Computing the channel capacity of a communication system affected by uncertain transition probabilities

We study the problem of computing the capacity of a discrete memoryless channel under uncertainty affecting the channel law matrix, and possibly with a constraint on the average cost of the input distribution. The problem has been formulated in the literature as a max-min problem. We use the robust optimization methodology to convert the max-min problem to a standard convex optimization problem. For small-sized problems, and for many types of uncertainty, such a problem can be solved in principle using interior point methods (IPM). However, for large-scale problems, IPM are not practical. Here, we suggest an $\mathcal{O}(1/T)$ first-order algorithm based on Nemirovski (2004) which is applied directly to the max-min problem.Comment: 22 pages, 2 figure

Low-Sensitivity Functions from Unambiguous Certificates

We provide new query complexity separations against sensitivity for total Boolean functions: a power $3$ separation between deterministic (and even randomized or quantum) query complexity and sensitivity, and a power $2.22$ separation between certificate complexity and sensitivity. We get these separations by using a new connection between sensitivity and a seemingly unrelated measure called one-sided unambiguous certificate complexity ($UC_{min}$). We also show that $UC_{min}$ is lower-bounded by fractional block sensitivity, which means we cannot use these techniques to get a super-quadratic separation between $bs(f)$ and $s(f)$. We also provide a quadratic separation between the tree-sensitivity and decision tree complexity of Boolean functions, disproving a conjecture of Gopalan, Servedio, Tal, and Wigderson (CCC 2016). Along the way, we give a power $1.22$ separation between certificate complexity and one-sided unambiguous certificate complexity, improving the power $1.128$ separation due to G\"o\"os (FOCS 2015). As a consequence, we obtain an improved $\Omega(\log^{1.22} n)$ lower-bound on the co-nondeterministic communication complexity of the Clique vs. Independent Set problem.Comment: 25 pages. This version expands the results and adds Pooya Hatami and Avishay Tal as author

Immunizing Conic Quadratic Optimization Problems Against Implementation Errors

We show that the robust counterpart of a convex quadratic constraint with ellipsoidal implementation error is equivalent to a system of conic quadratic constraints. To prove this result we first derive a sharper result for the S-lemma in case the two matrices involved can be simultaneously diagonalized. This extension of the S-lemma may also be useful for other purposes. We extend the result to the case in which the uncertainty region is the intersection of two convex quadratic inequalities. The robust counterpart for this case is also equivalent to a system of conic quadratic constraints. Results for convex conic quadratic constraints with implementation error are also given. We conclude with showing how the theory developed can be applied in robust linear optimization with jointly uncertain parameters and implementation errors, in sequential robust quadratic programming, in Taguchi’s robust approach, and in the adjustable robust counterpart.Conic Quadratic Program;hidden convexity;implementation error;robust optimization;simultaneous diagonalizability;S-lemma

Using Business Games in Teaching DSS

In this study a business game is used as a vehicle for implementing decision support systems (DSS). Eighteen companies, consisting of ninety graduating M.B.A. students, participating in a business game were required to develop DSS and to report on the systems developed. Each of the eighteen companies developed a system of their own choosing, without external guidance. Individual questionnaires were later used to evaluate a number of relevant variables: use of systems, contribution of systems, association with systems and user satisfaction. Findings, compared with reported results of previous empirical study, exhibit differentiations in success of DSS between companies. This indicates the potential of using business games as an educational tool for teaching management information systems (MIS) and DSS

The Changing Shape of Networks: Lessons for the Auto Industry

The global financial crisis has brought tougher times to carmakers as the auto industry around the world experiences a sharp decrease in sales. Today, carmakers must tailor their strategies to succeed in the global markets. One important strategic consideration for these firms is their position in the market, relative to competition. We know that it is advantageous for a company to be positioned centrally in a market, but we still do not fully understand how some companies emerge as central. This study examines how early relationships in company networks may predict performance. Using a business simulation run, we show that establishing early centrality predicts later performance. The paper also defines a way of classifying centrality trajectories in social networks, providing a method that can be used more generally to predict markets change for the auto industry

Measuring DSS Effectiveness in a Simulated Environment

This study uses a business game as a vehicle for implementing decision support systems (DSS). Fifty-Eight companies, consisting of about 300 senior graduate students participating in a business game, developed DSS and reported on the systems developed. Questionnaires were later used to evaluate a number of relevant variables: use of systems, contribution of systems, and user satisfaction. Findings, consistent with previous empirical studies, strengthen the validity of the simulation exercise as a useful tool for measuring DSS effectiveness

Simulating Decision Support Systems: A Laboratory Experiment

This study implements decision support systems (DSS) in a business simulation game. Fifty-Eight companies, consisting of about 300 senior graduate students participating in a business game, developed DSS and reported on the systems developed. We later evaluated a number of variables related to their DSS: use of systems, contribution of systems, and user satisfaction. Our findings validate the use of the simulation exercise as a practical tool for measuring DSS effectiveness

INVESTORS’ DECISION TO TRADE STOCKS – AN EXPERIMENTAL STUDY

This paper experimentally examines the behavior of investors when buying and selling stocks. This behavior was tested under different conditions, among them restrictions on asset holdings or different information conditions. Basic financial theory suggests that subjects buy and sell according to expectations regarding the future prices of assets. On the other hand, behavioral biases, such as the disposition effect, suggest that subjects are affected by past performance of assets. In a series of experiments, subjects were asked to allocate a given endowment among six assets. All the assets had the same normal distribution. The results show that when subjects were not restricted regarding the number of assets they were allowed to hold and were given information only on the asset they hold, the holding time for losing and winning assets was the same, indicating that there was no effect of past performance. On the other hand, when subjects were required to hold three assets at all times and replace one asset on each round, they tended to sell losing assets too soon and hold winning assets too long. The results also show that subjects who are given information on market returns tend to sell winning assets (relatively to the market) too soon and hold losing assets too long.Behavioral finance, Disposition effect, experimental economics, momentum, trading.