Abstract The problem of scheduling unrelated machines by a truthful mechanism to minimize the makespan was introduced in the seminal "Algorithmic Mechanism Design" paper by Nisan and Ronen. Nisan and …
Abstract The problem of scheduling unrelated machines by a truthful mechanism to minimize the makespan was introduced in the seminal "Algorithmic Mechanism Design" paper by Nisan and Ronen. Nisan and Ronen showed that there is a truthful mechanism that provides an approximation ratio of min( m , n ), where n is the number of machines and m is the number of jobs. They also proved that no truthful mechanism can provide an approximation ratio better than 2. Since then, the lower bound was improved to 1 + √2 ≈ 2.41 by Christodoulou, Kotsoupias, and Vidali, and then to 1 + Φ ≈ 2.618 by Kotsoupias and Vidali. The lower bound was improved to 2.755 by Giannakopoulos, Hammerl, and Pocas. In this paper we further improve the bound to 3- δ , for every constant δ > 0. Note that a gap between the upper bound and the lower bounds exists even when the number of machines and jobs is very small. In particular, the known 1 + √2 lower bound requires at least 3 machines and 5 jobs. In contrast, we show a lower bound of 2.2055 that uses only 3 machines and 3 jobs and a lower bound of 1 + √2 that uses only 3 machines and 4 jobs. For the case of two machines and two jobs we show a lower bound of 2. Similar bounds for two machines and two jobs were known before but only via complex proofs that characterized all truthful mechanisms that provide a finite approximation ratio in this setting, whereas our new proof uses a simple and direct approach.
The problem of scheduling unrelated machines by a truthful mechanism to minimize the makespan was introduced in the seminal "Algorithmic Mechanism Design" paper by Nisan and Ronen. Nisan and Ronen …
The problem of scheduling unrelated machines by a truthful mechanism to minimize the makespan was introduced in the seminal "Algorithmic Mechanism Design" paper by Nisan and Ronen. Nisan and Ronen showed that there is a truthful mechanism that provides an approximation ratio of $\min(m,n)$, where $n$ is the number of machines and $m$ is the number of jobs. They also proved that no truthful mechanism can provide an approximation ratio better than $2$. Since then, the lower bound was improved to $1 +\sqrt 2 \approx 2.41$ by Christodoulou, Kotsoupias, and Vidali, and then to $1+ϕ\approx 2.618$ by Kotsoupias and Vidali. Very recently, the lower bound was improved to $2.755$ by Giannakopoulos, Hammerl, and Pocas. In this paper we further improve the bound to $3-δ$, for every constant $δ>0$. Note that a gap between the upper bound and the lower bounds exists even when the number of machines and jobs is very small. In particular, the known $1+\sqrt{2}$ lower bound requires at least $3$ machines and $5$ jobs. In contrast, we show a lower bound of $2.2055$ that uses only $3$ machines and $3$ jobs and a lower bound of $1+\sqrt 2$ that uses only $3$ machines and $4$ jobs. For the case of two machines and two jobs we show a lower bound of $2$. Similar bounds for two machines and two jobs were known before but only via complex proofs that characterized all truthful mechanisms that provide a finite approximation ratio in this setting, whereas our new proof uses a simple and direct approach.
We introduce the notion of rigidity in auction design and use it to analyze some fundamental aspects of mechanism design. We focus on single-item auctions where the values of the …
We introduce the notion of rigidity in auction design and use it to analyze some fundamental aspects of mechanism design. We focus on single-item auctions where the values of the bidders are drawn from some (possibly correlated) distribution $\mathcal F$. Let $f$ be the allocation function of an optimal mechanism for $\mathcal F$. Informally, $S$ is (linearly) rigid in $\mathcal F$ if for every mechanism $M'$ with an allocation function $f'$ where $f$ and $f'$ agree on the allocation of at most $x$-fraction of the instances of $S$, the expected revenue of $M'$ is at most an $x$ fraction of the optimal revenue. We use rigidity to explain the singular success of Cremer and McLean's auction. Recall that the revenue of Cremer and McLean's auction is the optimal welfare if the distribution obeys a certain ``full rank'' condition, but no analogous constructions are known if this condition does not hold. Note that the Kolmogorov complexity of the allocation function of Cremer and McLean's auction is logarithmic, whereas we use rigidity to show that for some distributions that do not obey the full rank condition, the Kolmogorov complexity of the allocation function of every mechanism that provides a constant approximation is almost linear. We further investigate rigidity assuming different notions of individual rationality. Assuming ex-post individual rationality, if there is a rigid set, the structure of the optimal mechanism is simple: the player with the highest value ``usually'' wins the item and contributes most of the revenue. In contrast, assuming interim individual rationality, there are distributions with a rigid set $S$ where the optimal mechanism has no obvious allocation pattern (i.e., its Kolmogorov complexity is high). Our results help explain why we have little hope of developing good, simple and generic approximation mechanisms in the interim individual rationality world.
