Game Theoretic Approach to the Stabilization of Heterogeneous Multiagent Systems Using Subsidy

We consider a multiagent system consisting of selfish and heterogeneous agents. Its behavior is modeled by multipopulation replicator dynamics, where payoff functions of populations are different from each other. In general, there exist several equilibrium points in the replicator dynamics. In order to stabilize a desirable equilibrium point, we introduce a controller called a government which controls the behaviors of agents by offering them subsidies. In previous work, it is assumed that the government determines the subsidies based on the populations the agents belong to. In general, however, the government cannot identify the members of each population. In this paper, we assume that the government observes the action of each agent and determines the subsidies based on the observed action profile. Then, we model the controlled behaviors of the agents using replicator dynamics with feedback. We derive a stabilization condition of the target equilibrium point in the replicator dynamics.Comment: 6 pages, IEEE Conference on Decision and Control, 201

On balanced claw designs of complete multi-partite graphs

AbstractIn this paper, it is shown that a necessary and sufficient condition for the existence of a balanced claw design BCD(m, n, c, λ) of a complete m-partite graph λKm(n, n,…,n) is λ(m - 1)n ≡ 0 (mod 2c) and (m - 1)n ⩾ c

P3-Factorization of complete bipartite graphs

AbstractIn this paper, it is shown that a necessary and sufficient condition for the existence of a P3-factorization of Km,n, is (i) m+n≡0 (mod 3), (ii) m⩽2n, (iii) n⩽2m and (iv) 3mn2(m+n) is an integer

Cycle-factorization of symmetric complete multipartite digraphs

AbstractFirst, we show that a necessary and sufficient condition for the existence of a C3-factorization of the symmetric tripartite digraph Kn1,n2,n3∗, is n1 = n2 = n3. Next, we show that a necessary and sufficient condition for the existence of a C̄2k-factorization of the symmetric complete multipartite digraph Kn1, n2,…,nm is n1 = n2 = … = nm = 0 (mod k) for even m and n1 = n2 = … = ≡ 0 (mod 2k) for odd m

Star-factorization of symmetric complete bipartite multi-digraphs

AbstractWe show that a necessary and sufficient condition for the existence of an Sk-factorization of the symmetric complete bipartite multi-digraph λKm,n∗ is m=n≡0(modk(k−1)/d), where d=(λ,k−1)

(Hibiki) Resonance: Art, Healing, and the Holistic View of Life.

M.F.A. Thesis. University of Hawaiʻi at Mānoa 2018