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Nash Equilibria in a class of Markov stopping games

Rolando Cavazos-Cadena, Daniel Hernández-Hernández (2012)

Kybernetika

This work concerns a class of discrete-time, zero-sum games with two players and Markov transitions on a denumerable space. At each decision time player II can stop the system paying a terminal reward to player I and, if the system is no halted, player I selects an action to drive the system and receives a running reward from player II. Measuring the performance of a pair of decision strategies by the total expected discounted reward, under standard continuity-compactness conditions it is shown...

Nash equilibrium design and price-based coordination in hierarchical systems

Michał P. Karpowicz (2012)

International Journal of Applied Mathematics and Computer Science

This paper deals with the problem of designing Nash equilibrium points in noncooperative games in which agents anticipate values of Lagrange multipliers coordinating their payoff functions. The addressed model of agents' interactions, referred to as the price-anticipation game, is studied within the framework of coordination and mechanism design theory for hierarchical systems. Sufficient conditions are formulated for Nash implementation of a regular and isolated solution to a coordination problem....

Non-cooperative game approach to multi-robot planning

Adam Gałuszka, Andrzej Świerniak (2005)

International Journal of Applied Mathematics and Computer Science

A multi-robot environment with a STRIPS representation is considered. Under some assumptions such problems can be modelled as a STRIPS language (for instance, a Block World environment) with one initial state and a disjunction of goal states. If the STRIPS planning problem is invertible, then it is possible to apply the machinery for planning in the presence of incomplete information to solve the inverted problem and then to find a solution to the original problem. In the paper a planning algorithm...

Noncooperative games with noncompact joint strategies sets: increasing best responses and approximation to equilibrium points

Rosa María Flores-Hernández, Raúl Montes-de-Oca (2011)

Kybernetika

In this paper conditions proposed in Flores-Hernández and Montes-de-Oca [3] which permit to obtain monotone minimizers of unbounded optimization problems on Euclidean spaces are adapted in suitable versions to study noncooperative games on Euclidean spaces with noncompact sets of feasible joint strategies in order to obtain increasing optimal best responses for each player. Moreover, in this noncompact framework an algorithm to approximate the equilibrium points for noncooperative games is supplied....

Nonzero-sum semi-Markov games with countable state spaces

Wojciech Połowczuk (2000)

Applicationes Mathematicae

We consider nonzero-sum semi-Markov games with a countable state space and compact metric action spaces. We assume that the payoff, mean holding time and transition probability functions are continuous on the action spaces. The main results concern the existence of Nash equilibria for nonzero-sum discounted semi-Markov games and a class of ergodic semi-Markov games with the expected average payoff criterion.

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