We study the bilateral trade problem where a seller owns a single indivisible item, and a potential buyer seeks to purchase it. Previous mechanisms for this problem only considered the …
We study the bilateral trade problem where a seller owns a single indivisible item, and a potential buyer seeks to purchase it. Previous mechanisms for this problem only considered the case where the values of the buyer and the seller are drawn from independent distributions. In this paper, we study bilateral trade mechanisms when the values are drawn from a joint distribution. We prove that the buyer-offering mechanism guarantees an approximation ratio of $\frac e {e-1} \approx 1.582$ to the social welfare even if the values are drawn from a joint distribution. The buyer-offering mechanism is Bayesian incentive compatible, but the seller has a dominant strategy. We prove the buyer-offering mechanism is optimal in the sense that no Bayesian mechanism where one of the players has a dominant strategy can obtain an approximation ratio better than $\frac e {e-1}$. We also show that no mechanism in which both sides have a dominant strategy can provide any constant approximation to the social welfare when the values are drawn from a joint distribution. Finally, we prove some impossibility results on the power of general Bayesian incentive compatible mechanisms. In particular, we show that no deterministic Bayesian incentive-compatible mechanism can provide an approximation ratio better than $1+\frac {\ln 2} 2\approx 1.346$.
We consider the problem of designing auctions which maximize consumer surplus (i.e., the social welfare minus the payments charged to the buyers). In the consumer surplus maximization problem, a seller …
We consider the problem of designing auctions which maximize consumer surplus (i.e., the social welfare minus the payments charged to the buyers). In the consumer surplus maximization problem, a seller with a set of goods faces a set of strategic buyers with private values, each of whom aims to maximize their own individual utility. The seller, in contrast, aims to allocate the goods in a way which maximizes the total buyer utility. The seller must then elicit the values of the buyers in order to decide what goods to award each buyer. The canonical approach in mechanism design to ensure truthful reporting of the private information is to find appropriate prices to charge each buyer in order to align their objective with the objective of the seller. Indeed, there are many celebrated results to this end when the seller's objective is welfare maximization [Clarke, 1971, Groves, 1973, Vickrey, 1961] or revenue maximization [Myerson, 1981]. However, in the case of consumer surplus maximization the picture is less clear -- using high payments to ensure the highest value bidders are served necessarily decreases their surplus utility, but using low payments may lead the seller into serving lower value bidders. Our main result in this paper is a framework for designing mechanisms which maximize consumer surplus. We instantiate our framework in a variety of canonical multi-parameter auction settings (i.e., unit-demand bidders with heterogeneous items, multi-unit auctions, and auctions with divisible goods) and use it to design auctions achieving consumer surplus with optimal approximation guarantees against the total social welfare. Along the way, we answer an open question posed by Hartline and Roughgarden [2008], who, to our knowledge, were the first to study the question of consumer surplus approximation guarantees in single-parameter settings, regarding optimal mechanisms for two bidders.
We study the bilateral trade problem where a seller owns a single indivisible item, and a potential buyer seeks to purchase it. Previous mechanisms for this problem only considered the …
We study the bilateral trade problem where a seller owns a single indivisible item, and a potential buyer seeks to purchase it. Previous mechanisms for this problem only considered the case where the values of the buyer and the seller are drawn from independent distributions. In contrast, this paper studies bilateral trade mechanisms when the values are drawn from a joint distribution. We prove that the buyer-offering mechanism guarantees an approximation ratio of e/e−1 ≈ 1.582 to the social welfare even if the values are drawn from a joint distribution. The buyer-offering mechanism is Bayesian incentive compatible, but the seller has a dominant strategy. We prove the buyer-offering mechanism is optimal in the sense that no Bayesian mechanism where one of the players has a dominant strategy can obtain an approximation ratio better than e/e−1. We also show that no mechanism in which both sides have a dominant strategy can provide any constant approximation to the social welfare when the values are drawn from a joint distribution. Finally, we prove some impossibility results on the power of general Bayesian incentive compatible mechanisms. In particular, we show that no deterministic Bayesian incentive-compatible mechanism can provide an approximation ratio better than 1+ln2/2≈ 1.346.
