Denumerable state stochastic games with limiting average payoff

We study stochastic games with countable state space, compact action spaces, and limiting average payoff. ForN-person games, the existence of an equilibrium in stationary strategies is established under a certain Liapunov stability condition. For two-person zero-sum games, the existence of a value and optimal strategies for both players are established under the same stability condition.

Determination of rational strategies for players in two-target games

This paper addresses some of the basic issues involved in the determination of rational strategies for players in two-target games. We show that unlike single-target games where the task of role assignment and selection of strategies is conceptually straightforward, in two-target games, many factors like the preference ordering of outcomes by players, the relative configuration of the target sets and secured outcome regions, the uncertainty about the parameters of the game, etc., also influence the rational selection of strategies by players. The importance of these issues is illustrated through appropriate examples.

Stochastic differential games: Occupation measure based approach

A new approach based on occupation measures is introduced for studying stochastic differential games. For two-person zero-sum games, the existence of values and optimal strategies for both players is established for various payoff criteria. ForN-person games, the existence of equilibria in Markov strategies is established for various cases.

Survival of the fittest and zero sum games

Competition for available resources is natural amongst coexisting species, and the fittest contenders dominate over the rest in evolution. The. dynamics of this selection is studied using a simple linear model. It has similarities to features of quantum computation, in particular conservation laws leading to destructive interference. Compared to an altruistic scenario, competition introduces instability and eliminates the weaker species in a finite time.

Provider-Customer Coalitional Games

Efficacy of commercial wireless networks can be substantially enhanced through large-scale cooperation among involved entities such as providers and customers. The success of such cooperation is contingent upon the design of judicious resource allocation strategies that ensure that the individuals' payoffs are commensurate to the resources they offer to the coalition. The resource allocation strategies depend on which entities are decision-makers and whether and how they share their aggregate payoffs. Initially, we consider the scenario where the providers are the only decision-makers and they do not share their payoffs. We formulate the resource allocation problem as a nontransferable payoff coalitional game and show that there exists a cooperation strategy that leaves no incentive for any subset of providers to split from the grand coalition, i.e., the core of the game is nonempty. To compute this cooperation strategy and the corresponding payoffs, we subsequently relate this game and its core to an exchange market setting and its equilibrium, which can be computed by several efficient algorithms. Next, we investigate cooperation when customers are also decision-makers and decide which provider to subscribe to based on whether there is cooperation. We formulate a coalitional game in this setting and show that it has a nonempty core. Finally, we extend the formulations and results to the cases where the payoffs are vectors and can be shared selectively.

Zero-Sum Risk-Sensitive Stochastic Differential Games

We study zero-sum risk-sensitive stochastic differential games on the infinite horizon with discounted and ergodic payoff criteria. Under certain assumptions, we establish the existence of values and saddle-point equilibria. We obtain our results by studying the corresponding Hamilton-Jacobi-Isaacs equations. Finally, we show that the value of the ergodic payoff criterion is a constant multiple of the maximal eigenvalue of the generators of the associated nonlinear semigroups.

Existence of Value in Stochastic Differential Games of Mixed Type

In this article, we address stochastic differential games of mixed type with both control and stopping times. Under standard assumptions, we show that the value of the game can be characterized as the unique viscosity solution of corresponding Hamilton-Jacobi-Isaacs (HJI) variational inequalities.

General-sum stochastic games: Verifiability conditions for Nash equilibria

Unlike zero-sum stochastic games, a difficult problem in general-sum stochastic games is to obtain verifiable conditions for Nash equilibria. We show in this paper that by splitting an associated non-linear optimization problem into several sub-problems, characterization of Nash equilibria in a general-sum discounted stochastic games is possible. Using the aforementioned sub-problems, we in fact derive a set of necessary and sufficient verifiable conditions (termed KKT-SP conditions) for a strategy-pair to result in Nash equilibrium. Also, we show that any algorithm which tracks the zero of the gradient of the Lagrangian of every sub-problem provides a Nash strategy-pair. (c) 2012 Elsevier Ltd. All rights reserved.