Anti-Sharing.

Anti-Sharing may solve the sharing problem of teams: the team members promise a fixed payment to the Anti-Sharer. He collects the actual output and pays out its value to them. We prove that the internal Anti- Sharer is unproductive in equilibrium.

A Tight Algorithm for Strongly Connected Steiner Subgraph On Two Terminals With Demands

Given an edge-weighted directed graph $G=(V,E)$ on $n$ vertices and a set $T=\{t_1, t_2, \ldots, t_p\}$ of $p$ terminals, the objective of the \scss ($p$-SCSS) problem is to find an edge set $H\subseteq E$ of minimum weight such that $G[H]$ contains an $t_{i}\rightarrow t_j$ path for each $1\leq i\neq j\leq p$. In this paper, we investigate the computational complexity of a variant of $2$-SCSS where we have demands for the number of paths between each terminal pair. Formally, the \sharinggeneral problem is defined as follows: given an edge-weighted directed graph $G=(V,E)$ with weight function $\omega: E\rightarrow \mathbb{R}^{\geq 0}$, two terminal vertices $s, t$, and integers $k_1, k_2$ ; the objective is to find a set of $k_1$ paths $F_1, F_2, \ldots, F_{k_1}$ from $s\leadsto t$ and $k_2$ paths $B_1, B_2, \ldots, B_{k_2}$ from $t\leadsto s$ such that $\sum_{e\in E} \omega(e)\cdot \phi(e)$ is minimized, where $\phi(e)= \max \Big\{|\{i\in [k_1] : e\in F_i\}|\ ,\ |\{j\in [k_2] : e\in B_j\}|\Big\}$. For each $k\geq 1$, we show the following: The \sharing problem can be solved in $n^{O(k)}$ time. A matching lower bound for our algorithm: the \sharing problem does not have an $f(k)\cdot n^{o(k)}$ algorithm for any computable function $f$, unless the Exponential Time Hypothesis (ETH) fails. Our algorithm for \sharing relies on a structural result regarding an optimal solution followed by using the idea of a "token game" similar to that of Feldman and Ruhl. We show with an example that the structural result does not hold for the \sharinggeneral problem if $\min\{k_1, k_2\}\geq 2$. Therefore \sharing is the most general problem one can attempt to solve with our techniques.Comment: To appear in Algorithmica. An extended abstract appeared in IPEC '1

Anti-Sharing

Anti-Sharing may solve the sharing problem of teams: the team members promise a fixed payment to the Anti-Sharer. He collects the actual output and pays out its value to them. We prove that the internal Anti-Sharer is unproductive in equilibrium. -- Anti-Sharing kann das Teilungsproblem der Teamproduktion lösen: Die Teammitglieder versprechen dem Antisharer zunächst einen fixen Betrag. Der Anti-Sharer bekommt den tatsächlichen Teamoutput und zahlt dessen Wert an jedes Teammitglied aus (vermindert um die fixe Zahlung). Wir zeigen, daß der Anti-Sharer im Gleichgewicht unproduktiv ist.team production,sharing problem,bonding,theory of the firm

An Ordinal Shapley Value for Economic Environments

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The sharing problem is formulated in the preferences-endowments space. The solution is defined in a recursive manner incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (TU) games. We show a solution exists, and refer to it as an Ordinal Shapley value (OSV). The OSV associates with each problem an allocation as well as a matrix of concessions ``measuring'' the gains each agent foregoes in favor of the other agents. We analyze the structure of the concessions, and show they are unique and symmetric. Next we characterize the OSV using the notion of coalitional dividends, and furthermore show it is monotone in an agent's initial endowments and satisfies anonymity. Finally, similarly to the weighted Shapley value for TU games, we construct a weighted OSV as well.Non-Transferable utility games, Shapley value, consistency, fairness

Anti-Sharing.

The paper proposes a mechanism that may implement first-best effort in simultaneous teams. Within the framework of this mechanism, each team members is obliged to make a fixed, non-contingent payment, and chooses his individual effort. After the output is produced, each team member receives a gross payment that equals the actual team output. We demonstrate that a Nash equilibrium exists in which each team member chooses first-best effort. We call this mechanism ?Anti-Sharing? since it solves the sharing problem that causes the inefficiency in teams. The Anti-Sharing mechanism requires one player to specialize on the role of an ?Anti-Sharer?. With an external Anti-Sharer who works on a non-profit base, the mechanism can implement first-best effort. If, however, the Anti-Sharer comes from within the team and desires a positive payoff, then the mechanism may implement not more than second-best effort. The latter version of the model could be interpreted as a new theory of firms and partnerships in the sense of the theory of Alchian and Demsetz (1972). --Efficient Effort in Teams,Second-Best Solution,Partnerships

An Energy Sharing Game with Generalized Demand Bidding: Model and Properties

This paper proposes a novel energy sharing mechanism for prosumers who can produce and consume. Different from most existing works, the role of individual prosumer as a seller or buyer in our model is endogenously determined. Several desirable properties of the proposed mechanism are proved based on a generalized game-theoretic model. We show that the Nash equilibrium exists and is the unique solution of an equivalent convex optimization problem. The sharing price at the Nash equilibrium equals to the average marginal disutility of all prosumers. We also prove that every prosumer has the incentive to participate in the sharing market, and prosumers' total cost decreases with increasing absolute value of price sensitivity. Furthermore, the Nash equilibrium approaches the social optimal as the number of prosumers grows, and competition can improve social welfare.Comment: 16 pages, 7 figure

Distributed Reconstruction of Nonlinear Networks: An ADMM Approach

In this paper, we present a distributed algorithm for the reconstruction of large-scale nonlinear networks. In particular, we focus on the identification from time-series data of the nonlinear functional forms and associated parameters of large-scale nonlinear networks. Recently, a nonlinear network reconstruction problem was formulated as a nonconvex optimisation problem based on the combination of a marginal likelihood maximisation procedure with sparsity inducing priors. Using a convex-concave procedure (CCCP), an iterative reweighted lasso algorithm was derived to solve the initial nonconvex optimisation problem. By exploiting the structure of the objective function of this reweighted lasso algorithm, a distributed algorithm can be designed. To this end, we apply the alternating direction method of multipliers (ADMM) to decompose the original problem into several subproblems. To illustrate the effectiveness of the proposed methods, we use our approach to identify a network of interconnected Kuramoto oscillators with different network sizes (500~100,000 nodes).Comment: To appear in the Preprints of 19th IFAC World Congress 201