We study the bilateral trade problem where a seller owns a single indivisible item, and a potential buyer seeks to purchase it. Previous mechanisms for this problem only considered the …
We study the bilateral trade problem where a seller owns a single indivisible item, and a potential buyer seeks to purchase it. Previous mechanisms for this problem only considered the case where the values of the buyer and the seller are drawn from independent distributions. In contrast, this paper studies bilateral trade mechanisms when the values are drawn from a joint distribution. We prove that the buyer-offering mechanism guarantees an approximation ratio of e/e−1 ≈ 1.582 to the social welfare even if the values are drawn from a joint distribution. The buyer-offering mechanism is Bayesian incentive compatible, but the seller has a dominant strategy. We prove the buyer-offering mechanism is optimal in the sense that no Bayesian mechanism where one of the players has a dominant strategy can obtain an approximation ratio better than e/e−1. We also show that no mechanism in which both sides have a dominant strategy can provide any constant approximation to the social welfare when the values are drawn from a joint distribution. Finally, we prove some impossibility results on the power of general Bayesian incentive compatible mechanisms. In particular, we show that no deterministic Bayesian incentive-compatible mechanism can provide an approximation ratio better than 1+ln2/2≈ 1.346.
We consider the problem of designing auctions which maximize consumer surplus (i.e., the social welfare minus the payments charged to the buyers). In the consumer surplus maximization problem, a seller …
We consider the problem of designing auctions which maximize consumer surplus (i.e., the social welfare minus the payments charged to the buyers). In the consumer surplus maximization problem, a seller with a set of goods faces a set of strategic buyers with private values, each of whom aims to maximize their own individual utility. The seller, in contrast, aims to allocate the goods in a way which maximizes the total buyer utility. The seller must then elicit the values of the buyers in order to decide what goods to award each buyer. The canonical approach in mechanism design to ensure truthful reporting of the private information is to find appropriate prices to charge each buyer in order to align their objective with the objective of the seller. Indeed, there are many celebrated results to this end when the seller's objective is welfare maximization [Clarke, 1971, Groves, 1973, Vickrey, 1961] or revenue maximization [Myerson, 1981]. However, in the case of consumer surplus maximization the picture is less clear -- using high payments to ensure the highest value bidders are served necessarily decreases their surplus utility, but using low payments may lead the seller into serving lower value bidders. Our main result in this paper is a framework for designing mechanisms which maximize consumer surplus. We instantiate our framework in a variety of canonical multi-parameter auction settings (i.e., unit-demand bidders with heterogeneous items, multi-unit auctions, and auctions with divisible goods) and use it to design auctions achieving consumer surplus with optimal approximation guarantees against the total social welfare. Along the way, we answer an open question posed by Hartline and Roughgarden [2008], who, to our knowledge, were the first to study the question of consumer surplus approximation guarantees in single-parameter settings, regarding optimal mechanisms for two bidders.
Abstract The problem of scheduling unrelated machines by a truthful mechanism to minimize the makespan was introduced in the seminal "Algorithmic Mechanism Design" paper by Nisan and Ronen. Nisan and …
Abstract The problem of scheduling unrelated machines by a truthful mechanism to minimize the makespan was introduced in the seminal "Algorithmic Mechanism Design" paper by Nisan and Ronen. Nisan and Ronen showed that there is a truthful mechanism that provides an approximation ratio of min( m , n ), where n is the number of machines and m is the number of jobs. They also proved that no truthful mechanism can provide an approximation ratio better than 2. Since then, the lower bound was improved to 1 + √2 ≈ 2.41 by Christodoulou, Kotsoupias, and Vidali, and then to 1 + Φ ≈ 2.618 by Kotsoupias and Vidali. The lower bound was improved to 2.755 by Giannakopoulos, Hammerl, and Pocas. In this paper we further improve the bound to 3- δ , for every constant δ > 0. Note that a gap between the upper bound and the lower bounds exists even when the number of machines and jobs is very small. In particular, the known 1 + √2 lower bound requires at least 3 machines and 5 jobs. In contrast, we show a lower bound of 2.2055 that uses only 3 machines and 3 jobs and a lower bound of 1 + √2 that uses only 3 machines and 4 jobs. For the case of two machines and two jobs we show a lower bound of 2. Similar bounds for two machines and two jobs were known before but only via complex proofs that characterized all truthful mechanisms that provide a finite approximation ratio in this setting, whereas our new proof uses a simple and direct approach.
