Invited Session Fri.3.MA 005

Friday, 15:15 - 16:45 h, Room: MA 005

Cluster 8: Game theory [...]

Learning and computation for game-theoretic problems

 

Chair: Vinayak Shanbhag

 

 

Friday, 15:15 - 15:40 h, Room: MA 005, Talk 1

W. Ross Morrow
Computing equilibria in regulated differentiated product market models

Coauthors: Joshua Mineroff, Kate S. Whitefoot

 

Abstract:
Game theoretic models are applied to study markets for differentiated product such as personal vehicles, consumer electronics, and various food products and services. One of the most important applications concerns the impact of regulatory policy on market behavior. Practical insights from such models rests on the ability to compute equilibria, which in turn requires solving potentially large Mixed Complementarity Problems (MCPs). This seminar discusses several advances in the formulation of such models and the subsequent computation of equilibrium when firms face regulations with non-smooth regulatory costs. Equilibrium prices are modeled with MCPs, while product design decisions are modeled with a Stackelberg-type two-stage game that results in an MPEC/EPEC. One unique feature of these applications is a lack of regularity as prices increase without bound, a consequence of the type of demand model used. We solve this issue by identifying appropriately coercive problem formulations. Computational results obtained with state-of-the-art NLP software (PATH, KNITRO, SNOPT) are provided for fuel economy regulations in the U.S.

 

 

Friday, 15:45 - 16:10 h, Room: MA 005, Talk 2

Angelia Nedich
A gossip algorithm for aggregative games on graphs

Coauthors: Jayash Koshal, Uday V. Shanbhag

 

Abstract:
We consider a class of games, termed as aggregative games, being played over a distributed
multi-agent networked system. In an aggregative game, an agent's objective
function is coupled through a function of the aggregate of all agents decisions. Every
agent maintains an estimate of the aggregate and agents exchange this information
over a connected network. We study the gossip-based distributed algorithm for information
exchange and computation of equilibrium decisions of agents over the network.
Our primary emphasis is on proving the convergence of the algorithm under an assumption
of a diminishing (agent-specific) stepsize sequence. Under standard conditions,
we establish the almost-sure convergence of the algorithm to an equilibrium point. Finally,
we present numerical results to assess the performance of the gossip algorithm
for aggregative games.

 

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