Stronger Solution Concept Research Articles

Solutions and strong solutions of min-product fuzzy relation inequalities with application in supply chain

Min-product fuzzy relation inequalities are introduced to describe the price requirements in the supply chain system. We first investigate the resolution method and structure of the complete solution set to min-product fuzzy relation inequalities. Motivated by the practical application, we further define concept of strong solution. A strong solution represents a feasible pricing scheduling, enabling all the suppliers and retailers profitable in the trade activity. Relevant results about the strong solution are obtained. Based on such results, a step-by-step algorithm is developed for finding all the strong solutions to a system of min-product fuzzy relation inequalities. Numerical examples are given to illustrate the algorithm.

Optimal Strong Solution of the Weighted Minimax Problem With Fuzzy Relation Equation Constraints

Max–min fuzzy relation equations could be used to describe three-tier multimedia streaming architecture. To make all the regional servers take part in the system, we define a strong solution concept. The corresponding weighted minimax problem is studied in this paper. A novel resolution is developed for obtaining the optimal strong solution of our proposed fuzzy relation weighted minimax problem.

Trading Networks with Bilateral Contracts

We consider general networks of bilateral contracts that include supply chains. We define a new stability concept, called trail stability, and show that any network of bilateral contracts has a trail-stable outcome whenever agents' choice functions satisfy full substitutability. Trail stability is a natural extension of chain stability, but is a stronger solution concept in general contract networks. Trail-stable outcomes are not immune to deviations of arbitrary sets of firms. In fact, we show that outcomes satisfying an even more demanding stability property -- full trail stability -- always exist. For fully trail-stable outcomes, we prove results on the lattice structure, the rural hospitals theorem, strategy-proofness and comparative statics of firm entry and exit. We pin down a condition under which trail-stable and fully trail-stable outcomes coincide. We then completely describe the relationships between various other concepts. When contracts specify trades and prices, we also show that competitive equilibrium exists in networked markets even in the absence of fully transferable utility. The competitive equilibrium outcome is (fully) trail-stable.

Optimal collusion-resistant mechanisms with verification

We present the first general positive result on the construction of collusion-resistant mechanisms, that is, mechanisms that guarantee dominant strategies even when agents can form arbitrary coalitions and exchange compensations (sometimes referred to as transferable utilities or side payments). This is a much stronger solution concept as compared to truthful or even group strategyproof mechanisms, and only impossibility results were known for this type of mechanisms in the “classical” model.We describe collusion-resistant mechanisms with verification that return optimal solutions for a wide class of mechanism design problems (which includes utilitarian ones as a special case). Note that every collusion-resistant mechanism without verification must have an unbounded approximation factor and, in general, optimal solutions cannot be obtained even if we content ourselves with truthful (“non-collusion-resistant”) mechanisms. All these results apply to problems that have been extensively studied in the algorithmic mechanism design literature like, for instance, task scheduling and inter-domain routing.

Strong-Incentive, High-Throughput Channel Assignment for Noncooperative Wireless Networks

Channel assignment is a very important topic in wireless networks. In this paper, we study FDMA channel assignment in a noncooperative wireless network, where devices are selfish. Existing work on this problem has considered Nash Equilibrium (NE), which is not a very strong solution concept and may not guarantee a good system performance. In contrast, in this work, we introduce a payment formula to ensure the existence of a Strongly Dominant Strategy Equilibrium (SDSE), a different solution concept that gives participants much stronger incentives. We show that, when the system converges to an SDSE, it also achieves global optimality in terms of system throughput. Furthermore, we extend our work to the case in which some radios have a limited tunability. We show that in such a case, nevertheless, it is generally impossible to have a similar SDSE solution; with additional assumptions on the numbers of radios and the types of channels, etc., we can again achieve an SDSE solution that guarantees optimal system throughput. Besides this extension, we also consider other extensions of our strategic game to achieve throughput fairness and to deal with possibly inconsistent information caused by players joining and leaving. Finally, we evaluate our design with simulated experiments. Numerical results verify that the system does converge to the globally optimal channel assignment with the proposed payment formula, and that the system throughput is significantly higher than that achievable with the random-based and NE-based channel assignment schemes.

Admissibility and Event-Rationality

Brandenburger et al. (2008) establish epistemic foundations for rationality and common assumption of rationality (RCAR), where rationality includes admissibility, using lexicographic type structures. Their negative result that RCAR is empty whenever the type structure is complete and continuous suggests that iterated admissibility (IA) requires players to have prior knowledge about each other, and therefore is a strong solution concept, not at the same level as iterated elimination of strongly dominated strategies (IEDS). We follow an alternative approach using standard type structures and show that IA can be generated in a complete and continuous type structure. A strategy is event-rational if it is a best response to a conjecture, as usual, and in addition it passes a “tie-breaking” test based on a set E of strategies of the other player. Event-rationality and common belief in event-rationality (RCBER) is characterized by a solution concept we call hypo-admissible sets and, in a complete structure, generates the strategies that are admissible and survive the iterated elimination of strongly dominated strategies (Dekel and Fudenberg (1990)). Extending event-rationality by adding what a player is certain about the other’s strategies as a tie-breaking set to each round of mutual belief we get common belief of extended event-rationality (RCBeER), which generates a more restrictive solution concept than the SAS (Brandenburger et al. (2008)) and in a complete structure produces the IA strategies. Contrary to the negative result in Brandenburger et al. (2008), we show that RCBER and RCBeER are nonempty in complete, continuous and compact type structures, therefore providing an epistemic criterion for IA

Approval voting: three examples

In this paper we discuss three examples of approval voting games. The first one illustrates that a stronger solution concept than perfection is needed for a strategic analysis of this type of games. The second example shows that sophisticated voting can imply that the Condorcet winner gets no vote. The third example shows the possibility of insincere voting being a stable equilibrium.

Interactive beliefs, epistemic independence and strong rationalizability

We use a universal, extensive form interactive beliefs system to provide an epistemic characterization of a weak and a strong notion of rationalizability with independent beliefs. The weak solution concept is equivalent to backward induction in generic perfect information games where no player moves more than once in any play. The strong solution concept is related to explicability (Reny,22) and is outcome-equivalent to backward induction in generic games of perfect information.

Dominance or maximin: How to solve an English auction

It is widely believed that the English auction is solved after the dominated strategies are eliminated. This paper demonstrates that the dominance criterion is not very effective in many English auction models. To bid more than the true willingness to pay is dominated but a stronger solution concept is needed to deduce that the buyers increase the price in small steps up to their valuation. An iterated application of the dominance criterion does not solve the problem, but if it is assumed that the buyers use their maximin strategies the usual argument holds.