We study the bilateral trade problem where a seller owns a single indivisible item, and a potential buyer seeks to purchase it. Previous mechanisms for this problem only considered the …
We study the bilateral trade problem where a seller owns a single indivisible item, and a potential buyer seeks to purchase it. Previous mechanisms for this problem only considered the case where the values of the buyer and the seller are drawn from independent distributions. In this paper, we study bilateral trade mechanisms when the values are drawn from a joint distribution. We prove that the buyer-offering mechanism guarantees an approximation ratio of $\frac e {e-1} \approx 1.582$ to the social welfare even if the values are drawn from a joint distribution. The buyer-offering mechanism is Bayesian incentive compatible, but the seller has a dominant strategy. We prove the buyer-offering mechanism is optimal in the sense that no Bayesian mechanism where one of the players has a dominant strategy can obtain an approximation ratio better than $\frac e {e-1}$. We also show that no mechanism in which both sides have a dominant strategy can provide any constant approximation to the social welfare when the values are drawn from a joint distribution. Finally, we prove some impossibility results on the power of general Bayesian incentive compatible mechanisms. In particular, we show that no deterministic Bayesian incentive-compatible mechanism can provide an approximation ratio better than $1+\frac {\ln 2} 2\approx 1.346$.
We introduce the notion of rigidity in auction design and use it to analyze some fundamental aspects of mechanism design. We focus on single-item auctions where the values of the …
We introduce the notion of rigidity in auction design and use it to analyze some fundamental aspects of mechanism design. We focus on single-item auctions where the values of the bidders are drawn from some (possibly correlated) distribution $\mathcal F$. Let $f$ be the allocation function of an optimal mechanism for $\mathcal F$. Informally, $S$ is (linearly) rigid in $\mathcal F$ if for every mechanism $M'$ with an allocation function $f'$ where $f$ and $f'$ agree on the allocation of at most $x$-fraction of the instances of $S$, the expected revenue of $M'$ is at most an $x$ fraction of the optimal revenue. We use rigidity to explain the singular success of Cremer and McLean's auction. Recall that the revenue of Cremer and McLean's auction is the optimal welfare if the distribution obeys a certain ``full rank'' condition, but no analogous constructions are known if this condition does not hold. Note that the Kolmogorov complexity of the allocation function of Cremer and McLean's auction is logarithmic, whereas we use rigidity to show that for some distributions that do not obey the full rank condition, the Kolmogorov complexity of the allocation function of every mechanism that provides a constant approximation is almost linear. We further investigate rigidity assuming different notions of individual rationality. Assuming ex-post individual rationality, if there is a rigid set, the structure of the optimal mechanism is simple: the player with the highest value ``usually'' wins the item and contributes most of the revenue. In contrast, assuming interim individual rationality, there are distributions with a rigid set $S$ where the optimal mechanism has no obvious allocation pattern (i.e., its Kolmogorov complexity is high). Our results help explain why we have little hope of developing good, simple and generic approximation mechanisms in the interim individual rationality world.
The problem of scheduling unrelated machines by a truthful mechanism to minimize the makespan was introduced in the seminal "Algorithmic Mechanism Design" paper by Nisan and Ronen. Nisan and Ronen …
The problem of scheduling unrelated machines by a truthful mechanism to minimize the makespan was introduced in the seminal "Algorithmic Mechanism Design" paper by Nisan and Ronen. Nisan and Ronen showed that there is a truthful mechanism that provides an approximation ratio of $\min(m,n)$, where $n$ is the number of machines and $m$ is the number of jobs. They also proved that no truthful mechanism can provide an approximation ratio better than $2$. Since then, the lower bound was improved to $1 +\sqrt 2 \approx 2.41$ by Christodoulou, Kotsoupias, and Vidali, and then to $1+ϕ\approx 2.618$ by Kotsoupias and Vidali. Very recently, the lower bound was improved to $2.755$ by Giannakopoulos, Hammerl, and Pocas. In this paper we further improve the bound to $3-δ$, for every constant $δ>0$. Note that a gap between the upper bound and the lower bounds exists even when the number of machines and jobs is very small. In particular, the known $1+\sqrt{2}$ lower bound requires at least $3$ machines and $5$ jobs. In contrast, we show a lower bound of $2.2055$ that uses only $3$ machines and $3$ jobs and a lower bound of $1+\sqrt 2$ that uses only $3$ machines and $4$ jobs. For the case of two machines and two jobs we show a lower bound of $2$. Similar bounds for two machines and two jobs were known before but only via complex proofs that characterized all truthful mechanisms that provide a finite approximation ratio in this setting, whereas our new proof uses a simple and direct approach.
