We study cooperative games with supermodular costs. We show that supermodular costs arise in a variety of situations: in particular, we show that the problem of minimizing a linear function over a supermodular polyhedron–a problem that often arises in combinatorial optimization–has supermodular optimal costs. In addition, we examine the computational complexity of the least core … Read more
We propose a new gradient based scheme to approximate Nash equilibria of large sequential two-player, zero-sum games. The algorithm uses modern smoothing techniques for saddle-point problems tailored specifically for the polytopes used in the Nash equilibrium problem. Citation Working Paper, Tepper School of Business, Carnegie Mellon University Article Download View A gradient-based approach for computing … Read more
Hayrapetyan, Tardos and Wexler recently introduced a framework to study the impact of collusion in congestion games on the quality of Nash equilibria. We adopt their framework to network games and focus on the well established price of anarchy as a measure of this impact. We first investigate nonatomic network games with coalitions. For this … Read more
Reverse logistics networks often consist of several tiers with independent members competing at each tier. This paper develops a methodology to examine the individual entity behavior in reverse production systems where every entity acts to maximize its own benefits. We consider two tiers in the network, collectors and processors. The collectors determine individual flow functions … Read more
The computation of leastcore and prenucleolus is an efficient way of allocating a common resource among N players. It has, however, the drawback being a linear programming problem with 2^N-2 constraints. In this paper we show how, in the case of convex production games, generate constraints by solving small size linear programming problems, with both … Read more
We present polynomial-time interior-point algorithms for solving the Fisher and Arrow-Debreu competitive market equilibrium problems with linear utilities and $n$ players. Both of them have the arithmetic operation complexity bound of $O(n^4\log(1/\epsilon))$ for computing an $\epsilon$-equilibrium solution. If the problem data are rational numbers and their bit-length is $L$, then the bound to generate an … Read more
We extend the analysis of [27] to handling more general utility functions: piece-wise linear functions, which include Leontief’s utility. We show that the problem reduces to the general analytic center model discussed in [27]. Thus, the same linear programming complexity bound applies to approximating the Fisher equilibrium problem with these utilities. More importantly, we show … Read more
A notorious open problem in the field of rendezvous search is to decide the rendezvous value of the symmetric rendezvous search problem on the line, when the initial distance apart between the two players is 2. We show that the symmetric rendezvous value is within the interval (4.1520, 4.2574), which considerably improves the previous best … Read more
In this paper we show that if all agents are equipped with discrete concave production functions, then a feasible price allocation pair is a market equilibrium if and only if it solves a linear programming problem, similar to, but perhaps simpler than the one invoked in Yang (2001). Using this result, but assuming discrete concave … Read more
Given a finite set of outlets with joint normally distributed demands and identical holding and penalty costs, inventory centralization induces a cooperative cost allocation game with nonempty core. It is well known that for this newsvendor inventory setting the expected cost of centralization can be expressed as a constant multiple of the standard deviation of … Read more