer's time cost is strictly increasing and convex. We show that a pure-strategy equilibrium exists if and only if the preferences of the high-type freelancer satisfy one of the following two distinct conditions: (i) the high-type freelancer does {not} prefer providing his services for a price equal to the expected quality at the no-trade point; (ii) the high-type freelancer prefers providing his services for a price equal to the expected quality at any feasible trade point. If (i) holds, then in equilibrium, the high-type freelancer does not trade, whereas the low-type may not trade, trade efficiently, or exhaust all of his capacity. Moreover, the buyers make zero profit from each of their traded contracts. If (ii) holds, then both types of the freelancer trade at the capacity in equilibrium. Furthermore, the buyers make zero expected profit with cross-subsidization. In any equilibrium, the aggregate equilibrium trades are unique. Prophet Inequalities. Prophet inequalities bound the expected reward obtained in a class of stopping problems by the optimal reward of the corresponding offline problem. We show how to obtain prophet inequalities for a large class of stopping problems associated with selecting a point in a polyhedron. Our approach utilizes linear programming tools and is based on a reduced form representation of the stopping problem. We illustrate the usefulness of our approach by re-establishing three different prophet inequality results from the literature. (i) For polymatroids with nonnegative coefficients in their unique Minkowski sum of simplices, we prove the 1/2-prophet inequality. (ii) We prove the 1/n-prophet inequality when there are n stages, the stages have dependently distributed rewards, and we are restricted to choosing a strategy from an arbitrary polyhedron. (iii) When the feasible set of strategies can be described via K different constraints, we obtain the 1/(K+1)-prophet inequality.