Multilinear formulations for computing Nash equilibrium of multi-player matrix games

We present multilinear and mixed-integer multilinear programs to find a Nash equilibrium in multi-player strategic-form games. We compare the formulations to common algorithms in Gambit, and conclude that a multilinear feasibility program finds a Nash equilibrium faster than any of the methods we compare it to, including the quantal response equilibrium method, which is recommended … Read more

CliSAT: a SAT-based exact algorithm for hard maximum clique problems

Given a graph, the maximum clique problem (MCP) asks for determining a complete subgraph with the largest possible number of vertices. We propose a new exact algorithm, called CliSAT, to solve the MCP to proven optimality. This problem is of fundamental importance in graph theory and combinatorial optimization due to its practical relevance for a … Read more

A branch-and-prune algorithm for discrete Nash equilibrium problems

We present a branch-and-prune procedure for discrete Nash equilibrium problems with a convex description of each player’s strategy set. The derived pruning criterion does not require player convexity, but only strict convexity of some player’s objective function in a single variable. If satisfied, it prunes choices for this variable by stating activity of certain constraints. … Read more

Semi-infinite models for equilibrium selection

In their seminal work `A General Theory of Equilibrium Selection in Games’ (The MIT Press, 1988) Harsanyi and Selten introduce the notion of payoff dominance to explain how players select some solution of a Nash equilibrium problem from a set of nonunique equilibria. We formulate this concept for generalized Nash equilibrium problems, relax payoff dominance … Read more

Inefficiency of pure Nash equilibria in series-parallel network congestion games

We study the inefficiency of pure Nash equilibria in symmetric unweighted network congestion games defined over series-parallel networks. We introduce a quantity y(D) to upper bound the Price of Anarchy (PoA) for delay functions in class D. When D is the class of polynomial functions with highest degree p, our upper bound is 2^{p+1} − … Read more

Robust Integration of Electric Vehicles Charging Load in Smart Grid’s Capacity Expansion Planning

Battery charging of electric vehicles (EVs) needs to be properly coordinated by electricity producers to maintain network reliability. In this paper, we propose a robust approach to model the interaction between a large fleet of EV users and utilities in a long-term generation expansion planning problem. In doing so, we employ a robust multi-period adjustable … Read more

Nash Bargaining Partitioning in Decentralized Portfolio Management

In the context of decentralized portfolio management, understanding how to distribute a fixed budget among decentralized intermediaries is a relevant question for financial investors. We consider the Nash bargaining partitioning for a class of decentralized investment problems, where intermediaries are in charge of the portfolio construction in heterogeneous local markets and act as risk/disutility minimizers. … Read more

Solving Multiplicative Programs by Binary-encoding the Multiplication Operation

Multiplicative programs in the form of maximization and/or minimization have numerous applications in conservation planning, game theory, and multi-objective optimization settings. In practice, multiplicative programs are challenging to solve because of their multiplicative objective function (a product of continuous or integer variables). These challenges are twofold: 1. As the number of factors in the objective … Read more

An Exact Projection-Based Algorithm for Bilevel Mixed-Integer Problems with Nonlinearities

We propose an exact global solution method for bilevel mixed-integer optimization problems with lower-level integer variables and including nonlinear terms such as, \eg, products of upper-level and lower-level variables. Problems of this type are extremely challenging as a single-level reformulation suitable for off-the-shelf solvers is not available in general. In order to solve these problems … Read more

Cost-Sharing Mechanism Design for Ride-Sharing

In this paper, we focus on the cost-sharing problem for ride-sharing that determines how to allocate the total ride cost between the driver and the passengers. We identify the properties that a desirable cost-sharing mechanism should have and develop a general framework which can be used to create specific cost-sharing mechanisms. We propose specific mechanisms … Read more