We study the scheduling problem on unrelated machines in the mechanism design setting. This problem was proposed and studied in the seminal paper (Nisan and Ronen 1999), where they gave …
We study the scheduling problem on unrelated machines in the mechanism design setting. This problem was proposed and studied in the seminal paper (Nisan and Ronen 1999), where they gave a 1.75-approximation randomized truthful mechanism for the case of two machines. We improve this result by a 1.6737-approximation randomized truthful mechanism. We also generalize our result to a $0.8368m$-approximation mechanism for task scheduling with $m$ machines, which improve the previous best upper bound of $0.875m(Mu'alem and Schapira 2007).
We design simple mechanisms to approximate the Gains from Trade (GFT) in two-sided markets with multiple unit-supply sellers and multiple unit-demand buyers. A classical impossibility result by Myerson and Satterthwaite …
We design simple mechanisms to approximate the Gains from Trade (GFT) in two-sided markets with multiple unit-supply sellers and multiple unit-demand buyers. A classical impossibility result by Myerson and Satterthwaite showed that even with only one seller and one buyer, no Bayesian Incentive Compatible (BIC), Individually Rational (IR), and Budget-Balanced (BB) mechanism can achieve full GFT (trade whenever buyer's value is higher than the seller's cost). The same paper also proposed the ``second-best'' mechanism that maximizes the GFT subject to BIC, IR, and BB constraints, which is unfortunately rather complex for even the single-seller single-buyer case. Our mechanism is simple, BIC, IR, and BB and achieves 1/2 of the optimal GFT among all BIC, IR, and BB mechanisms. The result holds for arbitrary distributions of the buyers' and sellers' values and can accommodate any downward-closed feasibility constraints over the allocations. The analysis of our mechanism is facilitated by extending the Cai-Weinberg-Devanur duality framework to two-sided markets.
We consider reallocation problems in settings where the initial endowment of each agent consists of a subset of the resources. The private information of the players is their value for …
We consider reallocation problems in settings where the initial endowment of each agent consists of a subset of the resources. The private information of the players is their value for every possible subset of the resources. The goal is to redistribute resources among agents to maximize efficiency. Monetary transfers are allowed, but participation is voluntary.
We consider incentive compatible mechanisms for a domain that is very close to the domain of scheduling n unrelated machines: the single exception is that the valuation of just one …
We consider incentive compatible mechanisms for a domain that is very close to the domain of scheduling n unrelated machines: the single exception is that the valuation of just one machine is submodular. For the scheduling problem with such cost functions, we give a lower bound of Ω(√n) on the approximation ratio of incentive compatible deterministic mechanisms. This is a strong information-theoretic impossibility result on the approximation ratio of mechanisms that provides strong evidence for the Nisan-Ronen conjecture. This is the first non-constant lower bound that assumes no restriction on the mechanism side; in contrast, all previous general results hold for only special classes of mechanisms such as local, strongly monotone, and anonymous mechanisms. Our approach is based on a novel multi-player characterization of appropriately selected instances that allows us to focus on particular type of algorithms, linear mechanisms, and it is a potential stepping stone towards the full resolution of the conjecture.
We consider the minimum makespan problem for n tasks and two unrelated parallel selfish machines. Let Rn be the best approximation ratio of randomized monotone scale-free algorithms. This class contains …
We consider the minimum makespan problem for n tasks and two unrelated parallel selfish machines. Let Rn be the best approximation ratio of randomized monotone scale-free algorithms. This class contains the most efficient algorithms known for truthful scheduling on two machines. We propose a new Min − Max formulation for Rn, as well as upper and lower bounds on Rn based on this formulation. For the lower bound, we exploit pointwise approximations of cumulative distribution functions (CDFs). For the upper bound, we construct randomized algorithms using distributions with piecewise rational CDFs. Our method improves upon the existing bounds on Rn for small n. In particular, we obtain almost tight bounds for n = 2 showing that |R2 − 1.505996| < 10− 6.
