Repeated Multimarket Contact with Private Monitoring: A Belief-Free Approach

This paper studies repeated games where two players play multiple duopolistic games simultaneously (multimarket contact). A key assumption is that each player receives a noisy and private signal about the other's actions (private monitoring or observation errors). There has been no game-theoretic support that multimarket contact facilitates collusion or not, in the sense that more collusive equilibria in terms of per-market profits exist than those under a benchmark case of one market. An equilibrium candidate under the benchmark case is belief-free strategies. We are the first to construct a non-trivial class of strategies that exhibits the effect of multimarket contact from the perspectives of simplicity and mild punishment. Strategies must be simple because firms in a cartel must coordinate each other with no communication. Punishment must be mild to an extent that it does not hurt even the minimum required profits in the cartel. We thus focus on two-state automaton strategies such that the players are cooperative in at least one market even when he or she punishes a traitor. Furthermore, we identify an additional condition (partial indifference), under which the collusive equilibrium yields the optimal payoff.Comment: Accepted for the 9th Intl. Symp. on Algorithmic Game Theory; An extended version was accepted at the Thirty-Fourth AAAI Conference on Artificial Intelligence (AAAI-20

Coalition structure generation in cooperative games with compact representations

This paper presents a new way of formalizing the coalition structure generation problem (CSG) so that we can apply constraint optimization techniques to it. Forming effective coalitions is a major research challenge in AI and multi-agent systems. CSG involves partitioning a set of agents into coalitions to maximize social surplus. Traditionally, the input of the CSG problem is a black-box function called a characteristic function, which takes a coalition as input and returns the value of the coalition. As a result, applying constraint optimization techniques to this problem has been infeasible. However, characteristic functions that appear in practice often can be represented concisely by a set of rules, rather than treating the function as a black box. Then we can solve the CSG problem more efficiently by directly applying constraint optimization techniques to this compact representation. We present new formalizations of the CSG problem by utilizing recently developed compact representation schemes for characteristic functions. We first characterize the complexity of CSG under these representation schemes. In this context, the complexity is driven more by the number of rules than by the number of agents. As an initial step toward developing efficient constraint optimization algorithms for solving the CSG problem, we also develop mixed integer programming formulations and show that an off-the-shelf optimization package can perform reasonably well

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

Synthesis of magneto-optically active polyanilines

We report preparation of polyaniline (PANI) with radicals on the N-positions. Chirality of a PANI having optically active substituent is retained even upon oxidation by m-chloroperoxybenzoic acid in chloroform to generate spin species. Electron spin resonance and circular dichroism spectroscopy measurements suggest that the chiral paramagnetic properties of PANIs are derived from the combination of chiral side chains and oxyradicals in the structure of the polymer. This report focuses on a new synthetic approach for obtaining magneto-optically active polyanilines

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

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