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

Hyperfine transition induced by atomic motion above a paraffin-coated magnetic film

We measured transitions between the hyperfine levels of the electronic ground state of potassium-39 atoms (transition frequency: 460 MHz) as the atoms moved through a periodic magneto-static field produced above the magnetic-stripe domains of a magnetic film. The period length of the magnetic field was 3.8 um. The atoms were incident to the field as an impinging beam with the most probable velocity of 550 m/s and experienced a peak oscillating field of 20 mT. Unwanted spin relaxation caused by the collisions of the atoms with the film surface was suppressed by the paraffin coating on the film. We observed increasing hyperfine transition probabilities as the frequency of the field oscillations experienced by the atoms increased from 0 to 140 MHz for the atomic velocity of 550 m/s, by changing the incident angle of the atomic beam with respect to the stripe domains. Numerical calculation of the time evolution of the hyperfine states revealed that the oscillating magnetic field experienced by the atoms induced the hyperfine transitions, and the main process was not a single-quantum transition but rather multi-quanta transitions.Comment: 12 pages, 6 figure