Matchings under Preferences: Strength of Stability and Tradeoffs

We propose two solution concepts for matchings under preferences: robustness and near stability . The former strengthens while the latter relaxes the classical definition of stability by Gale and Shapley (1962). Informally speaking, robustness requires that a matching must be stable in the classical sense, even if the agents slightly change their preferences. Near stability, however, imposes that a matching must become stable (again, in the classical sense) provided the agents are willing to adjust their preferences a bit. Both of our concepts are quantitative; together they provide means for a fine-grained analysis of the stability of matchings. Moreover, our concepts allow the exploration of tradeoffs between stability and other criteria of social optimality, such as the egalitarian cost and the number of unmatched agents. We investigate the computational complexity of finding matchings that implement certain predefined tradeoffs. We provide a polynomial-time algorithm that, given agent preferences, returns a socially optimal robust matching (if it exists), and we prove that finding a socially optimal and nearly stable matching is computationally hard.

GAMES, game theory and artificial intelligence

PurposeThe purpose of this paper is to illustrate how game theoretic solution concepts inform what classes of problems will be amenable to artificial intelligence and machine learning (AI/ML), and how to evolve the interaction between human and artificial intelligence.Design/methodology/approachThe approach addresses the development of operational gaming to support planning and decision making. It then provides a succinct summary of game theory for those designing and using games, with an emphasis on information conditions and solution concepts. It addresses how experimentation demonstrates where human decisions differ from game theoretic solution concepts and how games have been used to develop AI/ML. It concludes by suggesting what classes of problems will be amenable to AI/ML, and which will not. It goes on to propose a method for evolving human/artificial intelligence.FindingsGame theoretic solution concepts inform classes of problems where AI/ML 'solutions' will be suspect. The complexity of the subject requires a campaign of learning.Originality/valueThough games have been essential to the development of AI/ML, practitioners have yet to employ game theory to understand its limitations.

Fuzzy Random Bimatrix Games Based on Possibility and Necessity Measures

In this study, we formulate bimatrix games with fuzzy random payoffs, and introduce equilibrium solution concepts based on possibility and necessity measures. It is assumed that each player has linear fuzzy goals for his/her payoff. To obtain equilibrium solutions based on the possibility and necessity measures, we propose two algorithms in which quadratic programming problems are solved repeatedly until equilibrium conditions are satisfied.

Dynamic Bargaining and Time-Consistency in Linear-State and Homogeneous Linear-Quadratic Cooperative Differential Games

Three different solution concepts are reviewed and computed for linear-state and homogeneous linear-quadratic cooperative differential games with asymmetric players. Discount rates can be nonconstant and/or different. Special attention is paid to the issues of time-consistency, agreeability and subgame-perfectness, both from the viewpoint of sustainability of cooperation and from the credibility of the announced equilibrium strategies.

Adversarial Risk Analysis for Auctions Using Mirror Equilibrium and Bayes Nash Equilibrium

In this paper, we use the adversarial risk analysis (ARA) methodology to model first-price sealed-bid auctions under quite realistic assumptions. We extend prior work to find ARA solutions for mirror equilibrium and Bayes Nash equilibrium solution concepts, not only for risk-neutral but also for risk-averse and risk-seeking bidders. We also consider bidders having different wealth and assume that the auctioned item has a reserve price.

Conceptual Study and Manufacturing of a Configurable and Weld-Free Lattice Base for Automatic Food Machines

The study is aimed at developing a modular lattice base for automatic food machines, starting with a solution already patented by some of the authors. In this case, welded carpentry modules were interlocked with a system of profiles and metal inserts, also in welded carpentry, and the union was stabilized by structural adhesive bonding. Since welding involves long processing times and thermal distortions to be restored later, the driver of this study is to limit the use of welding as much as possible while increasing the modularity of the construction. For this purpose, various solution concepts have been generated where a common feature is the presence of rods of the same geometry and section to be joined together in configurable structural nodes. The concepts are qualitatively evaluated in light of the requirements, and the selected concept is digitally and physically prototyped. The prototype has been in service from over 5 years without showing any problems whatsoever.