Agent-based analysis of technological diversification and specialization in electricity markets

This paper develops a model-based analysis of technological market structure evolution in electricity markets. This is done through the development of a power plant trading game that, via computational learning, simulates how players coordinate their behaviour in buying and selling power generation assets. In particular, we look at the question of how market performance depends upon the different technological types of plant owned by the generators, and whether, through the strategic adaptation of their power plant portfolios, there is a tendency for the market to evolve into concentrations of specialized or diversified companies.     

Quantum Russian roulette

We quantize the gamble known as Russian roulette and we study it in two versions for two- and three-persons when: (i) players use a fully loaded quantum gun; (ii) the quantum gun has only one quantum bullet.     

Nondominated Equilibrium Solutions of a Multiobjective Two-Person Nonzero-Sum Game and Corresponding Mathematical Programming Problem

With reference to a multiobjective two-person nonzero-sum game, we define nondominated equilibrium solutions and provide a necessary and sufficient condition for a pair of mixed strategies to be a nondominated equilibrium solution. Using the necessary and sufficient condition, we formulate a mathematical programming problem yielding nondominated equilibrium solutions. We give a numerical example and demonstrate that nondominated equilibrium solutions can be obtained by solving the formulated mathematical programming problem.     

Repeated games with asymmetric information and random price fluctuations at finance markets

This paper is concerned with multistage bidding models introduced in De Meyer and Moussa Saley (Int J Game Theory 31:285–319, 2002) to analyze the evolution of the price system at finance markets with asymmetric information. The repeated games are considered modelling the biddings with the admissible bids k/m, unlike the above mentioned paper, where arbitrary bids are allowed. It is shown that the sequence of values of n-step games is bounded from above and converges to the value of the game with infinite number of steps. The optimal strategies of infinite game generate a symmetric random walk of transaction prices over admissible bids with absorbing extreme points. The value of infinite game is equal to the expected duration of this random walk multiplied by the constant one-step gain of informed Player 1. This study was supported by the grant 04-06-80430 of Russian Foundation of Basic Research which is gratefully acknowledged. I am thankful to anonymous referees and to William Thomson for instructive and helpful remarks and comments.     

Totally balanced combinatorial optimization games

Combinatorial optimization games deal with cooperative games for which the value of every subset of players is obtained by solving a combinatorial optimization problem on the resources collectively owned by this subset. A solution of the game is in the core if no subset of players is able to gain advantage by breaking away from this collective decision of all players. The game is totally balanced if and only if the core is non-empty for every induced subgame of it.?We study the total balancedness of several combinatorial optimization games in this paper. For a class of the partition game [5], we have a complete characterization for the total balancedness. For the packing and covering games [3], we completely clarify the relationship between the related primal/dual linear programs for the corresponding games to be totally balanced. Our work opens up the question of fully characterizing the combinatorial structures of totally balanced packing and covering games, for which we present some interesting examples: the totally balanced matching, vertex cover, and minimum coloring games. Received: November 5, 1998 / Accepted: September 8, 1999?Published online February 23, 2000     

A note on system modelling and control in the case of conflicting objectives

The paper is concerned with the problem of system modelling in the case of many decision makers with conflicting goals. The suggested approach, preserving much of the tractability of the standard LQG problems, allows to take into account decision makers' risk attitudes. This revised version was published online in June 2006 with corrections to the Cover Date.     

Stationary equilibria in cyclic games: Search and structure

The existence of optimal stationary strategies for a cyclic game played on the vertices of a bipartite graph up to the first cycle with the payoff of one player to the other equaling the sum of the maximal and minimal local payoffs on this cycle is proved. This result implies that the problem belongs to the class NP ∩ co-NP; -a polynomial algorithm that yields optimal strategies for ergodic extensions of matrix games is given. Translated fromMatematicheskie Zametki, Vol. 67, No. 6, pp. 913–921, June, 2000.     

Equivalence between Nonlinear H ∞ Control Problems and Existence of Viscosity Solutions of Hamilton—Jacobi—Isaacs Equations rid="*" id="*" This work was written while the author was visiting the University of California at Santa Barbara. He was partially supported by Consiglio Nazionale delle Ricerche of Italy.

In this paper we extend to completely general nonlinear systems the result stating that the suboptimal control problem is solved if and only if the corresponding Hamilton—Jacobi—Isaacs (HJI) equation has a nonnegative (super)solution. This is well known for linear systems, using the Riccati equation instead of the HJI equation. We do this using the theory of differential games and viscosity solutions. Accepted 14 February 1997     

Existence of Risk-Sensitive Optimal Stationary Policies for Controlled Markov Processes

In this paper we are concerned with the existence of optimal stationary policies for infinite-horizon risk-sensitive Markov control processes with denumerable state space, unbounded cost function, and long-run average cost. Introducing a discounted cost dynamic game, we prove that its value function satisfies an Isaacs equation, and its relationship with the risk-sensitive control problem is studied. Using the vanishing discount approach, we prove that the risk-sensitive dynamic programming inequality holds, and derive an optimal stationary policy. Accepted 1 October 1997     

The Folk theorem for dominance solutions

The known variants of the Folk theorem characterize the sets of equilibria for repeated games. The present paper considers dominance solutions of finitely repeated games and discounted supergames with perturbed payoff functions. The paper shows that for a normal form game the set of dominance solution payoff vectors of the T-fold repetitions converges to the set of feasible and individually rational payoffs as T tends to infinity and the perturbation value tends to 0. A similar theorem is proved for supergames as the discount factor tends to 1. Received: May 1994/final version: September 1997