We study bilateral trade between two strategic agents. The celebrated result of Myerson and Satterthwaite states that in general, no incentive-compatible, individually rational and weakly budget balanced mechanism can be …
We study bilateral trade between two strategic agents. The celebrated result of Myerson and Satterthwaite states that in general, no incentive-compatible, individually rational and weakly budget balanced mechanism can be efficient. I.e., no mechanism with these properties can guarantee a trade whenever buyer value exceeds seller cost. Given this, a natural question is whether there exists a mechanism with these properties that guarantees a constant fraction of the first-best gains-from-trade, namely a constant fraction of the gains-from-trade attainable whenever buyer's value weakly exceeds seller's cost. In this work, we positively resolve this long-standing open question on constant-factor approximation, mentioned in several previous works, using a simple mechanism that obtains a 1/8.23 ≈ 0.121 fraction of the first-best.
Previous chapter Next chapter Full AccessProceedings Proceedings of the 2022 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)Fixed-Price Approximations in Bilateral TradeZi Yang Kang, Francisco Pernice, and Jan VondrákZi Yang Kang, …
Previous chapter Next chapter Full AccessProceedings Proceedings of the 2022 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)Fixed-Price Approximations in Bilateral TradeZi Yang Kang, Francisco Pernice, and Jan VondrákZi Yang Kang, Francisco Pernice, and Jan Vondrákpp.2964 - 2985Chapter DOI:https://doi.org/10.1137/1.9781611977073.115PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract We consider the bilateral trade problem, in which two agents trade a single indivisible item. It is known that the only dominant-strategy truthful mechanism is the fixed-price mechanism: given commonly known distributions of the buyer's value B and the seller's value S, a price p is offered to both agents and trade occurs if S ≤ p ≤ B. The objective is to maximize either expected welfare or expected gains from trade . We improve the approximation ratios for several welfare maximization variants of this problem. When the agents' distributions are identical, we show that the optimal approximation ratio for welfare is . With just one prior sample from the common distribution, we show that a 3/4-approximation to welfare is achievable. When agents' distributions are not required to be identical, we show that a previously best-known (1–1/e)-approximation can be strictly improved, but 1–1/e is optimal if only the seller's distribution is known. Previous chapter Next chapter RelatedDetails Published:2022eISBN:978-1-61197-707-3 https://doi.org/10.1137/1.9781611977073Book Series Name:ProceedingsBook Code:PRDA22Book Pages:xvii + 3771
We continue the study of the performance for fixed-price mechanisms in the bilateral trade problem, and improve approximation ratios of welfare-optimal mechanisms in several settings. Specifically, in the case where …
We continue the study of the performance for fixed-price mechanisms in the bilateral trade problem, and improve approximation ratios of welfare-optimal mechanisms in several settings. Specifically, in the case where only the buyer distribution is known, we prove that there exists a distribution over different fixed-price mechanisms, such that the approximation ratio lies within the interval of [0.71, 0.7381]. Furthermore, we show that the same approximation ratio holds for the optimal fixed-price mechanism, when both buyer and seller distributions are known. As a result, the previously best-known (1 − 1/e+0.0001)-approximation can be improved to 0.71. Additionally, we examine randomized fixed-price mechanisms when we receive just one single sample from the seller distribution, for both symmetric and asymmetric settings. Our findings reveal that posting the single sample as the price remains optimal among all randomized fixed-price mechanisms.
We study the problem of social welfare maximization in bilateral trade, where two agents, a buyer and a seller, trade an indivisible item. The seminal result of Myerson and Satterthwaite …
We study the problem of social welfare maximization in bilateral trade, where two agents, a buyer and a seller, trade an indivisible item. The seminal result of Myerson and Satterthwaite shows that no incentive compatible and budget balanced (i.e., the mechanism does not run a deficit) mechanism can achieve the optimal social welfare in bilateral trade. Motivated by this impossibility result, we focus on approximating the optimal social welfare. We consider arguably the simplest form of mechanisms – the fixed-price mechanisms, where the designer offers trade at a fixed price to the seller and buyer. Besides the simple form, fixed-price mechanisms are also the only dominant strategy incentive compatible and budget balanced mechanisms in bilateral trade.
Noam Nisan and Amir Ronen conjectured that the best approximation ratio of deterministic truthful mechanisms for makespan-minimization for n unrelated machines is n. This work validates the conjecture.
Noam Nisan and Amir Ronen conjectured that the best approximation ratio of deterministic truthful mechanisms for makespan-minimization for n unrelated machines is n. This work validates the conjecture.