Oligopolistic equilibrium and financial constraints

In this paper we present a model of oligopoly and financial constraints. We study allocations which are bankruptcy-free (BF) in the sense that no firm can drive another firm to bankruptcy without becoming bankrupt. We show how such allocations can be sustained as an equilibrium of a dynamic game. When there are two firms, all equilibria yield BF allocations. When there are more than two firms, allocations other than BF can be sustained as equilibria but in some cases the set of BF allocations still useful in explaining the shape of equilibrium set.

Oligopolistic Equilibrium and Financial Constraints

We provide a model of dynamic duopoly in which firms face financial constraints and disappear when they are unable to fulfill them. We show that, in some cases, Cournot outputs are no longer supported in equilibrium, because if these outputs were set, a firm may have incentives to ruin the other. In these cases, standard grim-trigger strategies in which collusion is sustained by infinite reversion to Cournot outputs cannot be used. We show that there is a stationary Markov equilibrium in mixed strategies where predation occurs with a positive probability. We also obtain a modified "folk theorem". We show that any bankruptcy-free outputs (outputs in which no firm can drive another firm to bankruptcy without becoming bankrupt itself) that attain individually rational profits (reflecting bankruptcy consideration) can be supported by a subgame perfect Nash equilibrium when firms are sufficiently long-sighted

Online education and the mental health of faculty during the COVID-19 pandemic in Japan

While the negative impact of the pandemic on students' mental health has been studied around the world, very little is known about the mental health of faculty and staff. This research aims to examine mental health among Japanese faculty members who taught online courses during the COVID-19 pandemic. We recruited 537 university faculty members and assessed their mental health using the World Health Organization-Five Well-Being Index (WHO-5), both retrospectively (during the academic year before the onset of the pandemic) and during the pandemic. We also evaluated workload (number of online lectures taught and preparation time per class), difficulty in using information technology (IT) for online classes, and satisfaction with the university support service for online education. As a result, the WHO-5 score during the COVID-19 pandemic was significantly lower than before, and 33.5% of the faculty members were recognized as being at risk for mental illness during the COVID-19 pandemic. A binomial logistic regression analysis revealed two significant risk factors for mental illness-faculty members were more at risk for mental illness when they experienced difficulty in using IT for online classes, and were unsatisfied with the administrative support for online education. The deterioration of mental health during the COVID-19 was not predicted by workload, such as the number of online lectures and preparation time. These results suggest the importance of improving workplace support services, especially IT support, to prevent mental health deterioration among faculty teaching online.Peer reviewe

Fast solution methods

International audienceThe standard boundary element method applied to the time harmonic Helmholtz equation yields a numerical method with $O(N^3)$ complexity when using a direct solution of the fully populated system of linear equations. Strategies to reduce this complexity are discussed in this paper. The $O(N^3)$ complexity issuing from the direct solution is first reduced to $O(N^2)$ by using iterative solvers. Krylov subspace methods as well as strategies of preconditioning are reviewed. Based on numerical examples the influence of different parameters on the convergence behavior of the iterative solvers is investigated. It is shown that preconditioned Krylov subspace methods yields a boundary element method of $O(N^2)$ complexity. A further advantage of these iterative solvers is that they do not require the dense matrix to be set up. Only matrix–vector products need to be evaluated which can be done efficiently using a multilevel fast multipole method. Based on real life problems it is shown that the computational complexity of the boundary element method can be reduced to $O(N \log_2 N)$ for a problem with $N$ unknowns

Strategyproof matching with regional minimum and maximum quotas

This paper considers matching problems with individual/regional minimum/maximum quotas. Although such quotas are relevant in many real-world settings, there is a lack of strategyproof mechanisms that take such quotas into account. We first show that without any restrictions on the regional structure, checking the existence of a feasible matching that satisfies all quotas is NP-complete. Then, assuming that regions have a hierarchical structure (i.e., a tree), we show that checking the existence of a feasible matching can be done in time linear in the number of regions. We develop two strategyproof matching mechanisms based on the Deferred Acceptance mechanism (DA), which we call Priority List based Deferred Acceptance with Regional minimum and maximum Quotas (PLDA-RQ) and Round-robin Selection Deferred Acceptance with Regional minimum and maximum Quotas (RSDA-RQ). When regional quotas are imposed, a stable matching may no longer exist since fairness and nonwastefulness, which compose stability, are incompatible. We show that both mechanisms are fair. As a result, they are inevitably wasteful. We show that the two mechanisms satisfy different versions of nonwastefulness respectively; each is weaker than the original nonwastefulness. Moreover, we compare our mechanisms with an artificial cap mechanism via simulation experiments, which illustrate that they have a clear advantage in terms of nonwastefulness and student welfare

Resolving Conflicting Preferences in School Choice

The Boston mechanism is among the most popular school choice procedures in use. Yet, the mechanism has been criticized for its poor incentive and welfare performances, which led the Boston Public Schools to recently replace it with Gale and Shapley's deferred acceptance algorithm (henceforth, DA). The DA elicits truthful revelation of "ordinal" preferences whereas the Boston mechanism does not; but the latter induces participants to reveal their "cardinal" preferences (i.e., their relative preference intensities) whereas the former does not. We show that cardinal preferences matter more when families have similar ordinal preferences and schools have coarse priorities, two common features of many school choice environments. Specifically, when students have the same ordinal preferences and schools have no priorities, the Boston mechanism Pareto dominates the DA in ex ante welfare. The Boston mechanism may not harm but rather benefit participants who may not strategize well. In the presence of school priorities, the Boston mechanism also tends to facilitate a greater access than the DA to good schools by those lacking priorities at those schools. These results contrast with the standard view, and cautions against a hasty rejection of the Boston mechanism in favor of mechanisms such as the DA

Oligopolistic equilibrium and financial constraints

We model a dynamic duopoly in which firms can potentially drive their rivals from the market. For some parameter values, the Cournot equilibrium outcome cannot be sustained in an infinitely repeated setting. In those cases, there is a Markov perfect equilibrium in mixed strategies in which one firm, eventually, will exit the market with probability one. Producer surplus in the maximum collusive outcome is greater under bankruptcy consideration, because the outcome that maximizes joint profits is skewed in favor of the more efficient firm. Consumer surplus and social welfare also increase in many cases, although those effects are generally ambiguous.Beviá acknowledges financial support from ECO2014 53051, SGR2014-515, and PROMETEO/2013/037. Corchón acknowledges financial support from MDM 2014-0431, ECO2017_87769_P, and S2015/HUM-3444. Yasuda acknowledges research support from Grant-in-Aid for Scientific Research, 23683002 and 17K13702, administered by the Japanese Ministry of Education

A Modular Approach to the Incompressibility of Block-Cipher-Based AEADs

Incompressibility is one of the most fundamental security goals in white-box cryptography. Given recent advances in the design of efficient and incompressible block ciphers such as SPACE, SPNbox and WhiteBlock, we demonstrate the feasibility of reducing incompressible AEAD modes to incompressible block ciphers. We first observe that several existing AEAD modes of operation, including CCM, GCM(-SIV), and OCB, would be all insecure against white-box adversaries even when used with an incompressble block cipher. This motivates us to revisit and formalize incompressibility-based security definitions for AEAD schemes and for block ciphers, so that we become able to design modes and reduce their security to that of the underlying ciphers. Our new security notion for AEAD, which we name whPRI, is an extension of the pseudo-random injection security in the black-box setting. Similar security notions are also defined for other cryptosystems such as privacy-only encryption schemes. We emphasize that whPRI ensures quite strong authenticity against white-box adversaries: existential unforgeability beyond leakage. This contrasts sharply with previous notions which have ensured either no authenticity or only universal unforgeability. For the underlying ciphers we introduce a new notion of whPRP, which extends that of PRP in the black-box setting. Interestingly, our incompressibility reductions follow from a variant of public indifferentiability. In particular, we show that a practical whPRI-secure AEAD mode can be built from a whPRP-secure block cipher: We present a SIV-like composition of the sponge construction (utilizing a block cipher as its underlying primitive) with the counter mode and prove that such a construction is (in the variant sense) public indifferentiable from a random injection. To instantiate such an AEAD scheme, we propose a 256-bit variant of SPACE, based on our conjecture that SPACE should be a whPRP-secure cipher

Improving Fairness and Efficiency in Matching with Distributional Constraints: An Alternative Solution for the Japanese Medical Residency Match

Regional imbalance of doctors is a serious issue in many countries. In an attempt to average the geographical distribution of doctors, the Japanese government introduced ``regional caps'' recently, restricting the total number of medical residents matched within each region. Motivated by this policy change, Kamada and Kojima (2013) proposed a mechanism called the flexible deferred acceptance mechanism (FDA) that makes every doctor weakly better off than the current system. In this paper, we further study this problem and develop an alternative mechanism that we call the priority-list based deferred acceptance mechanism (PLDA). Both mechanisms enable hospitals in the same region to fill their capacities flexibly until the regional cap is filled. FDA lets hospitals take turns to (tentatively) choose the best remaining doctor, while PLDA lets each region directly decide which doctor is (tentatively) matched with which hospital based on its priority list. We show that PLDA performs better than FDA in terms of efficiency and fairness through theoretical and computational analyses